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Auswahl der wissenschaftlichen Literatur zum Thema „Coarse time discretization“
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Zeitschriftenartikel zum Thema "Coarse time discretization"
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Bar-Sinai, Yohai, Stephan Hoyer, Jason Hickey, and Michael P. Brenner. "Learning data-driven discretizations for partial differential equations." Proceedings of the National Academy of Sciences 116, no. 31 (2019): 15344–49. http://dx.doi.org/10.1073/pnas.1814058116.
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The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods.
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Xu, Hong Mei, Yong Gao Jin, and Li Jun Zhang. "Analysis of Symbolic Time Series of DC-DC Converter Based on Topological Conjugacy." Advanced Materials Research 694-697 (May 2013): 1413–16. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.1413.
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The converter topologically conjugates with its symbolic time series by mathematical demonstration, the time series of converter are translated into symbolic series based on return map. This study takes one-order DCM Boost as examples, time irreversibility and block entropy of different word lengths in DC-DC converters are analyzed by using coarse-grained discretization. Reasonable coding method of symbolic series is determined from statistics perspective, which can provide theory basis for digging into nonlinear characteristic and chaos in DC-DC converter.
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Fortes, Lucas Lobo Latorre, and Sandro Trindade Mordente Gonçalves. "Wideband performance limitations of the C-FDTD in the discretization impoverishment of a curved surface." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 5 (2020): 1005–15. http://dx.doi.org/10.1108/compel-01-2020-0048.
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Purpose This paper aims to explore the limitations of the conformal finite difference time-domain method (C-FDTD or Dey–Mittra) when modeling perfect electric conducting (PEC) and lossless dielectric curved surfaces in coarse meshes. The C-FDTD is a widely known approach to reduce error of curved surfaces in the FDTD method. However, its performance limitations are not broadly described in the literature, which are explored as a novelty in this paper. Design/methodology/approach This paper explores the C-FDTD method applied on field scattering simulations of two curved surfaces, a dielectric and a PEC sphere, through the frequency range from 0.8 to 10 GHz. For each sphere, the mesh was progressively impoverished to evaluate the accuracy drop and performance limitations of the C-FDTD with the mesh impoverishment, along with the wideband frequency range described. Findings This paper shows and quantifies the C-FDTD method’s accuracy drops as the mesh is impoverished, reducing C-FDTD’s performance. It is also shown how the performance drops differently according to the frequency of interest. Practical implications With this study, coarse meshes, with smaller execution time and reduced memory usage, can be further explored reliably accounting the desired accuracy, enabling a better trade-off between accuracy and computational effort. Originality/value This paper quantifies the limitations of the C-FDTD in coarse meshes in a wideband manner, which brings a broader and newer insight upon C-FDTD’s limitations in coarse meshes or relatively small objects in electromagnetic simulation.
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Gibson, Richard L., Kai Gao, Eric Chung, and Yalchin Efendiev. "Multiscale modeling of acoustic wave propagation in 2D media." GEOPHYSICS 79, no. 2 (2014): T61—T75. http://dx.doi.org/10.1190/geo2012-0208.1.
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Conventional finite-difference methods produce accurate solutions to the acoustic and elastic wave equation for many applications, but they face significant challenges when material properties vary significantly over distances less than the grid size. This challenge is likely to occur in reservoir characterization studies, because important reservoir heterogeneity can be present on scales of several meters to ten meters. Here, we describe a new multiscale finite-element method for simulating acoustic wave propagation in heterogeneous media that addresses this problem by coupling fine- and coarse-scale grids. The wave equation is solved on a coarse grid, but it uses basis functions that are generated from the fine grid and allow the representation of the fine-scale variation of the wavefield on the coarser grid. Time stepping also takes place on the coarse grid, providing further speed gains. Another important property of the method is that the basis functions are only computed once, and time savings are even greater when simulations are repeated for many source locations. We first present validation results for simple test models to demonstrate and quantify potential sources of error. These tests show that the fine-scale solution can be accurately approximated when the coarse grid applies a discretization up to four times larger than the original fine model. We then apply the multiscale algorithm to simulate a complete 2D seismic survey for a model with strong, fine-scale scatterers and apply standard migration algorithms to the resulting synthetic seismograms. The results again show small errors. Comparisons to a model that is upscaled by averaging densities on the fine grid show that the multiscale results are more accurate.
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Ibdah, Hussain A., Cecilia F. Mondaini, and Edriss S. Titi. "Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates." IMA Journal of Numerical Analysis 40, no. 4 (2019): 2584–625. http://dx.doi.org/10.1093/imanum/drz043.
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Abstract Our aim is to approximate a reference velocity field solving the two-dimensional Navier–Stokes equations (NSE) in the absence of its initial condition by utilizing spatially discrete measurements of that field, available at a coarse scale, and continuous in time. The approximation is obtained via numerically discretizing a downscaling data assimilation algorithm. Time discretization is based on semiimplicit and fully implicit Euler schemes, while spatial discretization (which can be done at an arbitrary scale regardless of the spatial resolution of the measurements) is based on a spectral Galerkin method. The two fully discrete algorithms are shown to be unconditionally stable, with respect to the size of the time step, the number of time steps and the number of Galerkin modes. Moreover, explicit, uniform-in-time error estimates between the approximation and the reference solution are obtained, in both the $L^2$ and $H^1$ norms. Notably, the two-dimensional NSE, subject to the no-slip Dirichlet or periodic boundary conditions, are used in this work as a paradigm. The complete analysis that is presented here can be extended to other two- and three-dimensional dissipative systems under the assumption of global existence and uniqueness.
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Daba, Imiru Takele, and Gemechis File Duressa. "An Efficient Computational Method for Singularly Perturbed Delay Parabolic Partial Differential Equations." International Journal of Mathematical Models and Methods in Applied Sciences 15 (July 21, 2021): 105–17. http://dx.doi.org/10.46300/9101.2021.15.14.
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In this communication, a parameter uniform numerical scheme is proposed to solve singularly perturbed delay parabolic convection-diffusion equations. Taylor’s series expansion is applied to approximate the shift term. Then the resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for temporal discretization on uniform mesh and hybrid numerical scheme based on a midpoint upwind scheme in the coarse mesh regions and a cubic spline method in the fine mesh regions on a piecewise uniform Shishkin mesh for the spatial discretization. The proposed numerical scheme is shown to be an ε−uniformly convergent accuracy of first-order in time and almost second-order in space directions. Some test examples are considered to testify the theoretical predictions.
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Partzsch, Marian, Michael Beitelschmidt, and Michael M. Khonsari. "A method for correcting a moving heat source in analyses with coarse temporal discretization." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 15 (2017): 2736–50. http://dx.doi.org/10.1177/0954406217722807.
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The numerical simulation of a moving heat source from a fixed point observer is often done by discretely adjusting its position over the steps of a thermal transient analysis. The efficiency of these simulations is increased when using a coarse temporal discretization whilst maintaining the quality of results. One systematic error source is the rare update of a nonconstant moving heat source with regard to its magnitude and location. In this work, we present an analysis of the error and propose a correction approach based on conserving the specified heat from a continuous motion in analyses with large time-step sizes. Deficiencies associated with the correction in special motion situations are identified by means of performance studies and the approach is extended accordingly. The advantages of applying the proposed correction are demonstrated through examples.
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CHUNG, ERIC T., YALCHIN EFENDIEV, and RICHARD L. GIBSON. "AN ENERGY-CONSERVING DISCONTINUOUS MULTISCALE FINITE ELEMENT METHOD FOR THE WAVE EQUATION IN HETEROGENEOUS MEDIA." Advances in Adaptive Data Analysis 03, no. 01n02 (2011): 251–68. http://dx.doi.org/10.1142/s1793536911000842.
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Seismic data are routinely used to infer in situ properties of earth materials on many scales, ranging from global studies to investigations of surficial geological formations. While inversion and imaging algorithms utilizing these data have improved steadily, there are remaining challenges that make detailed measurements of the properties of some geologic materials very difficult. For example, the determination of the concentration and orientation of fracture systems is prohibitively expensive to simulate on the fine grid and, thus, some type of coarse-grid simulations are needed. In this paper, we describe a new multiscale finite element algorithm for simulating seismic wave propagation in heterogeneous media. This method solves the wave equation on a coarse grid using multiscale basis functions and a global coupling mechanism to relate information between fine and coarse grids. Using a mixed formulation of the wave equation and staggered discontinuous basis functions, the proposed multiscale methods have the following properties. • The total wave energy is conserved. • Mass matrix is diagonal on a coarse grid and explicit energy-preserving time discretization does not require solving a linear system at each time step. • Multiscale basis functions can accurately capture the subgrid variations of the solution and the time stepping is performed on a coarse grid. We discuss various subgrid capturing mechanisms and present some preliminary numerical results.
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Ziv, Alexander, and Elena Solov’eva. "Approximate noise maps as instrument for evaluation of the city environment quality." Noise Mapping 8, no. 1 (2021): 260–67. http://dx.doi.org/10.1515/noise-2021-0021.
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Abstract The paper discusses noise mapping from the prospective of general evaluation of the state of the city environment. Suggested is a noise evaluation procedure based on a two-step spatial discretization - coarse and fine grids. The coarse grid is used for evaluation of average noise levels (background noise). For this, rather simple method is proposed, where average noise levels are estimated directly for the whole coarse grid cells instead of averaging the noise levels computed point-wise. The fine grid is used for finding the obstacle density to apply in calculations over the coarse grid. It may be used also for additional noise levels detailing in the close vicinity of noise sources where noise propagation is strongly affected by surrounding structures. The detailed results allow correction of the averages over the coarse grid. In comparison with other approaches, the suggested procedure takes little computing time to execute for the entire city. Test example shows reasonable agreement with results computed using the ‘Ecolog-Noise’ software package that has gained popularity in Russian Federation since its introduction in 2008. Another example describes the application of the proposed method for a moderate size densely built city.
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WANG, XUEJIAO, PENGJIAN SHANG, JINGJING HUANG, and GUOCHEN FENG. "DATA DISCRETIZATION FOR THE TRANSFER ENTROPY IN FINANCIAL MARKET." Fluctuation and Noise Letters 12, no. 04 (2013): 1350019. http://dx.doi.org/10.1142/s0219477513500193.
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Recently, an information theoretic inspired concept of transfer entropy has been introduced by Schreiber. It aims to quantify in a nonparametric and explicitly nonsymmetric way the flow of information between two time series. This model-free based on Shannon entropy approach in principle allows us to detect statistical dependencies of all types, i.e., linear and nonlinear temporal correlations. However, we always analyze the transfer entropy based on the data, which is discretized into three partitions by some coarse graining. Naturally, we are interested in investigating the effect of the data discretization of the two series on the transfer entropy. In our paper, we analyze the results based on the data which are generated by the linear modeling and the ARFIMA modeling, as well as the dataset consists of seven indices during the period 1992–2002. The results show that the higher the degree of data discretization get, the larger the value of the transfer entropy will be, besides, the direction of the information flow is unchanged along with the degree of data discretization.
Dissertationen zum Thema "Coarse time discretization"
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Partzsch, Marian, Michael Beitelschmidt, and Michael M. Khonsari. "A method for correcting a moving heat source in analyses with coarse temporal discretization." Sage, 2018. https://tud.qucosa.de/id/qucosa%3A35380.
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The numerical simulation of a moving heat source from a fixed point observer is often done by discretely adjusting its position over the steps of a thermal transient analysis. The efficiency of these simulations is increased when using a coarse temporal discretization whilst maintaining the quality of results. One systematic error source is the rare update of a nonconstant moving heat source with regard to its magnitude and location. In this work, we present an analysis of the error and propose a correction approach based on conserving the specified heat from a continuous motion in analyses with large time-step sizes. Deficiencies associated with the correction in special motion situations are identified by means of performance studies and the approach is extended accordingly. The advantages of applying the proposed correction are demonstrated through examples.
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Partzsch, Marian. "Neue Verfahren zur Effizienten Simulation Thermischer Systeme mit Translatorischen Strukturvariabilitäten." Doctoral thesis, 2017. https://tud.qucosa.de/id/qucosa%3A31157.
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Aktuelle technologische Herausforderungen, z.B. in der Werkzeugmaschinenentwicklung, erfordern aufgrund der steigenden Genauigkeitsanforderungen an die thermische Simulation eines zu betrachtenden Systems, dass ebenfalls die Auswirkungen relevanter, translatorischer Relativbewegungen zwischen unterschiedlichen Teilen des Systems berücksichtigt werden. Das Vorgehen, diese Bewegung in den Simulationen durch diskrete Verschiebungen zwischen den Lastschritten einer transienten Analyse umzusetzen, führt bei der Verwendung einer infinit kleinen Zeitschrittweite auf die Abbildung einer kontinuierlichen Bewegung, bringt aber gleichzeitig eine problematische Steigerung des notwendigen Rechenaufwands mit sich.
Die Anwendung einer langen Zeitschrittweite bei gleichzeitiger Konservierung der Ergebnisgenauigkeit stellt nun einen Ansatz dar, die Effizienz solcher Analysen über den eingesparten Aufwand der nicht auszuwertenden Lastschritte zu steigern. In dieser Arbeit wurden durch eine gezielte Partitionierung der aus einer Ortsdiskretisierung resultierenden Systemmatrizen zunächst vier qualitativ unterscheidbare Fehlerquellen identifiziert, welche die Verwendung einer groben Zeitdiskretisierung potentiell nach sich ziehen kann. Konkret gehören dazu die Leistungsfähigkeit des zur transienten Auswertung verwendeten Integrationsverfahrens, die diskrete Umsetzung der Bewegung sowie die seltene Aktualisierung der beiden Arten von Kontaktlasten. Für die einzelnen Fehler werden die möglichen Auswirkungen jeweils allgemein quantifiziert. Für zwei, dabei als relevant identifizierte Fehlerquellen werden mit der BD- und der RUMHI-Korrektur zugehörige Verfahren entwickelt, mit denen die Ergebnisgenauigkeit trotz grober Zeitdiskretisierung aufwandsarm bewahrt werden kann. Dass ein strukturvariables, thermisches Problem durch die kombinierte dieser Korrekturverfahren deutlich effizienter berechnet werden kann, wird in der Arbeit abschließend an zwei stellvertretenden Problemen beispielhaft gezeigt.
Konferenzberichte zum Thema "Coarse time discretization"
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Eça, Luís, Cristiano Silva, João Muralha, Christiaan Klaij, Serge Toxopeus, and Martin Hoekstra. "Discretization Error Estimation in Subsonic, Transonic and Supersonic Flows of an Inviscid Fluid Over a Bump." In ASME 2021 Verification and Validation Symposium. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/vvs2021-65290.
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Abstract This paper presents a solution verification exercise for the simulation of subsonic, transonic and supersonic flows of an inviscid fluid over a circular arc (bump). Numerical simulations are performed with a pressure-based, single-phase compressible flow solver. Sets of geometrically similar grids covering a wide range of refinement ratios have been generated. The goal of these grids is twofold: obtain a reference solution from power series expansion fits applied to the finest grids; check the numerical uncertainties obtained from coarse grids that do not guarantee monotonic convergence of the quantities of interest. The results show that even with very fine grids it is not straightforward to define a reference solution from power series expansions. The level of discretization errors required to obtain reliable reference solutions implies iterative errors reduced to machine accuracy, which may be extremely time consuming even in two-dimensional inviscid flows. Quantitative assessment of the estimated uncertainties for coarse grids depends on the selected reference solution.
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Eça, Luís, Filipe S. Pereira, Guilherme Vaz, Rui Lopes, and Serge Toxopeus. "On the Role of Discretization Errors in the Quantification of Parameter Uncertainties." In ASME 2020 Verification and Validation Symposium. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/vvs2020-8825.
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Abstract The independence of numerical and parameter uncertainties is investigated for the flow around the KVLCC2 tanker at Re = 4.6 × 106 using the time-averaged RANS equations supplemented by the k–ω two-equation SST model. The uncertain input parameter is the inlet velocity that varies ±0.25% and ±0.50% for the determination of sensitivity coefficients using finite-difference approximations. The quantities of interest are the friction and pressure coefficients of the ship and the Cartesian velocity components and turbulence kinetic energy at the propeller plane. A grid refinement study is performed for the nominal conditions to allow the estimation of the discretization error with power series expansions. However, for grids between 6 × 106 and 47.6 × 106 cells, not all the selected quantities of interest exhibit monotonic convergence. Therefore, the estimates of the sensitivity coefficients of the selected quantities of interest using the local sensitivity method and finite-differences performed for refinement levels that correspond to 0.764 × 106, 6 × 106 and 47.6 × 106 cells lead to significantly different values. Nonetheless, for a given grid, negligible differences are obtained for the sensitivity coefficients obtained with two different intervals in the finite-differences approximation. Discrepancies between sensitivity coefficients are compared with the estimated numerical uncertainties. Results obtained in the study suggest that uncertainty quantification performed in coarse grids may be significantly affected by discretization errors.
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Nejat, Amir, and Ehsan Mirzakhalili. "A Newton-Krylov Algorithm for High-Order Finite Element Computation of Heat Conduction Problems." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89131.
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The solution of a high-order conduction problem with different orders of accuracy has been investigated in this paper. The high-order solutions are obtained using Discontinuous Galerkin (DG) finite element method. The problem is solved by implicit Newton-Krylov method for different accuracy orders. The convergence of the implicit technique is investigated in terms of the CPU time. The results show the possibility of achieving an accurate and smooth solution over a coarse mesh when the higher-order discretization is employed.
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Ruparel, Tejas, Azim Eskandarian, and James Lee. "Multiple Grid and Multiple Time-Scale (MGMT) Simulations in Continuum Mechanics." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87651.
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The work presented in this paper describes a general formulation for implementation of Multiple Grid and Multiple Time-scale (MGMT) simulations in continuum mechanics. Using this method one can solve problems in structural dynamics in which the domain under consideration can be selectively discretized (spatially and temporally) in critical and remote regions, hence allowing the user to obtain a desired level of accuracy and save computational time. The formulation is based upon the fundamental principles of Domain Decomposition Methods (DDM) used to obtain the semi-discrete equation of motion for coupled sub-domains augmented with interface energy. Lagrange Multipliers, based on Schur’s dual formulation, are used to enforce interface conditions since they not only ensure energy balance but also enforce continuity of kinematic quantities across the interface. The Finite Element Tearing and Interconnecting (FETI) based Multi Time-step (MTS) coupling algorithm proposed by Prakash and Hjelmstad [1] is then used to obtain the evolution of unknown quantities in respective sub-domains using different time-steps and/or different variants of the Newmark Implicit Method. Our work is in the direction of coupling this MTS algorithm with multiple grid discretizations in respective subdomains. We propose using coarse grid discretization to define the mortar space between non-conforming sub-domains and show that this particular choice when combined with the implicit integration scheme yields a stable algorithm for MGMT simulations. The formulation is implemented, comprehensively, using Finite Element Methods and programming in FORTRAN 90. Several scenarios with different mesh densities and time-steps are evaluated to analyze the efficiency of MGMT simulations. The purpose of this paper is to study and evaluate its accuracy and stability by looking at evolution and distribution of quantities across the connecting interface. Results show that the interface coupling for non-conforming sub-domains with distinct integration time-steps can be efficiently modeled using this approach.
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Enright, Doug, Duc Nguyen, Frederic Gibou, and Ron Fedkiw. "Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45144.
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In this paper, we present an enhanced resolution capturing method for topologically complex two and three dimensional incompressible free surface flows. The method is based upon the level set method of Osher and Sethian to represent the interface combined with two recent advances in the treatment of the interface, a second order accurate discretization of the Dirichlet pressure boundary condition at the free surface (2002, J. Comput. Phys.176, 205) and the use of massless marker particles to enhance the resolution of the interface through the use of the particle level set method (2002, J. Comput. Phys., 183, 83). Use of these methods allow for the accurate movement of the interface while at the same time preserving the mass of the liquid, even on coarse computational grids. Also, these methods complement the level set method in its ability to handle changes in interface topology in a robust manner. Surface tension effects can be easily included in our method. The method is presented in three spatial dimensions, with numerical examples in both two and three spatial dimensions.
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Gupta, Anish Kumar, Douglas Ramerth, and Dhinagaran Ramachandran. "Validation of CFD Predicted Discharge Coefficients for Thick Plate Orifices With Approach Flow Perpendicular and Inclined to the Orifice Axis." In ASME Turbo Expo 2008: Power for Land, Sea, and Air. ASMEDC, 2008. http://dx.doi.org/10.1115/gt2008-50742.
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The flow discharge through thick orifices with approaching flow normal and inclined to the orifice axis was numerically predicted. The objective is to validate Fluent code predictions of discharge coefficient against Rohde et al. experimental data and arrive at an optimum mesh in terms of effort, simulation time and accuracy. CFD simulations were performed on several Rohde et al. experimental models with orifice thickness to length ratio varying from 0.5 to 4.0, with sharp and rounded inlet edges and orifice axis inclined 45 degrees to the approaching flow. The approach Mach number varies from 0.07 to 0.55 and orifice velocity head ratio ranges from 1.3 to 200. Simulations are performed using FLUENT V6.3 with k-ω SST model and 2nd order discretization scheme. Coarse mesh results at selected test points were compared with fine mesh results and a best meshing practice was determined. CFD computation at selected points was also performed with Realizable K-ε, v2f and RSM turbulence model. CFD predictions of discharge coefficient show good agreement with Rohde et al. experimental data.
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Nazeer, S. Mohamed, Francisco Chinesta, and Adrien Leygue. "A Novel Proper Generalized Decomposition (PGD) Based Approach for Non-Matching Grids." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82506.
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Proper Generalized Decomposition (PGD) is a recent model reduction technique, successfully employed to solve many multidimensional problems. This method is able to circumvent, or at least alleviate, the curse of dimensionality. This method is based on the use of separated representations. By avoiding the exponential complexity of standard grid based discretization techniques, the PGD circumvents the curse of dimensionality in a variety of problems. With the PGD, the problem’s usual coordinates (e.g. space, time), but also model parameters, boundary conditions, and other sources of variability can be viewed globally as coordinates of a high-dimensional space wherein an approximate solution can efficiently be computed at once. Non-matching grids are very common in advanced scientific computing (e.g. contact problems, sub-domains coupling,).In this framework, approximate solutions from one grid to a non-matching second grid needs to be projected. This approach poses substantial numerical complexity which increases when going from one to higher dimensional interfaces. In this paper, we try to simulate a domain, which has a coarse mesh on one side and a fine mesh on other side by PGD. We show that PGD can handle these non -matching grids by using a smooth transition of the separated representation description.
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Zhou, Xiafeng, and Fu Li. "Research on Nodal Expansion Method for Transient Convection Diffusion Equation." In 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icone22-30074.
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Nodal expansion method (NEM), well known for its high accuracy and efficiency, has been widely applied to reactor physics analysis. It is proven that NEM has an advantage over traditional finite difference method (FDM) and finite volume method (FVM). However, for most reactor thermal hydraulic codes, traditional FDM or FVM is still in use, and the NEM is barely utilized. Therefore, to make full use of the advantages of NEM and effectively solve the thermal hydraulic problems, the derivation and analytical process of nodal expansion method for transient convection-diffusion equation is studied in this paper. First, time discretization is derived by finite difference method, and then is manipulated to ensure that the form of convection-diffusion equation is consistent with that of neutron diffusion equation. After that, the approach of NEM for neutron diffusion equation can be easily utilized in the thermal hydraulic codes, and the code TNEM based on NEM is developed to solve the multi-dimensional transient convection-diffusion equation. At last, through the numerical benchmarks and error analysis, the numerical results of TNEM are found to agree well with the reference solutions and are superior to that of center difference scheme and first order upwind scheme as for the one-dimensional problem and multi-dimensional problem. Furthermore, good accuracy can be maintained even for coarse meshes.
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Nyssen, Florence, and Alain Batailly. "Thermo-Mechanical Modeling of Abradable Coating Wear in Aircraft Engines." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75824.
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In modern turbomachine designs, the nominal clearances between rotating bladed-disks and their surrounding casing are reduced to improve aerodynamic performances of the engine. This clearance reduction increases the risk of contacts between components and may lead to hazardous interaction phenomena. A common technical solution to mitigate such interactions consists in the deposition of an abradable coating along the casing inner surface. This enhances the engine efficiency while ensuring operational safety. However, contact interactions between blade-tips and an abradable layer may yield unexpected wear removal phenomena. The aim of this work is to investigate the numerical modeling of thermal effects within the abradable layer during contact interactions and compare it with experimental data. A dedicated thermal finite element mesh is employed. At each time step, a weak thermo-mechanical coupling is assumed: thermal effects affect the mechanics of the system, but the mechanical deformation of the elements has no effect on temperatures. Weak coupling is well appropriated in the case of rapid dynamics using small time step and explicit resolution schemes. Moreover, only heat transfer by conduction is considered in this work. To reduce computational times, a coarser spatial discretization is used for the thermal mesh comparing to the mechanical one. The time step used to compute the temperature evolution is larger than the one used for the mechanical iterations since the time constant of thermal effect is larger than contact events. The proposed numerical modeling strategy is applied on an industrial blade to analyze the impact of thermal effects on the blade’s dynamics.
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Narumanchi, Sreekant V. J., Jayathi Y. Murthy, and Cristina H. Amon. "Computations of Sub-Micron Heat Transport in Silicon Accounting for Phonon Dispersion." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47490.
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In recent years, the Boltzmann transport equation (BTE) has begun to be used for predicting thermal transport in dielectrics and semiconductors at the sub-micron scale. However, most published studies make a gray assumption and do not account for either dispersion or polarization. In this study, we propose a model based on the BTE, accounting for transverse acoustic (TA) and longitudinal acoustic (LA) phonons as well as optical phonons. This model incorporates realistic phonon dispersion curves for silicon. The interactions among the different phonon branches and different phonon frequencies are considered, and the proposed model satisfies energy conservation. Frequency-dependent relaxation times, obtained from perturbation theory, and accounting for phonon interaction rules, are used. In the present study, the BTE is numerically solved using a structured finite volume approach. For a problem involving a film with two boundaries at different temperatures, the numerical results match the analogous exact solutions from radiative transport literature for various acoustic thicknesses. For the same problem, the transient thermal response in the acoustically thick limit matches results from the solution to the parabolic Fourier diffusion equation. Also, in the acoustically thick limit, the bulk experimental value of thermal conductivity of silicon at different temperatures is recovered from the model even at coarse phonon frequency band discretization.