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1
Holdych, D. J., D. Rovas, J. G. Georgiadis, and R. O. Buckius. "An Improved Hydrodynamics Formulation for Multiphase Flow Lattice-Boltzmann Models." International Journal of Modern Physics C 09, no. 08 (1998): 1393–404. http://dx.doi.org/10.1142/s0129183198001266.
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Lattice-Boltzmann (LB) models provide a systematic formulation of effective-field computational approaches to the calculation of multiphase flow by replacing the mathematical surface of separation between the vapor and liquid with a thin transition region, across which all magnitudes change continuously. Many existing multiphase models of this sort do not satisfy the rigorous hydrodynamic constitutive laws. Here, we extend the two-dimensional, seven-speed Swift et al. LB model1 to rectangular grids (nine speeds) by using symbolic manipulation (MathematicaTM) and compare the LB model predictions with benchmark problems, in order to evaluate its merits. Particular emphasis is placed on the stress tensor formulation. Comparison with the two-phase analogue of the Couette flow and with a flow involving shear and advection of a droplet surrounded by its vapor reveals that additional terms have to be introduced in the definition of the stress tensor in order to satisfy the Navier–Stokes equation in regions of high density gradients. The use of Mathematica obviates many of the difficulties with the calculations "by-hand," allowing at the same time more flexibility to the computational analyst to experiment with geometrical and physical parameters of the formulation.
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HUANG, HAIBO, JUN-JIE HUANG, XI-YUN LU, and MICHAEL C. SUKOP. "ON SIMULATIONS OF HIGH-DENSITY RATIO FLOWS USING COLOR-GRADIENT MULTIPHASE LATTICE BOLTZMANN MODELS." International Journal of Modern Physics C 24, no. 04 (2013): 1350021. http://dx.doi.org/10.1142/s0129183113500216.
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Originally, the color-gradient model proposed by Rothman and Keller (R–K) was unable to simulate immiscible two-phase flows with different densities. Later, a revised version of the R–K model was proposed by Grunau et al. [D. Grunau, S. Chen and K. Eggert, Phys. Fluids A: Fluid Dyn. 5, 2557 (1993).] and claimed it was able to simulate two-phase flows with high-density contrast. Some studies investigate high-density contrast two-phase flows using this revised R–K model but they are mainly focused on the stationary spherical droplet and bubble cases. Through theoretical analysis of the model, we found that in the recovered Navier–Stokes (N–S) equations which are derived from the R–K model, there are unwanted extra terms. These terms disappear for simulations of two-phase flows with identical densities, so the correct N–S equations are fully recovered. Hence, the R–K model is able to give accurate results for flows with identical densities. However, the unwanted terms may affect the accuracy of simulations significantly when the densities of the two fluids are different. For the simulations of spherical bubbles and droplets immersed in another fluid (where the densities of the two fluids are different), the extra terms may not be important and hence, in terms of surface tension, accurate results can be obtained. However, generally speaking, the unwanted term may be significant in many flows and the R–K model is unable to obtain the correct results due to the effect of the extra terms. Through numerical simulations of parallel two-phase flows in a channel, we confirm that the R–K model is not appropriate for general two-phase flows with different densities. A scheme to eliminate the unwanted terms is also proposed and the scheme works well for cases of density ratios less than 10.
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CHIAPPINI, DANIELE, GINO BELLA, SAURO SUCCI, and STEFANO UBERTINI. "APPLICATIONS OF FINITE-DIFFERENCE LATTICE BOLTZMANN METHOD TO BREAKUP AND COALESCENCE IN MULTIPHASE FLOWS." International Journal of Modern Physics C 20, no. 11 (2009): 1803–16. http://dx.doi.org/10.1142/s0129183109014746.
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We present an application of the hybrid finite-difference Lattice-Boltzmann model, recently introduced by Lee and coworkers for the numerical simulation of complex multiphase flows.1–4 Three typical test-case applications are discussed, namely Rayleigh–Taylor instability, liquid droplet break-up and coalescence. The numerical simulations of the Rayleigh–Taylor instability confirm the capability of Lee's method to reproduce literature results obtained with previous Lattice-Boltzmann models for non-ideal fluids. Simulations of two-dimensional droplet breakup reproduce the qualitative regimes observed in three-dimensional simulations, with mild quantitative deviations. Finally, the simulation of droplet coalescence highlights major departures from the three-dimensional picture.
4
Koplik, J., and T. J. Lasseter. "Two-Phase Flow in Random Network Models of Porous Media." Society of Petroleum Engineers Journal 25, no. 01 (1985): 89–100. http://dx.doi.org/10.2118/11014-pa.
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Abstract To explore how the microscopic geometry of a pore space affects the macroscopic characteristics of fluid flow in porous media, we have used approximate solutions of the porous media, we have used approximate solutions of the Navier-Stokes equations to calculate the flow of two fluids in random networks. The model pore space consists of an array of pores of variable radius connected to a random number of nearest neighbors by throats of variable length and radius. The various size and connectedness distributions may be arbitrarily assigned, as are the wetting characteristics of the two fluids in the pore space. The fluids are assumed to be incompressible, immiscible. Newtonian, and of equal viscosity. In the calculation, we use Stokes flow results for the motion of the individual fluids and incorporate microscopic capillary force by using the Washburn approximation. At any time, the problem is mathematically identical to a random electrical network of resistors, batteries, and diodes. From the numerical solution of the latter, we compute the fluid velocities and saturation rates of change and use a discrete timestepping procedure to follow the subsequent motion. The scale of the computation has restricted us so far to networks of hundreds of pores in two dimensions (2D). Within these limitations, we discuss the dependence of residual oil saturations and interface shapes on network geometry and flow conditions. Introduction A significant limitation to our understanding of the dynamics of multiphase fluids in porous media is the inability to connect the physics at the microscopic scale to the macroscopic phenomena observed in the laboratory and in the field. Within individual pores, the motion of fluids and menisci can be discussed, at least approximately, in terms of the microgeometry and the physical characteristics of the liquids. gases, and solids present. On the macroscopic scale, the multiphase Darcy equations involving several empirical parameters-relative permeabilities and average capillary pressures permeabilities and average capillary pressures conventionally are used. The connection between these two levels of description, if there is one, has never been elucidated despite years of effort (as reviewed by Scheidegger ). In consequence, it is difficult to predict the behavior of oil reservoirs in advance, and considerable waste of money, effort, and resources can ensue. Economic issues aside, this situation provides another example of a pervasive problem in physics: macroscopic averaging of a random problem in physics: macroscopic averaging of a random microscopically disordered medium to predict large-scale behavior from a knowledge of small-scale dynamics. In optimal circumstances, existing methods in the physics literature (i.e., Ziman ) can be used to carry out physics literature (i.e., Ziman ) can be used to carry out the averaging. For fluid problems, for example, percolation theory has been applied to the spatial distribution of percolation theory has been applied to the spatial distribution of fluids in a pore space, both in static situations and in quasistatic displacement. Another set of ideas, effective medium theories, has been applied to electrical conductivity and its fluid analog, absolute permeability. The general fluid displacement problem, when both permeability. The general fluid displacement problem, when both capillary and viscous forces are present, is related to a class of physics problems that are as yet unresolved, such as crystal growth, surface evolution, and dynamic percolation. In this situation, we are forced to resort to percolation. In this situation, we are forced to resort to brute-force numerical modeling, both as a means of obtaining statistical information and as a guide to approximations that may permit future analytical work. In this paper, we describe our initial efforts to calculate the motion of two fluids in porous media from the microscopic scale up, starting from the Stokes equations and boundary conditions in this pore space. As usual, we model the porous medium as a network of similarly shaped, but randomly sized, elements. The key to the calculation is the mathematical analogy between the fluid problem and an appropriate electrical network of random problem and an appropriate electrical network of random resistors, batteries, and diodes. The calculation is a very difficult one, numerically speaking, and to date we have been restricted to fairly small 2D networks of hundreds of pores. We expect, however, that with more sophisticated programming methods our approach can be applied to three-dimensional (3D) networks of thousands of pores. pores. After this work was in progress, we came across a paper of Singhal and Somerton where a similar calculational framework was used but with a different emphasis. Those authors considered a single realization of a small network of triangular channels of random sizes with flow regimes randomly assigned in each channel and compute the relative permeabilities and capillary pressure curves of the network. Our emphasis in this paper is on time-dependent phenomena and statistical averaging of flow quantities. We also note the somewhat related work by Payatakes et al., who considered a square lattice of Payatakes et al., who considered a square lattice of converging/diverging tubes meeting at point nodes and simulate the dislodgement of blobs of trapped oil. Subsequently, Dias and Payatakes used the same geometry and calculational rules similar to those employed here to study fluid displacement. SPEJ P. 89
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Huang, Haibo, Lei Wang, and Xi-yun Lu. "Evaluation of three lattice Boltzmann models for multiphase flows in porous media." Computers & Mathematics with Applications 61, no. 12 (2011): 3606–17. http://dx.doi.org/10.1016/j.camwa.2010.06.034.
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Uzun, Ilkay, Basak Kurtoglu, and Hossein Kazemi. "Multiphase Rate-Transient Analysis in Unconventional Reservoirs: Theory and Application." SPE Reservoir Evaluation & Engineering 19, no. 04 (2016): 553–66. http://dx.doi.org/10.2118/171657-pa.
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Summary In unconventional reservoirs, production data are generally analyzed by use of rate-transient techniques derived from single-phase linear-flow models. Such linear-flow models use rate-normalized pressure, which is pressure drop divided by reservoir-flow rate vs. square root of time. In practice, the well-fluid production includes water, oil, and gas. The oil can be light oil, volatile oil, and gas/condensate as in the Bakken, Eagle Ford, and Barnett, respectively. Thus, single-phase analysis needs modification to account for production of fluid mixtures. In this paper, we present a multiphase-pressure-diffusivity equation to analyze multiphase flow in single- and dual-porosity models of unconventional reservoirs. Our approach is similar to the work presented by Perrine (1956); however, our approach has a theoretical foundation, whereas Perrine (1956) used pragmatic engineering analogy for constant flow rate in vertical wells only. In addition to oil, gas, and formation brine, our method accounts for gas/condensate production, and the flowback of the injected hydraulic-fracturing fluids. Overall, our proposed approach is more comprehensive than the single-phase models but maintains the simplicity of the conventional methods. Our paper includes diagnostic plots of rate-normalized well pressure for light oils and gas/condensates in unconventional reservoirs. Data from two Bakken and two Eagle Ford wells will be presented to demonstrate the usefulness of our approach. In addition to the mathematical analysis of flow-rate and pressure data, we will present the effect of well-stimulation and fluid-lift methods on the flow-rate characteristics of Bakken and Eagle Ford wells.
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Han, Xin Feng, Jian Long Li, and Ning Xu. "CFD Simulation of the Fluidized Bed Applied in the Synthesis of Benzene Series Organosilicon." Advanced Materials Research 753-755 (August 2013): 2663–66. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.2663.
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The mathematical model of gas-solid flow 2D fluidized bed was established. The CFD simulation was carried out with commercial software FLUENT6.3 by using Eulerian-Eulerian multiphase models, based on the kinetic theory of granular flow and PC-SIMPLE algorithm. In order to provide a basis on optimizing the operating conditions of the fluidized bed applied in benzene series organosilicon reactor, the processes of bubble formation, growth and disappearance under different cases were analyzed.
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SBRAGAGLIA, M., K. SUGIYAMA, and L. BIFERALE. "Wetting failure and contact line dynamics in a Couette flow." Journal of Fluid Mechanics 614 (October 16, 2008): 471–93. http://dx.doi.org/10.1017/s0022112008003649.
Texte intégralRésumé :
Liquid–liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters – capillary number, viscosity ratio and separation of scale – i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau–Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models.
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LEI, G., P. C. DONG, S. Y. MO, S. H. GAI, and Z. S. WU. "A NOVEL FRACTAL MODEL FOR TWO-PHASE RELATIVE PERMEABILITY IN POROUS MEDIA." Fractals 23, no. 02 (2015): 1550017. http://dx.doi.org/10.1142/s0218348x15500176.
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Multiphase flow in porous media is very important in various scientific and engineering fields. It has been shown that relative permeability plays an important role in determination of flow characteristics for multiphase flow. The accurate prediction of multiphase flow in porous media is hence highly important. In this work, a novel predictive model for relative permeability in porous media is developed based on the fractal theory. The predictions of two-phase relative permeability by the current mathematical models have been validated by comparing with available experimental data. The predictions by the proposed model show the same variation trend with the available experimental data and are in good agreement with the existing experiments. Every parameter in the proposed model has clear physical meaning. The proposed relative permeability is expressed as a function of the immobile liquid film thickness, pore structural parameters (pore fractal dimension Dfand tortuosity fractal dimension DT) and fluid viscosity ratio. The effects of these parameters on relative permeability of porous media are discussed in detail.
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PREMNATH, KANNAN N., and JOHN ABRAHAM. "LATTICE BOLTZMANN SIMULATIONS OF DROP–DROP INTERACTIONS IN TWO-PHASE FLOWS." International Journal of Modern Physics C 16, no. 01 (2005): 25–44. http://dx.doi.org/10.1142/s0129183105006930.
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In this paper, three-dimensional computations of drop–drop interactions using the lattice Boltzmann method (LBM) are reported. The LBM multiphase flow model employed is evaluated for single drop problems and binary drop interactions. These include the verification of Laplace–Young relation for static drops, drop oscillations, and drop deformation and breakup in simple shear flow. The results are compared with experimental data, analytical solutions and numerical solutions based on other computational methods, as applicable. Satisfactory agreement is shown. Initial studies of drop–drop interactions involving the head-on collisions of drops in quiescent medium and off-center collision of drops in the presence of ambient shear flow are considered. As expected, coalescence outcome is observed for the range of parameters studied.
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Coskun, S. B., and T. Tokdemir. "Modelling of Permeation Grouting Through Soils." Journal of Applied Engineering Sciences 10, no. 1 (2020): 11–16. http://dx.doi.org/10.2478/jaes-2020-0003.
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AbstractIn this study, mathematical modeling of permeation grouting through fully saturated soil is proposed based on immiscible multiphase flow theory. Grout flow in the medium is modeled together with the existing water as the simultaneous flow of two immiscible fluids. In the model, the porous medium is assumed as isotropic and rigid, fluids are assumed as incompressible and capillary pressure is assumed as negligible. Governing equations are discretized using upstream weighted finite element technique and results show that, proposed models give good results and may be used in the numerical simulation of grouting through fully saturated soils.
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Mao, Qian Jun. "Transfer Heat Mechanism of Oil-Gas-Water Three-Phase Flow in Pipeline." Advanced Materials Research 199-200 (February 2011): 1609–12. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.1609.
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It is well known that the oil-gas-water three-phase flow belongs to the field of multiphase flow,transfer heat mechanism of which is very complicated.Transfer heat mechanism is affected not only by different buries in oil gathering pipeline, but also by soil temperature periodicity change. Both domestic and oversea scholars have already studied on the transfer heat mechanisms of oil-gas-water three phase,but they are still in the level of fundamental theory and laboratory.This paper establishes transfer heat models of the oil-gas-water three-phase flow in buried oil gathering pipeline, including the physical model and the mathematical model,and testing in experiment .The purpose of this paper is to analyze value between the calculation and the testing . The results show that the mathematical model of this paper is accurate , and the relative error is ≤ 10%.
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LI, ZHI-TAO, GAO-JIN LI, HAI-BO HUANG, and XI-YUN LU. "LATTICE BOLTZMANN STUDY OF ELECTROHYDRODYNAMIC DROP DEFORMATION WITH LARGE DENSITY RATIO." International Journal of Modern Physics C 22, no. 07 (2011): 729–44. http://dx.doi.org/10.1142/s0129183111016580.
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The lattice Boltzmann method (LBM) has been applied to electrohydrodynamics (EHD) in recent years. In this paper, Shan–Chen (SC) single-component multiphase LBM is developed to study large-density-ratio EHD problems. The deformation/motion of a droplet suspended in a viscous liquid under an applied external electric field is studied with three different electric field models. The three models are leaky dielectric model, perfect dielectric model and constant surface charge model. They are used to investigate the effects of the electric field, electric properties of liquids and electric charges. The leaky dielectric model and the perfect dielectric model are validated by the comparison of LBM results with theoretical analysis and available numerical data. It shows that the SC LBM coupled with these electric field models is able to predict the droplet deformation under an external electric field. When net charges are present on the droplet surface and an electric field is applied, both droplet deformation and motion are reasonably predicted. The current numerical method may be an effective approach to analyze more complex EHD problems.
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Hasslacher, Brosl, and David A. Meyer. "Modeling Dynamical Geometry with Lattice-Gas Automata." International Journal of Modern Physics C 09, no. 08 (1998): 1597–605. http://dx.doi.org/10.1142/s0129183198001448.
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Conventional lattice-gas automata consist of particles moving discretely on a fixed lattice. While such models have been quite successful for a variety of fluid flow problems, there are other systems, e.g., flow in a flexible membrane or chemical self-assembly, in which the geometry is dynamical and coupled to the particle flow. Systems of this type seem to call for lattice gas models with dynamical geometry. We construct such a model on one-dimensional (periodic) lattices and describe some simulations illustrating its nonequilibrium dynamics.
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ZHENG, H. W., C. SHU, Y. T. CHEW, and J. QIU. "A PLATFORM FOR DEVELOPING NEW LATTICE BOLTZMANN MODELS." International Journal of Modern Physics C 16, no. 01 (2005): 61–84. http://dx.doi.org/10.1142/s0129183105006954.
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This paper presents a platform to develop new lattice Boltzmann models. It gives a general framework for different applications. It also presents basic velocity models and a set of basic conditions to construct new models which can recover Navier–Stokes equations. Besides, the equilibrium function can be easily obtained through a set of equations. By using the platform, we can easily recover the existing models. Some new models are derived from the platform and validated by their application to simulate the two-dimensional driven cavity flow. The obtained numerical results agree very well with available data in the literature.
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Biscarini, Chiara, Silvia Di Francesco, Fernando Nardi, and Piergiorgio Manciola. "Detailed Simulation of Complex Hydraulic Problems with Macroscopic and Mesoscopic Mathematical Methods." Mathematical Problems in Engineering 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/928309.
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The numerical simulation of fast-moving fronts originating from dam or levee breaches is a challenging task for small scale engineering projects. In this work, the use of fully three-dimensional Navier-Stokes (NS) equations and lattice Boltzmann method (LBM) is proposed for testing the validity of, respectively, macroscopic and mesoscopic mathematical models. Macroscopic simulations are performed employing an open-source computational fluid dynamics (CFD) code that solves the NS combined with the volume of fluid (VOF) multiphase method to represent free-surface flows. The mesoscopic model is a front-tracking experimental variant of the LBM. In the proposed LBM the air-gas interface is represented as a surface with zero thickness that handles the passage of the density field from the light to the dense phase and vice versa. A single set of LBM equations represents the liquid phase, while the free surface is characterized by an additional variable, the liquid volume fraction. Case studies show advantages and disadvantages of the proposed LBM and NS with specific regard to the computational efficiency and accuracy in dealing with the simulation of flows through complex geometries. In particular, the validation of the model application is developed by simulating the flow propagating through a synthetic urban setting and comparing results with analytical and experimental laboratory measurements.
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Teixeira, Christopher M. "Incorporating Turbulence Models into the Lattice-Boltzmann Method." International Journal of Modern Physics C 09, no. 08 (1998): 1159–75. http://dx.doi.org/10.1142/s0129183198001060.
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The Lattice-Boltzmann method (LBM) is extended to allow incorporation of traditional turbulence models. Implementation of a two-layer mixing-length algebraic model and two versions of the k-ε two-equation model, Standard and RNG, in conjunction with a wall model, are presented. Validation studies are done for turbulent flows in a straight pipe at three Re numbers and over a backwards facing step of expansion ratio 1.5 and Re H=44 000. All models produce good agreement with experiment for the straight pipes but the RNG k-ε model is best able to capture both the recirculation length, within 2% of experiment, and the detailed structure of the mean fluid flow for the backwards facing step.
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Wang, Zimeng, and Junfeng Zhang. "Simulating anisotropic flows with isotropic lattice models via coordinate and velocity transformation." International Journal of Modern Physics C 30, no. 10 (2019): 1941001. http://dx.doi.org/10.1142/s0129183119410018.
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We propose a rectangular lattice Boltzmann model for anisotropic flows based on coordinate and velocity transformation. Unlike other existing rectangular models which tuned the lattice Boltzmann algorithm to fit the rectangular or cuboid lattice grids, here we apply the general lattice Boltzmann method to solve the transformed system over regular square lattice grids. The method is tested with simulations of representative anisotropic flows, including flows in narrow straight and wavy channels, the Taylor–Green vortex flow, and the flow through an elliptical particle array. These simulations show that in general our method produces satisfactory results; however, the aspect ratio [Formula: see text] is limited to relatively large values ([Formula: see text]). The effects of [Formula: see text] on simulation accuracy and stability have been carefully examined, and a possible remedy to improve these concerns has been proposed. The method and analysis could be useful for future development of more robust and practical anisotropic lattice Boltzmann models for realistic simulations.
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Filippova, O., and D. Hänel. "Boundary-Fitting and Local Grid Refinement for Lattice-BGK Models." International Journal of Modern Physics C 09, no. 08 (1998): 1271–79. http://dx.doi.org/10.1142/s012918319800114x.
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Lattice-Boltzmann models, proposed at the end of the 1980s as the noise-free version of lattice-gas models are based on gas-kinetical-like representation of fluid flow. Their recent modifications, the lattice-BGK models, provide especially simple, effective and stable algorithms for the solution of incompressible flows. The boundary-fitting concept and local grid refinement proposed for the lattice-BGK model conserve the second order accuracy of the original algorithm for flows around complicated geometries in regions of small and moderate Reynolds numbers.
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Wang, D. Q., C. J. Wu, and R. C. Yang. "An Insight into the Analytical Models of Granular Particle Damping." Advanced Materials Research 819 (September 2013): 13–19. http://dx.doi.org/10.4028/www.scientific.net/amr.819.13.
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Granular particle damping technique is a means for achieving high structural damping by the use of metal particles filled into an enclosure which is attached to the structure in a region of high vibration levels. The particle dampers are now preferred over traditional dampers due to the stability, robustness, cost effectiveness and the lower noise level than the impact damper. Such a promising technique has been used successfully in many fields over the past 20 years. In this paper, a state-of-art review on the development of modeling for particle damping is presented. The fundamentals and individual features of three main mathematical models of the granular particle damping are briefly summarized, i.e. the lumped mass model, the Discrete Element Method (DEM) and the approach based on the multiphase flow (MPF) theory of gas-particle. It is worth noting that an improved analytical model of the particle damping based on MPF theory is also introduced. The co-simulation of the COMSOL Multiphysics live link for MATLAB is conducted using this improved model. It can be shown that this model makes the complicated modeling problem more simply and offers the possibility to analyze the more complex particle-damping vibrating system.
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Sokolovska, I., and K. Demin. "FEATURES OF MODELING THE TRACTION OF MOVEMENT OF MATERIAL PARTICLES IN A VORTICAL LAYER." Collection of scholarly papers of Dniprovsk State Technical University (Technical Sciences) 1, no. 38 (2021): 99–105. http://dx.doi.org/10.31319/2519-2884.38.2021.12.
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In the given article the actual modern scientific problem is solved — on the basis of experimental data the mathematical model of movement of a particle in a vortex layer at heat treatment taking into account multiphase of a stream is created.
 At the current level of development of vortex devices, the relevance of research aimed at in-depth study of processes, improvement of structures and manufacturing technology of individual components has increased. The lack of a strict theory is felt most acutely in the design of systems and installations in which the vortex apparatus is one of the main units. In this regard, the priority remains the development of a theory that allows to obtain a fairly reliable mathematical description of the processes occurring in the vortex chamber of the apparatus.
 The patterns of propagation of the swirling jet depend on a large number of different conditions (design features of the nozzle, the intensity of the twist) and flow parameters (their density and speed). The flow in the jet has a complex non-automodal character, in connection with which in other works it was considered expedient to use for calculation numerical methods of integration of equations of motion to describe the non-automodal flow in ordinary jets.
 The disadvantage of these models is that when solving the model of vortex flows go into the model of laminar flows. In this case, many quantities cannot be determined analytically or experimentally. When dividing the flow into the zone of the vortex and the zone of the main vortex, the error in the calculations of the hydrodynamics of the flow, and especially the particles, increases significantly due to the use of different equations of the turbulent viscosity, which is taken for each zone constant. These models are written for a continuous medium and are therefore not suitable for multiphase flow.
 The peculiarities of the trajectory of the material particle in the vortex apparatus are determined and the dependences are obtained, which allow to control the heat treatment time and on the basis of which it is possible to design the optimal vortex device for drying dispersed materials. The mathematical models obtained in this work can be used in methods of calculations and design of vortex heat and mass transfer devices.
 The calculations performed according to the equations of the proposed model show satisfactory agreement with the experimental data. When estimating the relative velocities of the particle in the unloading part of the vortex apparatus, it is obvious that the use of equations for laminar flow, which are traditionally used in calculations, leads to significant errors.
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SURMAS, RODRIGO, CARLOS ENRIQUE PICO, LUÍS ORLANDO EMERICH DOS SANTOS, and PAULO CESAR PHILIPPI. "VOLUME EXCLUSION FOR REDUCING COMPRESSIBILITY EFFECTS IN LATTICE BOLTZMANN MODELS." International Journal of Modern Physics C 18, no. 04 (2007): 576–84. http://dx.doi.org/10.1142/s0129183107010814.
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Lattice Boltzmann (LB) models for ideal gases retrieve the Navier-Stokes equation in the incompressible limit. Nevertheless, the high values of the isothermal compressibility introduce serious drawbacks. In the simulation of liquid flows through porous media, the high pressure gradients through throats and tortuous paths produce significant errors when conventional LB models are used, especially when the interest is the transient flow. In this work a significant reduction of the isothermal compressibility is reached by adjusting the equilibrium distribution moments to those obtained imposing a van der Waals pressure-density dependence and adopting a lattice with a high number of speeds. Simulation results for the shock tube problem, the velocity step problem and the transient pressure response in a tortuous channel are presented and compared with available analytical results.
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GEERDINK, JOOST B. W., and ALFONS G. HOEKSTRA. "COMPARING ENTROPIC AND MULTIPLE RELAXATION TIMES LATTICE BOLTZMANN METHODS FOR BLOOD FLOW SIMULATIONS." International Journal of Modern Physics C 20, no. 05 (2009): 721–33. http://dx.doi.org/10.1142/s0129183109013947.
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We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries. The Lattice BGK shows predictable stability and is the fastest method in terms of lattice node updates per second. The Multiple Relaxation Times LBM shows erratic stability which depends strongly on the relaxation times set chosen and is slightly slower. The Entropic LBM gives the best stability at the price of fewer lattice node updates per second. A parameter constraint optimization technique is used to determine which is the fastest model given a certain preset accuracy. It is found that the Lattice BGK performs best at most arterial flows, except for the high Reynolds number flow in the aorta, where the Entropic LBM is the fastest method due to its better stability. However we also conclude that the Entropic LBM with velocity/pressure inlet/outlet conditions shows much worse performance.
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CHAI, ZHEN-HUA, BAO-CHANG SHI, and LIN ZHENG. "LATTICE BOLTZMANN SIMULATION OF VISCOUS DISSIPATION IN ELECTRO-OSMOTIC FLOW IN MICROCHANNELS." International Journal of Modern Physics C 18, no. 07 (2007): 1119–31. http://dx.doi.org/10.1142/s0129183107011200.
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In this paper, the effects of viscous dissipation in electro-osmotic flow in microchannels are numerically analyzed with lattice Boltzmann method (LBM), and three different lattice Boltzmann models that can recover the macroscopic governing equations for electro-osmotic flow (EOF) are proposed. As the dimensions of the channels approach the microlevel, viscous dissipation could be significant due to a high velocity gradient in electric double layer (EDL). Numerical results show that viscous dissipation plays an important role in EOF in microchannels.
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DU, RUI, and BAOCHANG SHI. "A NOVEL SCHEME FOR FORCE TERM IN THE LATTICE BGK MODEL." International Journal of Modern Physics C 17, no. 07 (2006): 945–58. http://dx.doi.org/10.1142/s0129183106009461.
Texte intégralRésumé :
In this paper a novel scheme of the lattice BGK (LBGK) model with a force term has been proposed. Unlike the existing models, an appropriate term was added in the evolutionary equation. Through the Chapman–Enskog (C–E) procedure the Navier–Stokes (N–S) equations with a force term can be recovered with the kinetic viscosity. Three discrete methods of the added term have been discussed in detail. It can be proved that some existing models are the special cases of the model in this paper. We have taken the numerical simulation of the generalized Poiseuille flow driven by a constant force in a channel filled with a porous medium of porosity flow in 2D with different values of the parameters and compared the three models of different discrete schemes in the aspect of the numerical accuracy and stability.
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ANSUMALI, SANTOSH, SHYAM SUNDER CHIKATAMARLA, CHRISTOS EMMANOUIL FROUZAKIS, and KONSTANTINOS BOULOUCHOS. "ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW PAST SQUARE CYLINDER." International Journal of Modern Physics C 15, no. 03 (2004): 435–45. http://dx.doi.org/10.1142/s012918310400584x.
Texte intégralRésumé :
Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier–Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re ~O(10) to Re ≤1000 was predicted by a single simulation algorithm.1–5
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Hosseini, Amir, Masoud Iranmanesh, Ebrahim Jahanshahi Javaran, and Abed Zadehgol. "Application of lattice kinetic models with Tsallis entropy in simulating fluid flow through porous media." International Journal of Modern Physics C 28, no. 09 (2017): 1750110. http://dx.doi.org/10.1142/s0129183117501108.
Texte intégralRésumé :
In this work, application of the recently introduced constant speed kinetic model (CSKM) [A. Zadehgol and M. Ashrafizaadeh, J. Comp. Phys. 274 803, (2014); A. Zadehgol, Phys. Rev. E 91, 063311 (2015)] in simulating fluid flow through porous media is explored. Discrete forms of Tsallis and Burg entropy functions were first introduced by Boghosian et al. [Phys. Rev. E [Formula: see text], 025103, (2003)], in the context of lattice Boltzmann model (LBM). In the CSKM, the virtual particles are concentrated on n-dimensional (nD-) spheres centered at the computational nodes. Using continuous forms of the unconventional entropies of Burg, [Formula: see text] (for 2D), and Tsallis, [Formula: see text] (for nD with [Formula: see text]), the CSKM extends the work of Boghosian et al., in the limit of fixed speed continuous velocities. In this work, the second-order accuracy, efficiency, and thermodynamic consistency of the 2D- and 3D-projections of the 4D-CSKM are explored and numerically verified.
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LI, ZHIPENG, XINGLI LI, and FUQIANG LIU. "STABILIZATION ANALYSIS AND MODIFIED KdV EQUATION OF LATTICE MODELS WITH CONSIDERATION OF RELATIVE CURRENT." International Journal of Modern Physics C 19, no. 08 (2008): 1163–73. http://dx.doi.org/10.1142/s0129183108012868.
Texte intégralRésumé :
In this paper, the lattice model which depends not only on the difference of the optimal current and the local current but also on the relative current is presented and analyzed in detail. We derive the stability condition of the extended model by considering a small perturbation around the homogeneous flow solution with finding that the improvement in the stability of the traffic flow is obtained by taking into account the relative current, which is also confirmed by direct simulations. Moreover, from the nonlinear analysis to the extended models, the relative current dependence of the propagating kink solutions for traffic jam is obtained by deriving the modified KdV equation near the critical point by using the reductive perturbation method.
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LI, XINGLI, ZHIPENG LI, XIANGLIN HAN, and SHIQIANG DAI. "JAMMING TRANSITION IN EXTENDED COOPERATIVE DRIVING LATTICE HYDRODYNAMIC MODELS INCLUDING BACKWARD-LOOKING EFFECT ON TRAFFIC FLOW." International Journal of Modern Physics C 19, no. 07 (2008): 1113–27. http://dx.doi.org/10.1142/s0129183108012698.
Texte intégralRésumé :
Two extended cooperative driving lattice hydrodynamic models are proposed by incorporating the intelligent transportation system and the backward-looking effect in traffic flow under certain conditions. They are the lattice versions of the hydrodynamic model of traffic: one (model A) is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other (model B) is the difference-difference equation in which both time and space variables are discrete. In light of the real traffic situations, the appropriate forward and backward optimal velocity functions are selected, respectively. Then the stability conditions for the two models are investigated with the linear stability theory and it is found that the new consideration leads to the improvement of the stability of traffic flow. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. Moreover, the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.
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Ujita, Hiroshi, Satoru Nagata, Minoru Akiyama, Masanori Naitoh, and Hirotada Ohashi. "Development of LGA & LBE 2D Parallel Programs." International Journal of Modern Physics C 09, no. 08 (1998): 1203–20. http://dx.doi.org/10.1142/s0129183198001096.
Texte intégralRésumé :
A lattice-gas Automata two-dimensional program was developed for analysis of single and two-phase flow behaviors, to support the development of integrated software modules for Nuclear Power Plant mechanistic simulations. The program has single-color, which includes FHP I, II, and III models, two-color (Immiscible lattice gas), and two-velocity methods including a gravity effect model. Parameter surveys have been performed for Karman vortex street, two-phase separation for understanding flow regimes, and natural circulation flow for demonstrating passive reactor safety due to the chimney structure vessel. In addition, lattice-Boltzmann Equation two-dimensional programs were also developed. For analyzing single-phase flow behavior, a lattice-Boltzmann-BGK program was developed, which has multi-block treatments. A Finite Differential lattice-Boltzmann Equation program of parallelized version was introduced to analyze boiling two-phase flow behaviors. Parameter surveys have been performed for backward facing flow, Karman vortex street, bent piping flow with/without obstacles for piping system applications, flow in the porous media for demonstrating porous debris coolability, Couette flow, and spinodal decomposition to understand basic phase separation mechanisms. Parallelization was completed by using a domain decomposition method for all of the programs. An increase in calculation speed of at least 25 times, by parallel processing on 32 processors, demonstrated high parallelization efficiency. Application fields for microscopic model simulation to hypothetical severe conditions in large plants were also discussed.
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Leclaire, Sébastien, Andrea Parmigiani, Bastien Chopard, and Jonas Latt. "Three-dimensional lattice Boltzmann method benchmarks between color-gradient and pseudo-potential immiscible multi-component models." International Journal of Modern Physics C 28, no. 07 (2017): 1750085. http://dx.doi.org/10.1142/s0129183117500851.
Texte intégralRésumé :
In this paper, a lattice Boltzmann color-gradient method is compared with a multi-component pseudo-potential lattice Boltzmann model for two test problems: a droplet deformation in a shear flow and a rising bubble subject to buoyancy forces. With the help of these two problems, the behavior of the two models is compared in situations of competing viscous, capillary and gravity forces. It is found that both models are able to generate relevant scientific results. However, while the color-gradient model is more complex than the pseudo-potential approach, numerical experiments show that it is also more powerful and suffers fewer limitations.
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MARCONI, STEFAN, BASTIEN CHOPARD, and JONAS LATT. "REDUCING THE COMPRESSIBILITY OF A LATTICE BOLTZMANN FLUID USING A REPULSIVE FORCE." International Journal of Modern Physics C 14, no. 08 (2003): 1015–26. http://dx.doi.org/10.1142/s0129183103005157.
Texte intégralRésumé :
This paper investigates the possibility to reduce the compressibility of lattice Boltzmann fluid models by introducing a repulsive force between nearest neighbor lattice Boltzmann particles. This new interaction is based on the Shan–Chen model. The interest of this approach is that it implements the physical mechanism responsible for the incompressibility of real fluids and retains the natural interpretation of the fluid density and fluid momentum. The new state equation shows that the compressibility factor decreases as the repulsive interaction increases. However, numerical instabilities limit the value of the acceptable repulsion. We investigate several situations, such as the Poiseuille flow with pressure gradient, a static fluid subject to gravity and the Womersley flow to evaluate the benefits of our approach. Globally, the compressibility of lattice Boltzmann fluids can be reduced by a factor of 4.
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SZALMÁS, LAJOS. "LATTICE BOLTZMANN METHOD WITH OPTIMIZED BOUNDARY LAYER AT FINITE KNUDSEN NUMBERS." International Journal of Modern Physics C 19, no. 02 (2008): 249–57. http://dx.doi.org/10.1142/s0129183108012078.
Texte intégralRésumé :
We present an optimization procedure in high-order lattice Boltzmann models in order to fine-tune the method for micro-channel flows in the transition region. Both the first and second slip coefficients are tunable, and the hydrodynamic and Knudsen layer solutions can be tailored. Very good results are obtained in comparison with the continuous solution for hard sphere molecules. For the first time, we provide an accurate description of Poiseuille flow in the transition region.
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TIAN, ZHI-WEI, CHUN ZOU, H. J. LIU, Z. H. LIU, Z. L. GUO, and C. G. ZHENG. "THERMAL LATTICE BOLTZMANN MODEL WITH VISCOUS HEAT DISSIPATION IN THE INCOMPRESSIBLE LIMIT." International Journal of Modern Physics C 17, no. 08 (2006): 1131–39. http://dx.doi.org/10.1142/s0129183106009631.
Texte intégralRésumé :
A novel thermal lattice Boltzmann (LB) model is proposed to obtain the viscous heat term expediently. Unlike the existing thermal LB models, this model is entirely based on the framework of the LB method and directly derived from the macro temperature equation. Moreover, the computation cost decreases because the computation of complicated material derivative term has been avoided successfully. To testify the simulation capability of this model, the thermal Couette flow is simulated and the results indicate agreement with the analytical solutions.
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Grubert, Dietmar. "Using the FHP-BGK-Model to Get Effective Dispersion Constants for Spatially Periodic Model Geometries." International Journal of Modern Physics C 08, no. 04 (1997): 817–25. http://dx.doi.org/10.1142/s0129183197000709.
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Tracer dispersion is governed by the velocity fluctuations that the particles are subjected to during their movement. The fluctuation of particle velocity is due to deviations from the mean velocity in the flow field and also to the change of the streamline caused by diffusion. The lattice-BGK method is a good tool to investigate the interaction of both of them, because it models the flow field in detail with even small flow structures. A serious drawback of direct simulations are the requirements in computer time and memory. For spatially periodic media, this can be overcome by using the generalized Taylor-dispersion method to calculate the asymptotic effective dispersion from a solution in an elementary cell. This solution is obtained by simulations with an FHP-BGK-lattice gas. Joining the two methods yields a tool to study the effective dispersion constant of a given periodic geometry.
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WANG, Y., Y. L. HE, Q. LI, G. H. TANG, and W. Q. TAO. "LATTICE BOLTZMANN MODEL FOR SIMULATING VISCOUS COMPRESSIBLE FLOWS." International Journal of Modern Physics C 21, no. 03 (2010): 383–407. http://dx.doi.org/10.1142/s0129183110015178.
Texte intégralRésumé :
A lattice Boltzmann model is developed for viscous compressible flows with flexible specific-heat ratio and Prandtl number. Unlike the Maxwellian distribution function or circle function used in the existing lattice Boltzmann models, a polynomial kernel function in the phase space is introduced to recover the Navier–Stokes–Fourier equations. A discrete equilibrium density distribution function and a discrete equilibrium total energy distribution function are obtained from the discretization of the polynomial kernel function with Lagrangian interpolation. The equilibrium distribution functions are then coupled via the equation of state. In this framework, a model for viscous compressible flows is proposed. Several numerical tests from subsonic to supersonic flows, including the Sod shock tube, the double Mach reflection and the thermal Couette flow, are simulated to validate the present model. In particular, the discrete Boltzmann equation with the Bhatnagar–Gross–Krook approximation is solved by the finite-difference method. Numerical results agree well with the exact or analytic solutions. The present model has potential application in the study of complex fluid systems such as thermal compressible flows.
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Huang, Jian, Feng Xu, Michel Vallières, et al. "A Thermal LBGK Model for Large Density and Temperature Differences." International Journal of Modern Physics C 08, no. 04 (1997): 827–41. http://dx.doi.org/10.1142/s0129183197000710.
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We present a new lattice-Boltzmann method for hydrodynamic simulations, which is capable of handling very large density and temperature gradients. Unlike other LBGK models, the discrete velocities we used center at the local mean flow velocity, and their values vary according to the local temperature. The adiabatic index of the gas can be easily controlled by a parameter.
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Stockman, Harlan W., Robert J. Glass, Clay Cooper, and Harihar Rajaram. "Accuracy and Computational Efficiency in 3D Dispersion via Lattice-Boltzmann: Models for Dispersion in Rough Fractures and Double-Diffusive Fingering." International Journal of Modern Physics C 09, no. 08 (1998): 1545–57. http://dx.doi.org/10.1142/s0129183198001394.
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In the presence of buoyancy, multiple diffusion coefficients, and porous media, the dispersion of solutes can be remarkably complex. The lattice-Boltzmann (LB) method is ideal for modeling dispersion in flow through complex geometries; yet, LB models of solute fingers or slugs can suffer from peculiar numerical conditions (e.g., denormal generation) that degrade computational performance by factors of 6 or more. Simple code optimizations recover performance and yield simulation rates up to ~3 million site updates per second on inexpensive, single-CPU systems. Two examples illustrate limits of the methods: (1) Dispersion of solute in a thin duct is often approximated with dispersion between infinite parallel plates. However, Doshi, Daiya and Gill (DDG) showed that for a smooth-walled duct, this approximation is in error by a factor of ~8. But in the presence of wall roughness (found in all real fractures), the DDG phenomenon can be diminished. (2) Double-diffusive convection drives "salt-fingering", a process for mixing of fresh-cold and warm-salty waters in many coastal regions. Fingering experiments are typically performed in Hele-Shaw cells, and can be modeled with the 2D (pseudo-3D) LB method with velocity-proportional drag forces. However, the 2D models cannot capture Taylor–Aris dispersion from the cell walls. We compare 2D and true 3D fingering models against observations from laboratory experiments.
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RAN, ZHENG, and YUPENG XU. "ENTROPY AND WEAK SOLUTIONS IN THE THERMAL MODEL FOR THE COMPRESSIBLE EULER EQUATIONS." International Journal of Modern Physics C 20, no. 10 (2009): 1493–519. http://dx.doi.org/10.1142/s0129183109014369.
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Among the existing lattice Boltzmann models (LBMs) for compressible flow, the one by Kataoka and Tsutahara [KT model, Phys. Rev. E69, 056702 (2004)] has a simple and rigorous theoretical background. The drawback of this KT model is that it can cause numerical instability if the local Mach number exceeds 1. The precise mechanism of this instability has not yet been clarified. In this paper, we derive entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the lattice Boltzmann method for the KT model. Numerical examples are also given, which are consistent with the above theoretical arguments, and show that the entropy condition is not fully guaranteed in KT model. The negative entropy may be the inherent cause for the nonphysical oscillations in the vicinity of the shock. In contrast to these Karlin's microscopic entropy approach, the corresponding subsidiary entropy condition in the LBM calculation could also be deduced explicitly from the macroscopic version, which provides some insights on the numerical instability of the LBM for shock calculation.
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Settari, A. "A New General Model of Fluid Loss in Hydraulic Fracturing." Society of Petroleum Engineers Journal 25, no. 04 (1985): 491–501. http://dx.doi.org/10.2118/11625-pa.
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Abstract This paper gives a new formulation of fluid loss in hydraulic fracturing that is much more general than the classical theory while retaining its simplicity. The model allows many parameters to vary during filtration and can, therefore, simulate nonlinear effects. The model has been validated against laboratory data for Newtonian fluids and crosslinked gels. The results show that the finite length of the core, viscosity screenout, and shear sensitivity are important parameters that can be represented by the model. The standard analysis gives values of leakoff coefficients that will give incorrect, considerably higher leakoff when applied to field conditions. Introduction The estimate of fluid loss is an important part of a hydraulic fracturing treatment design. Although the control of fluid loss has improved with the use of modern fracturing fluids, the size of the generated fracture areas increases with the size of a job. Consequently, fluid loss can be important even in low-permeability reservoirs for large treatments. For design calculations, fluid loss has been treated in the past by use of the simplified theory proposed by Howard and Fast, which expresses the rate of filtration perpendicular to a fracture wall as a simple function of perpendicular to a fracture wall as a simple function of leakoff coefficients. The advantage of this approach, besides its simplicity, is that it can be directly (if not always correctly) related to experimental data on fluid filtration obtained in a laboratory. Apart from the correction of the derivation of the combined leakoff coefficient, very little has been done to improve the classical theory. With the recent development of a simulation approach to fracturing design, it has been recognized that fluid loss can be computed directly by solving the basic multiphase flow equations in porous media. Such an approach is more general and does not have many of the assumptions that limit the classical theory. However, the computational cost is much higher and the data required to describe the process are difficult to measure. This paper presents a generalization of the classical approach that includes the effect of several parameters that are variable in the field. The mathematical formulation includes the model of filter-cake behavior developed by the author and the results of the work of Blot et al., which improves the calculation of flow in the reservoir. The model is then formulated numerically, which allows us to introduce the effects of variable pressure, fluid viscosity, and different fluids contacting the wall in the filtration process, in accordance with real conditions during the treatment. Comparison with the experimental data of McDaniel et al. shows that the model is capable of exhibiting nonlinear behavior matching the laboratory data, which cannot be explained in terms of the previous simple theory. An important feature of the model is incorporation of the length of the core, which produces nonlinear behavior and can cause large errors in calculating the true value of the leakoff coefficient when the simple formulas are used. The new model retains the simplicity of the classical leakoff theory, although it is more comprehensive and potentially more accurate than the simulation-type potentially more accurate than the simulation-type leakoff calculations, because it is formulated in terms of measurable variables. Leak-off Models vs. Simulation The flow of fracturing fluid into the reservoir can be described, at least in principle, by the equations of multiphase flow in porous media. It would thus seem natural that an improved treatment of fluid loss would use numerical simulation of flow in the reservoir with the properties and pressure at the wall (behind the filter properties and pressure at the wall (behind the filter cake) as the boundary conditions. This approach, which we have taken in our current work, is indeed more general. It is not restricted by the assumption of one-dimensional (1D) flow, and it includes the effects of relative permeability and capillary pressure and handles changing conditions at the fracture face. However, the simulation approach also has problems. First, the process of fracture fluid filtration is more complicated than the reservoir multiphase flow. The properties of the invading fluid are greatly different from the properties of the invading fluid are greatly different from the reservoir fluid and are changing with time because of breakers, temperature changes, and mixing. The fluid can be miscible with one of the resident fluids. The proper formulation would require solution of three-phase proper formulation would require solution of three-phase flow (one phase being the fracture fluid) with relative permeability, capillary pressure, and viscosities permeability, capillary pressure, and viscosities changing with time. Even though such a formulation and solution is possible, the multiphase data are almost impossible to obtain because of the nonlinearity and instability of the gets. Consequently, one must make simplifying assumptions (e.g., the filtrate assumes the properties of the reservoir water). On the numerical level, an extremely fine grid would be required owing to usually very small penetration of the fracture fluid. SPEJ P. 491
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SHAPOVAL, A. B., and M. G. SHNIRMAN. "SAND DENSITY AS SANDPILE DESCRIPTOR." International Journal of Modern Physics C 19, no. 06 (2008): 995–1006. http://dx.doi.org/10.1142/s0129183108012637.
Texte intégralRésumé :
We investigate a collection of one-parametric families of isotropic sandpile models. The models involve the square lattice slowly accumulating the grains and quickly transferring them as the local piles become over-critical. The paper groups the sand-piles with respect to two features influencing the model dynamics. They are the value of the local transfer's stochasticity and the number of the transferred grains. Every pair generates one-parametric family of the sand-piles. The parameter reflects the relative height of an over-critical pile with respect to the incoming flow of sand. If the stochasticity disappears with the growth of the parameter, the families with the fixed number of the transferred grains have much in common with Bak et al.'s sand-pile [Phys. Rev. Lett.59, 381 (1987)], while the families, whose over-critical piles lose all their grains, tend to the Zhang sand-pile [Phys. Rev. Lett.63, 470 (1989)]. The families with non-disappearing variance give rise to new properties described in terms of the probability distribution of the pile heights.
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Rahon, Daniel, Paul Francis Edoa, and Mohamed Masmoudi. "Identification of Geological Shapes in Reservoir Engineering By History Matching Production Data." SPE Reservoir Evaluation & Engineering 2, no. 05 (1999): 470–77. http://dx.doi.org/10.2118/57922-pa.
Texte intégralRésumé :
Summary This paper discusses a method which helps identify the geometry of geological features in an oil reservoir by history matching of production data. Following an initial study on single-phase flow and applied to well tests (Rahon, D., Edoa, P. F., and Masmoudi, M.: "Inversion of Geological Shapes in Reservoir Engineering Using Well Tests and History Matching of Production Data," paper SPE 38656 presented at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5–8 October.), the research presented here was conducted in a multiphase flow context. This method provides information on the limits of a reservoir being explored, the position and size of faults, and the thickness and dimensions of channels. The approach consists in matching numerical flow simulation results with production measurements. This is achieved by modifying the geometry of the geological model. The identification of geometric parameters is based on the solution of an inverse problem and boils down to minimizing an objective function integrating the production data. The minimization algorithm is rendered very efficient by calculating the gradients of the objective function with respect to perturbations of these geometric parameters. This leads to a better characterization of the shape, the dimension, and the position of sedimentary bodies. Several examples are presented in this paper, in particular, an application of the method in a two-phase water/oil case. Introduction A number of semiautomatic history matching techniques have been developed in recent years to assist the reservoir engineer in his reservoir characterization task. These techniques are generally based on the resolution of an inverse problem by the minimization of an objective function and require the use of a numerical simulator. The matching parameters of the inverse problem comprise two types of properties: petrophysical/porosity and permeability and geometric position, shape, and size of the sedimentary bodies present in the reservoir. To be efficient, minimization algorithms require the calculation of simulated production gradients with respect to matching parameters. Such gradients are usually calculated by deriving discrete state equations solved in the numerical simulator1–5 or by using a so-called adjoint-state method.6,7 Therefore, most of these gradient-based methods only allow the identification of petrophysical parameters which appear explicitly in the discrete equations of state. The case of geometric parameters is much more complex, as the gradients of the objective function with respect to these parameters cannot be determined directly from the flow equation. Recent works8–10 have handled this problem by defining geological objects using mathematical functions to describe porosity or permeability fields. But, generalizing these solutions to complex geological models remains difficult. The method proposed in this paper is well suited to complex geometries and heterogeneous environments. The history matching parameters are the geometric elements that describe the geological objects generated, for example, with a geomodeling tool. A complete description of the method with the calculation of the sensitivities was presented in Ref. 11, within the particular framework of single-phase flow adapted to well-test interpretations. In this paper we will introduce an extension of the method to multiphase equations in order to match production data. Several examples are presented, illustrating the efficiency of this technique in a two-phase context. Description of the Method The objective is to develop an automatic or semiautomatic history matching method which allows identification of geometric parameters that describe geological shapes using a numerical simulator. To be efficient, the optimization process requires the calculation of objective function gradients with respect to the parameters. With usual fluid flow simulators using a regular grid or corner point geometry, the conventional methods for calculating well response gradients on discrete equations are not readily usable when dealing with geometric parameters. These geometric parameters do not appear explicitly in the model equations. With these kinds of structured models the solution is to determine the expression of the sensitivities of the objective function in the continuous problem using mathematical theory and then to calculate a discrete set of gradients. Sensitivity Calculation. Here, we present a sensitivity calculation to the displacement of a geological body in a two-phase water/oil flow context. State Equations. Let ? be a two- or three-dimensional spatial field, with a boundary ? and let ]0,T[ be the time interval covering the pressure history. We assume that the capillary pressure is negligible. The pressure p and the water saturation S corresponding to a two-phase flow in the domain ? are governed by the following equations: ∂ ϕ ( p ) S ∂ t − ∇ . ( k k r o ( S ) μ o ∇ ( p + ρ o g z ) ) = q o ρ o , ∂ ϕ ( p ) S ∂ t − ∇ . ( k k r w ( S ) μ w ∇ ( p + ρ w g z ) ) = q w ρ w , ( x , y , z ) ∈ Ω , t ∈ ] 0 , T [ , ( 1 ) with a no-flux boundary condition on ? and an initial equilibrium condition
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Bublík, Ondřej, Libor Lobovský, Václav Heidler, Tomáš Mandys, and Jan Vimmr. "Experimental validation of numerical simulations of free-surface flow within casting mould cavities." Engineering Computations ahead-of-print, ahead-of-print (2021). http://dx.doi.org/10.1108/ec-08-2020-0458.
Texte intégralRésumé :
PurposeThe paper targets on providing new experimental data for validation of the well-established mathematical models within the framework of the lattice Boltzmann method (LBM), which are applied to problems of casting processes in complex mould cavities.Design/methodology/approachAn experimental campaign aiming at the free-surface flow within a system of narrow channels is designed and executed under well-controlled laboratory conditions. An in-house lattice Boltzmann solver is implemented. Its algorithm is described in detail and its performance is tested thoroughly using both the newly recorded experimental data and well-known analytical benchmark tests.FindingsThe benchmark tests prove the ability of the implemented algorithm to provide a reliable solution when the surface tension effects become dominant. The convergence of the implemented method is assessed. The two new experimentally studied problems are resolved well by simulations using a coarse computational grid.Originality/valueA detailed set of original experimental data for validation of computational schemes for simulations of free-surface gravity-driven flow within a system of narrow channels is presented.
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Zadehgol, Abed. "A virtual force method to rectify the equation of state of the lattice Boltzmann models." International Journal of Modern Physics C, September 8, 2021, 2250025. http://dx.doi.org/10.1142/s0129183122500255.
Texte intégralRésumé :
In this work, to rectify the equation of state (EOS) of a recently introduced constant speed entropic kinetic model (CSKM), a virtual force method is proposed. The CSKM, as shown in Zadehgol and Ashrafizaadeh [J. Comp. Phys. 274, 803 (2014)] and Zadehgol [Phys. Rev. E 91, 063311 (2015)], is an entropic kinetic model with unconventional entropies of Burg and Tsallis. The dependence of the pressure on the velocity, in the CSKM, was addressed and it was shown that it can be rectified by inserting rest particles into the model. This work shows that this dependence can also be removed by treating the pressure gradient as a pseudo force term, expanding the source term using the Fourier series, and applying the modified method of Khazaeli et al. [Phys. Rev. E 98, 053303 (2018)]. The proposed method can potentially be used to remove other pseudo-force error terms of the CSKM, e.g. the residual error terms which become significant at high Mach numbers, ensuring thermodynamic consistency of the entropic model, at the compressible flow regimes. The accuracy of the method is verified by simulating benchmark flows.