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Leitão, V. M. A. "Generalized finite differences using fundamental solutions". International Journal for Numerical Methods in Engineering 81, nr 5 (24.07.2009): 564–83. http://dx.doi.org/10.1002/nme.2697.
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Akanda, M. A. Salam, S. Reaz Ahmed i M. Wahhaj Uddin. "Stress analysis of gear teeth using displacement potential function and finite differences". International Journal for Numerical Methods in Engineering 53, nr 7 (2002): 1629–40. http://dx.doi.org/10.1002/nme.355.
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Slak, Jure, i Gregor Kosec. "Adaptive radial basis function–generated finite differences method for contact problems". International Journal for Numerical Methods in Engineering 119, nr 7 (22.04.2019): 661–86. http://dx.doi.org/10.1002/nme.6067.
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Benito, J. J., A. García, L. Gavete, M. Negreanu, F. Ureña i A. M. Vargas. "On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences". Engineering Analysis with Boundary Elements 113 (kwiecień 2020): 181–90. http://dx.doi.org/10.1016/j.enganabound.2020.01.002.
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Harizanov, Stanislav, Raytcho Lazarov i Svetozar Margenov. "A survey on numerical methods for spectral Space-Fractional diffusion problems". Fractional Calculus and Applied Analysis 23, nr 6 (16.12.2020): 1605–46. http://dx.doi.org/10.1515/fca-2020-0080.
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AbstractThe survey is devoted to numerical solution of the equation $ {\mathcal A}^\alpha u=f $, 0 < α<1, where $ {\mathcal A} $ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain Ω in ℝd. The fractional power $ {\mathcal A}^\alpha $ is a non-local operator and is defined though the spectrum of $ {\mathcal A} $. Due to growing interest and demand in applications of sub-diffusion models to physics and engineering, in the last decade, several numerical approaches have been proposed, studied, and tested. We consider discretizations of the elliptic operator $ {\mathcal A} $ by using an N-dimensional finite element space Vh or finite differences over a uniform mesh with N points. In the case of finite element approximation we get a symmetric and positive definite operator $ {\mathcal A}_h: V_h \to V_h $, which results in an operator equation $ {\mathcal A}_h^{\alpha} u_h = f_h $ for uh ∈ Vh.The numerical solution of this equation is based on the following three equivalent representations of the solution: (1) Dunford-Taylor integral formula (or its equivalent Balakrishnan formula, (2.5), (2) extension of the a second order elliptic problem in Ω × (0, ∞)⊂ ℝd+1 [17,55] (with a local operator) or as a pseudo-parabolic equation in the cylinder (x, t) ∈ Ω × (0, 1), [70, 29], (3) spectral representation (2.6) and the best uniform rational approximation (BURA) of zα on [0, 1], [37,40].Though substantially different in origin and their analysis, these methods can be interpreted as some rational approximation of $ {\mathcal A}_h^{-\alpha} $. In this paper we present the main ideas of these methods and the corresponding algorithms, discuss their accuracy, computational complexity and compare their efficiency and robustness.
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Milovanović, Slobodan, i Lina von Sydow. "A high order method for pricing of financial derivatives using Radial Basis Function generated Finite Differences". Mathematics and Computers in Simulation 174 (sierpień 2020): 205–17. http://dx.doi.org/10.1016/j.matcom.2020.02.005.
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Zhao, Shan, i G. W. Wei. "Matched interface and boundary (MIB) for the implementation of boundary conditions in high-order central finite differences". International Journal for Numerical Methods in Engineering 77, nr 12 (19.03.2009): 1690–730. http://dx.doi.org/10.1002/nme.2473.
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Gautam, Narayan Prasad. "Flow routing with Semi-distributed hydrological model HEC- HMS in case of Narayani River Basin". Journal of the Institute of Engineering 10, nr 1 (31.07.2014): 45–58. http://dx.doi.org/10.3126/jie.v10i1.10877.
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Routing is the modeling process to determine the outflow at an outlet from given inflow at upstream of the channel. A hydrological simulation model use mathematical equations that establish relationships between inputs and outputs of water system and simulates the catchment response to the rainfall input. Several hydrological models have been developed to assist in understanding of hydrologic system and water resources management. A model, once calibrated and verified on catchments, provides a multi-purpose tool for further analysis. Semi-Distributed models in hydrology are usually physically based in that they are defined in terms of theoretically acceptable continuum equations. They do, however, involve some degree of lumping since analytical solutions to the equations cannot be found, and so approximate numerical solutions, based on a finite difference or finite element discretization of the space and time dimensions, are implemented. Many rivers in Nepal are either ungauged or poorly gauged due to extreme complex terrains, monsoon climate and lack of technical and financial supports. In this context the role of hydrological models are extremely useful. In practical applications, hydrological routing methods are relatively simple to implement reasonably accurate. In this study, Gandaki river basin was taken for the study area. Kinematic wave method was used for overland routing and Muskingum cunge method was applied for channel routing to describe the discharge on Narayani river and peak flow attenuation and dispersion observed in the direct runoff hydrograph. Channel cross section parameters are extracted using HEC- GeoRAS extension tool of GIS. From this study result, Annual runoff, Peak flow and time of peak at the outlet are similar to the observed flow in calibration and verification period using trapezoidal channel. Hence Hydrological modeling is a powerful technique in the planning and development of integrated approach for management of water resources. DOI: http://dx.doi.org/10.3126/jie.v10i1.10877Journal of the Institute of Engineering, Vol. 10, No. 1, 2014 pp. 45-58
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Brocchini, Maurizio. "A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, nr 2160 (8.12.2013): 20130496. http://dx.doi.org/10.1098/rspa.2013.0496.
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This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.
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Moravej, Hans, Tommy H. T. Chan, Andre Jesus i Khac-Duy Nguyen. "Computation-Effective Structural Performance Assessment Using Gaussian Process-Based Finite Element Model Updating and Reliability Analysis". International Journal of Structural Stability and Dynamics 20, nr 10 (wrzesień 2020): 2042003. http://dx.doi.org/10.1142/s0219455420420031.
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Structural health monitoring data has been widely acknowledged as a significant source for evaluating the performance and health conditions of structures. However, a holistic framework that efficiently incorporates monitored data into structural identification and, in turn, provides a realistic life-cycle performance assessment of structures is yet to be established. There are different sources of uncertainty, such as structural parameters, computer model bias and measurement errors. Neglecting to account for these factors results in unreliable structural identifications, consequent financial losses, and a threat to the safety of structures and human lives. This paper proposes a new framework for structural performance assessment that integrates a comprehensive probabilistic finite element model updating approach, which deals with various structural identification uncertainties and structural reliability analysis. In this framework, Gaussian process surrogate models are replaced with a finite element model and its associate discrepancy function to provide a computationally efficient and all-round uncertainty quantification. Herein, the structural parameters that are most sensitive to measured structural dynamic characteristics are investigated and used to update the numerical model. Sequentially, the updated model is applied to compute the structural capacity with respect to loading demand to evaluate its as-is performance. The proposed framework’s feasibility is investigated and validated on a large lab-scale box girder bridge in two different health states, undamaged and damaged, with the latter state representing changes in structural parameters resulted from overloading actions. The results from the box girder bridge indicate a reduced structural performance evidenced by a significant drop in the structural reliability index and an increased probability of failure in the damaged state. The results also demonstrate that the proposed methodology contributes to more reliable judgment about structural safety, which in turn enables more informed maintenance decisions to be made.
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Klyshnikov, K. Yu, V. I. Ganyukov, A. V. Batranin, D. V. Nushtaev i E. A. Ovcharenko. "Simulation of Transcatheter Aortic Valve Implantation Procedure". Mathematical Biology and Bioinformatics 14, nr 1 (20.05.2019): 204–19. http://dx.doi.org/10.17537/2019.14.204.
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The study is devoted to numerical modeling of transcatheter aortic valve implantation (TAVI) from the position of prognostic value in comparison with clinical data. The finite element method implemented in the Abaqus/CAE software and the reconstruction of three-dimensional models based on the computer microtomography of the CoreValve bioprosthesis of a size of 29 mm and the patient-specific data of functional studies (multispiral tomography) were used in the work. The study included three variations in the modeling of the aortic valve prosthesis procedure, which determine the level of detalization of the numerical experiment. All stages of the TAVI process were reproduced: the crimp of the prosthesis, the movement of the delivery system, the interaction of the guide - guidewire with the elements of the “prosthesis-root” of the aorta system, implantation itself. In silico experiment demonstrated significant quantitative and qualitative agreement with the data of intraoperative fluorography and computed tomography after the TAVI procedure. It is shown that the inclusion of additional elements – the guidewire and catheter of the delivery system into the “aortic root” has a positive effect on the convergence of the data with the clinical results. The analysis of the stress-strain state of the elements interacting in the experiment demonstrated a significant contribution to the analyzed parameters of the prosthetic motion stage along the guidewire as part of the delivery system catheter. Nevertheless, a comparison with the results of the clinical evaluation of the TAVI procedure revealed a number of differences in the response of the model of the bioprosthesis at the later stages of modeling, which requires further researches of a level of detalization. The approach is extremely promising both for practitioners and for research work of prosthetic designers, it can be applied in further R&D tasks.
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Ragab, Saad A. "An Adjoint Formulation for Shape Optimization in Free-Surface Potential Flow". Journal of Ship Research 45, nr 04 (1.12.2001): 269–78. http://dx.doi.org/10.5957/jsr.2001.45.4.269.
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This paper is a step towards the application of automatic shape optimization techniques to the hydrodynamic design of marine vehicles. The flow is assumed to be irrotational and free-surface conditions are linearized. Several objective functionals of relevance to free-surface flow are proposed, and adjoint formulations for the determination of their gradients are derived. The accuracy of the gradient using the adjoint formulations has been verified by comparisons with direct calculations using second-order finite differences. The method is then used to obtain an optimal solution to the inverse problem for a three-dimensional body submerged near a free surface, and to design a minimum wave resistance body.
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Noblesse, Francis, Woei-Min Lin i Robert Mellish. "Alternative Mathematical Expressions for the Steady Wave Spectrum of a Ship". Journal of Ship Research 34, nr 03 (1.09.1990): 149–62. http://dx.doi.org/10.5957/jsr.1990.34.3.149.
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The study presents a modified mathematical expression for the wave-spectrum function in the Fourier representation of the wave pattern of a ship advancing at constant speed in calm water. This new expression is obtained from the well-known usual expression via several applications of Stokes' theorem resulting in the combining of the integrals along the top waterline and over the hull surface of the ship. The modified expression for the wave-spectrum function is considerably better suited than the usual expression for accurate numerical evaluation because the significant numerical cancellations which occur between the waterline and hull integrals in the usual expression are automatically and exactly accounted for in the modified mathematical expression, as is demonstrated mathematically and confirmed numerically. Whereas the values of both the velocity potential and its gradient at the hull are required in the usual expression for the wave-spectrum function, the new expression only involves the tangential velocity at the hull, not the potential. This new expression thus defines the wave-spectrum function in terms of the speed and the size of the ship, the shape of the mean wetted-hull surface, and the tangential velocity at the mean hull surface. It provides a practical method for coupling a far-field Neumann-Kelvin flow representation with any near-field flow-calculation method, including methods based on the use of Rankine sources or finite differences.
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Hajhashemkhani, M., MR Hematiyan i S. Goenezen. "Inverse determination of elastic constants of a hyper-elastic member with inclusions using simple displacement/length measurements". Journal of Strain Analysis for Engineering Design 53, nr 7 (10.08.2018): 529–42. http://dx.doi.org/10.1177/0309324718792452.
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There are many engineering parts and natural soft members, which consist of several phases with different mechanical properties. Identification of material parameters of multi-material members is an important issue that has attracted considerable attention. In this article, a finite-element-based inverse method for identification of material parameters of a body made of several hyper-elastic materials is presented. In the presented inverse method, the unknowns are computed using a few simple displacement/length measurements in a few elasto-static experiments. The inverse analysis can be carried out without any full-field measurements. Both plane strain and plane stress conditions are considered. In the plane strain case, displacements of several sampling points on the boundary of the problem domain are used as measured data. In the plane stress case, some characteristic lengths of the member in the deformed configuration are used as measured data. A cost function in terms of the differences between calculated and measured values is defined and the Gauss–Newton method is used to minimize it. The multi-material sensitivity analysis in the optimization process is made by analytical differentiation of the weak form of the problem. Both numerical and experimental studies are made to demonstrate the effectiveness and accuracy of the proposed methods.
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Andreozzi, Assunta. "Numerical study of mixed convection in a horizontal no parallel-plates channel with an unheated moving plate". International Journal of Numerical Methods for Heat & Fluid Flow 28, nr 3 (5.03.2018): 547–70. http://dx.doi.org/10.1108/hff-09-2016-0340.
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Purpose The purpose of this paper is to analyze the thermal and fluid dynamic behaviors of mixed convection in air because of the interaction between a buoyancy flow and a moving plate induced flow in a horizontal no parallel-plates channel to investigate the effects of the minimum channel spacing, wall heat flux, moving plate velocity and converging angle. Design/methodology/approach The horizontal channel is made up of an upper inclined plate heated at uniform wall heat flux and a lower adiabatic moving surface (belt). The belt moves from the minimum channel spacing section to the maximum channel spacing section at a constant velocity so that its effect interferes with the buoyancy effect. The numerical analysis is accomplished by means of the finite volume method, using the commercial code Fluent. Findings Results in terms of heated upper plate and moving lower plate temperatures and stream function fields are presented. The paper underlines the thermal and fluid dynamic differences when natural convection or mixed convection takes place, varying minimum channel spacing, wall heat flux, moving plate velocity and converging angle. Research limitations/implications The hypotheses on which the present analysis is based are two-dimensional, laminar and steady state flow and constant thermo physical properties with the Boussinesq approximation. The minimum distance between the upper heated plate of the channel and its lower adiabatic moving plate is 10 and 20 mm. The moving plate velocity varies in the range 0-1 m/s; the belt moves from the right reservoir to the left one. Three values of the uniform wall heat flux are considered, 30, 60 and 120 W/m2, whereas the inclination angle of the upper plate θ is 2° and 10°. Practical implications Mixed convection because of moving surfaces in channels is present in many industrial applications; examples of processes include continuous casting, extrusion of plastics and other polymeric materials, bonding, annealing and tempering, cooling and/or drying of paper and textiles, chemical catalytic reactors, nuclear waste repositories, petroleum reservoirs, composite materials manufacturing and many others. The investigated configuration is used in applications such as re-heating of billets in furnaces for hot rolling process, continuous extrusion of materials and chemical vapor deposition, and it could also be used in thermal control of electronic systems. Originality/value This paper evaluates the thermal and velocity fields to detect the maximum temperature location and the presence of fluid recirculation. The paper is useful to thermal designers.
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Castro-Triguero, Rafael, Enrique Garcia-Macias, Erick Saavedra Flores, M. I. Friswell i Rafael Gallego. "Multi-scale model updating of a timber footbridge using experimental vibration data". Engineering Computations 34, nr 3 (2.05.2017): 754–80. http://dx.doi.org/10.1108/ec-09-2015-0284.
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Purpose The purpose of this paper is to capture the actual structural behavior of the longest timber footbridge in Spain by means of a multi-scale model updating approach in conjunction with ambient vibration tests. Design/methodology/approach In a first stage, a numerical pre-test analysis of the full bridge is performed, using standard beam-type finite elements with isotropic material properties. This approach offers a first structural model in which optimal sensor placement (OSP) methodologies are applied to improve the system identification process. In particular, the effective independence (EFI) method is used to determine the optimal locations of a set of sensors. Ambient vibration tests are conducted to determine experimentally the modal characteristics of the structure. The identified modal parameters are compared with those values obtained from this preliminary model. To improve the accuracy of the numerical predictions, the material response is modeled by means of a homogenization-based multi-scale computational approach. In a second stage, the structure is modeled by means of three-dimensional solid elements with the above material definition, capturing realistically the full orthotropic mechanical properties of wood. A genetic algorithm (GA) technique is adopted to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally. Findings An overall good agreement is found between the results of the updated numerical simulations and the corresponding experimental measurements. The longitudinal and transverse Young's moduli, sliding and rolling shear moduli, density and natural frequencies are computed by the present approach. The obtained results reveal the potential predictive capabilities of the present GA/multi-scale/experimental approach to capture accurately the actual behavior of complex materials and structures. Originality/value The uniqueness and importance of this structure leads to an intensive study of its structural behavior. Ambient vibration tests are carried out under environmental excitation. Extraction of modal parameters is obtained from output-only experimental data. The EFI methodology is applied for the OSP on a large-scale structure. Information coming from several length scales, from sub-micrometer dimensions to macroscopic scales, is included in the material definition. The strong differences found between the stiffness along the longitudinal and transverse directions of wood lumbers are incorporated in the structural model. A multi-scale model updating approach is carried out by means of a GA technique to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.
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Ivanchuk, Natalia, Petro Martyniuk, Olga Michuta, Yevhenii Malanchuk i Hanna Shlikhta. "Constructing a mathematical model and studying numerically the effect of bio-clogging on soil filtration consolidation". Eastern-European Journal of Enterprise Technologies 2, nr 10 (110) (30.04.2021): 27–34. http://dx.doi.org/10.15587/1729-4061.2021.230238.
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Mathematical modeling and computer simulation methods have been used to investigate the extent of influence exerted by bio-clogging on the dynamics of excess head scattering in the soil massif. To this end, the classical equation of filtration consolidation has been modified for the case of variable porosity resulting from changes in the biomass. The numerical solution to the constructed mathematical model in the form of a nonlinear boundary problem was derived by a finite-element method. Numerical experiments were carried out and their analysis was performed. Specifically, this paper shows the charts of pressure differences in the soil array when neglecting bio-clogging and when estimating the effects exerted by bio-clogging at specific points in time. The numerical experiments demonstrated that in two years after the onset of the consolidation process in the neighborhood of the lower limit of the examined soil mass with a thickness of 10 meters, excess heads fall from the initial value of 10 m to 4 m. The greatest impact from the clogging of pores by microorganisms is revealed in the neighborhood of an upper limit. At a depth of 1 m, at t=180 days, the pressure difference reaches 2.4 m. This is about 200 % of the pressure distribution without taking into account the effects of bio-clogging. Over time, the effect of bacteria on the distribution of pressures in the neighborhood of the upper boundary decreases. However, this effect extends to the entire soil mass, up to the lower limit. Thus, at t=540 days, at the lower limit, the effect of bio-clogging leads to that excess heads are 1.8 m greater than for the case of pure water filtration (a relative increase of about 80 %). Bio-clogging processes are intensified as a result of the development of microorganisms when organic chemicals enter the porous environment. Therefore, from a practical point of view, studying them is especially relevant for household waste storage facilities and the stability of their soil bases. It is advisable to undertake research by using the methods of mathematical modeling and computer simulation
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Allen, Myron B., i George F. Pinder. "The Convergence of Upstream Collocation in the Buckley-Leverett Problem(includes associated papers 14810 and 14970 )". Society of Petroleum Engineers Journal 25, nr 03 (1.06.1985): 363–70. http://dx.doi.org/10.2118/10978-pa.
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Abstract Upstream collocation is a fast and accurate scheme for simulating multiphase flows in oil reservoirs. In contrast to standard orthogonal collocation, upstream collocation yields numerical solutions to the Buckley-Leverett problem that converge to correct solutions physically. The failure of standard orthogonal collocation is not surprising, since the Buckley-Leverett problem as commonly stated is posed incompletely. The equal-area rule of Buckley and Leverett and the Welge tangent construction both specify additional constraints needed to close the problem properly. An error analysis of upstream collocation shows that this method forces convergence through an artificial dissipative term analogous to the "vanishing viscosity" used in shock fitting. This constraint is mathematically equivalent to the more familiar constructions and should prove beneficial in stimulating EOR schemes based on frontal displacement. Introduction The Buckley-Leverett saturation equation is of fundamental importance in the mechanics of oil recovery, yet solving the equation poses difficulties when saturation shocks are present. Analytic or graphic methods must negotiate triple-valued saturations, while naively applied numerical solutions may yield incorrect solutions. Orthogonal collocation is a noteworthy example: it conserves mass but, like centered difference schemes, misplaces shocks. All these problems reflect the fact that the usual statements of Cauchy problems for the Buckley-Leverett saturation equation are incomplete. To guarantee uniqueness of discontinuous solutions requires, in addition to initial data, the specification of a shock condition that is mathematically equivalent to several physically reasonable constraints. The Buckley-Leverett equal-area rule and Welge's tangent construction both implement this extra condition. A recently developed numerical method called upstream collocation overcomes the convergence failures of orthogonal collocation, generating solutions with steep gradients at the correct shock location. The intent of this paper is to demonstrate that upstream collocation enforces the correct shock condition through an error term that mimics dissipation but vanishes on refinement of the spatial grid. This error term parallels the lowest-order error terms in upstream-weighted finite differences and achieves the same effects as the artificial capillary pressures used in several earlier finite-element formulations. The analysis leading to the form of the error rests on a correspondence between collocation and Galerkin schemes and follows a line of reasoning originally developed for the linear, parabolic convection-diffusion equation. The gist of the argument is that upstream collocation corresponds to an erroneous approximation of the integrals arising in Galerkin's method. Calculation of the quadrature error leads to an expression for the artificial dissipation induced by upstream collocation. To clarify why such an error term is appropriate, we precede the error analysis with a brief review of the physical setting, solutions, and mathematics of the Buckley-Leverett problem. Physical Setting The Buckley-Leverett saturation equation describes the simultaneous flow of two immiscible, incompressible fluids through a homogeneous porous medium. The equation is important in oil production because fluid injection and displacement are common to essentially all EOR schemes. In simple applications the displaced fluid is oil, and the displacing fluid may be either water or gas. The equation arises from a material balance on water and the two-phase extension of Darcy's law, as Buckley and Leverett describe in their original paper. For a one-dimensional reservoir with uniform rock properties, combining this set of governing equations yields ............................(1) where S is water saturation, q is the effective total flow rate [L/T], and f(s) signifies the fraction of flowing fluid that is water. We assume a consistent set of units. In a horizontal, vertically uniform reservoir, the fractional flow function off is related to saturation-dependent rock and fluid properties as follows: ............................(2) where (S) and (S) are the oil and water mobilities, respectively, and(S) is the capillary pressure. SPEJ P. 363^
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Dopico, Daniel, Yitao Zhu, Adrian Sandu i Corina Sandu. "Direct and Adjoint Sensitivity Analysis of Ordinary Differential Equation Multibody Formulations". Journal of Computational and Nonlinear Dynamics 10, nr 1 (12.09.2014). http://dx.doi.org/10.1115/1.4026492.
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Sensitivity analysis of multibody systems is essential for several applications, such as dynamics-based design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences. This procedure is computationally expensive when the number of parameters is large, and numerical errors can severely limit its accuracy. This paper explores several analytical approaches to perform sensitivity analysis of multibody systems. Direct and adjoint sensitivity equations are developed in the context of Maggi's formulation of multibody dynamics equations. The approach can be generalized to other formulations of multibody dynamics as systems of ordinary differential equations (ODEs). The sensitivity equations are validated numerically against the third party code fatode and against finite difference solutions with real and complex perturbations.