Gotowe bibliografie tematyczne / Cell-Centered Finite-Volume Methods

Gotowa bibliografia na temat „Cell-Centered Finite-Volume Methods”

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Data publikacji: 20 lipca 2024

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Artykuły w czasopismach na temat "Cell-Centered Finite-Volume Methods"

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Zhang, Wenjuan, i Mohammed Al Kobaisi. "Cell-Centered Nonlinear Finite-Volume Methods With Improved Robustness". SPE Journal 25, nr 01 (2.07.2019): 288–309. http://dx.doi.org/10.2118/195694-pa.

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Summary We present a nonlinear finite-volume method (NFVM) that is either positivity-preserving or extremum-preserving with improved robustness. The key ingredient of the method is the construction of one-sided fluxes, which involves decomposition of conormal vectors by introducing harmonic-averaging points as auxiliary points. The original NFVM using harmonic-averaging points is not robust in the sense that decomposition of conormal vectors with nonnegative coefficients can easily run into difficulties for heterogeneous and anisotropic permeability tensors on general nonorthogonal meshes. To improve NFVM robustness, we first present an alternative derivation of harmonic-averaging points and give a different formula that shows more clearly a point's location. On the basis of the derivation of the new formula, a correction algorithm is proposed to make modifications to those problematic harmonic-averaging points so that all the conormal vectors can be decomposed with nonnegative coefficients successfully. As a result, the resulting NFVM can be applied to more-challenging problems when conormal decomposition with nonnegative coefficients is not possible without correction. The correction algorithm is a compromise between robustness and accuracy. While it improves the robustness of the resulting NFVM, results of numerical convergence tests show that the effect of our correction algorithm on accuracy is problem-dependent. Optimal order of convergence is still maintained for some problems, and the convergence rate is reduced for others. Monotonicity and extremum-preserving properties are verified by numerical experiments. Finally, a field test case is used to demonstrate that the NFVM combined with our correction algorithm can be applied to simulate real-life reservoirs of industry-standard complexity.
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Nicaise, Serge. "A posteriori error estimations of some cell-centered finite volume methods". SIAM Journal on Numerical Analysis 43, nr 4 (styczeń 2005): 1481–503. http://dx.doi.org/10.1137/s0036142903437787.

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Bidégaray, B., i J. M. Ghidaglia. "Multidimensional corrections to cell-centered finite volume methods for Maxwell equations". Applied Numerical Mathematics 44, nr 3 (luty 2003): 281–98. http://dx.doi.org/10.1016/s0168-9274(02)00171-x.

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Chen, Long, i Ming Wang. "Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods". Advances in Applied Mathematics and Mechanics 5, nr 05 (październik 2013): 705–27. http://dx.doi.org/10.4208/aamm.12-m1279.

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AbstractA cell conservative flux recovery technique is developed here for vertex-centered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant freea posteriorierror estimator which is proven to be reliable and efficient. Some numerical tests are presented to confirm the theoretical results. Our method works for general order finite volume methods and the recovery-based and residual-baseda posteriorierror estimators is the first result ona posteriorierror estimators for high order finite volume methods.
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Terekhov, Kirill M., Bradley T. Mallison i Hamdi A. Tchelepi. "Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem". Journal of Computational Physics 330 (luty 2017): 245–67. http://dx.doi.org/10.1016/j.jcp.2016.11.010.

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Jahandari, Hormoz, i Colin G. Farquharson. "Forward modeling of gravity data using finite-volume and finite-element methods on unstructured grids". GEOPHYSICS 78, nr 3 (1.05.2013): G69—G80. http://dx.doi.org/10.1190/geo2012-0246.1.

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Minimum-structure inversion is one of the most effective tools for the inversion of gravity data. However, the standard Gauss-Newton algorithms that are commonly used for the minimization procedure and that employ forward solvers based on analytic formulas require large memory storage for the formation and inversion of the involved matrices. An alternative to the analytical solvers are numerical ones that result in sparse matrices. This sparsity suits gradient-based minimization methods that avoid the explicit formation of the inversion matrices and that solve the system of equations using memory-efficient iterative techniques. We have developed several numerical schemes for the forward modeling of gravity data using the finite-element and finite-volume methods on unstructured grids. In the finite-volume method, a Delaunay tetrahedral grid and its dual Voronoï grid are used to find the primary solution (i.e., gravitational potential) at the centers and vertices of the tetrahedra, respectively (cell-centered and vertex-centered schemes). In the finite-element method, Delaunay tetrahedral grids are used to develop linear and quadratic finite-element schemes. Different techniques are used to recover the vertical component of gravitational acceleration from the gravitational potential. In the finite-volume scheme, a differencing method is used; in the finite-element method, basis functions are used. The capabilities of the finite-volume and finite-element schemes were tested on simple and realistic synthetic examples. The results showed that the quadratic finite-element scheme is the most accurate but also the most computationally demanding scheme. The best trade-offs between accuracy and computational resource requirement were achieved by the linear finite-element and vertex-centered finite-volume schemes.
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Berzins, M., i J. M. Ware. "Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes". Applied Numerical Mathematics 16, nr 4 (luty 1995): 417–38. http://dx.doi.org/10.1016/0168-9274(95)00007-h.

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Zou, Dongyang, Chunguang Xu, Haibo Dong i Jun Liu. "A shock-fitting technique for cell-centered finite volume methods on unstructured dynamic meshes". Journal of Computational Physics 345 (wrzesień 2017): 866–82. http://dx.doi.org/10.1016/j.jcp.2017.05.047.

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Vakilipour, Shidvash, Masoud Mohammadi, Vahid Badrkhani i Scott Ormiston. "Developing a physical influence upwind scheme for pressure‐based cell‐centered finite volume methods". International Journal for Numerical Methods in Fluids 89, nr 1-2 (październik 2018): 43–70. http://dx.doi.org/10.1002/fld.4682.

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Asmouh, Ilham, Mofdi El-Amrani, Mohammed Seaid i Naji Yebari. "A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations". Computational and Mathematical Methods 2022 (13.02.2022): 1–18. http://dx.doi.org/10.1155/2022/8192192.

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A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.
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Rozprawy doktorskie na temat "Cell-Centered Finite-Volume Methods"

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Ravikumar, Devaki. "2D Compressible Viscous Flow Computations Using Acoustic Flux Vector Splitting (AFVS) Scheme". Thesis, Indian Institute of Science, 2001. https://etd.iisc.ac.in/handle/2005/277.

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The present work deals with the extension of Acoustic Flux Vector Splitting (AFVS) scheme for the Compressible Viscous flow computations. Accurate viscous flow computations require much finer grids with adequate clustering of grid points in certain regions. Viscous flow computations are performed on unstructured triangulated grids. Solving Navier-Stokes equations involves the inviscid Euler part and the viscous part. The inviscid part of the fluxes are computed using the Acoustic Flux Vector Splitting scheme and the viscous part which is diffusive in nature does not require upwinding and is taken care using a central difference type of scheme. For these computations both the cell centered and the cell vertex finite volume methods are used. Higher order accuracy on unstructured meshes is achieved using the reconstruction procedure. Test cases are chosen in such a way that the performance of the scheme can be evaluated for different range of mach numbers. We demonstrate that higher order AFVS scheme in conjunction with a suitable grid adaptation strategy produce results that compare well with other well known schemes and the experimental data. An assessment of the relative performance of the AFVS scheme with the Roe scheme is also presented.
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Ravikumar, Devaki. "2D Compressible Viscous Flow Computations Using Acoustic Flux Vector Splitting (AFVS) Scheme". Thesis, Indian Institute of Science, 2001. http://hdl.handle.net/2005/277.

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The present work deals with the extension of Acoustic Flux Vector Splitting (AFVS) scheme for the Compressible Viscous flow computations. Accurate viscous flow computations require much finer grids with adequate clustering of grid points in certain regions. Viscous flow computations are performed on unstructured triangulated grids. Solving Navier-Stokes equations involves the inviscid Euler part and the viscous part. The inviscid part of the fluxes are computed using the Acoustic Flux Vector Splitting scheme and the viscous part which is diffusive in nature does not require upwinding and is taken care using a central difference type of scheme. For these computations both the cell centered and the cell vertex finite volume methods are used. Higher order accuracy on unstructured meshes is achieved using the reconstruction procedure. Test cases are chosen in such a way that the performance of the scheme can be evaluated for different range of mach numbers. We demonstrate that higher order AFVS scheme in conjunction with a suitable grid adaptation strategy produce results that compare well with other well known schemes and the experimental data. An assessment of the relative performance of the AFVS scheme with the Roe scheme is also presented.
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Tetelin, Arthur. "Reconstruction des variables vectorielles dans le cadre des méthodes volumes finis sur maillages non-structurés généraux". Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0029.

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Les simulations numériques dans le domaine de l’énergétique peuvent présenter de forts gradients et des discontinuités, ainsi qu’une forte disparité d’échelles spatiales et temporelles. C’est typiquement le cas des simulations menées avec le code Cedre, développé par le département multi-physique pour l’énergétique de l’ONERA. Il est donc nécessaire de développer des méthodes numériques précises, robustes et performantes. Dans ce cadre, la reconstruction des variables aux faces des volumes de contrôle est l’un des éléments clé de la résolution des équations de conservation hyperboliques dans les approches volumes finis. Ces reconstructions permettent en effet d’améliorer la précision du calcul des flux numériques, ce qui a une influence majeure sur la précision globale du schéma. En outre, il est bien connu qu’une reconstruction linéaire ne suffit pas à assurer la stabilité du schéma dans le cas général, ce qui nécessite l’utilisation de reconstructions limitées. Si la reconstructions des variables scalaires a fait l’objet d’un grand nombre de travaux ces dernières décennies, très peu d’études se sont jusqu’à présent intéressées aux reconstructions des variables vectorielles. La plupart des approches des codes de calculs industriels comme Cedre consiste en effet à reconstruire chaque composante des vecteurs indépendamment des autres avec une approche scalaire. Néanmoins, une telle approche se révèle être dépendante du repère : la solution obtenue change en fonction du repère choisi, engendrant divers problèmes de précision ou de conservation sur des maillages présentant des frontières périodiques par rotation. L’objectif de cette thèse est donc double. Il vise dans un premier temps à étudier théoriquement la précision et la stabilité des reconstructions vectorielles, puis dans un second temps à développer une méthode de reconstruction vectorielle de type MUSCL multipente qui soit efficace, précise et robuste. Pour cela, nous introduisons les κ-schémas limités, qui permettent d’obtenir une reconstruction d’ordre 2 invariante par rotation, et facilement adaptable à n’importe quelle condition de monotonie choisie. Nous introduisons aussi la notion de reconstruction fictive afin d’obtenir une écriture du schéma mettant en évidence ses propriétés de stabilité. Nous en déduisons deux conditions de monotonie adaptées aux variables vectorielles, que nous éprouvons ensuite sur différents cas-tests numériques. Enfin, nous présentons une troisième approche, basée sur l’extension directe de la condition de monotonie du cas scalaire vers le cas vectoriel. Bien qu’aucune preuve de stabilité n’ait pu être écrite pour cette approche, elle présente tout de même le meilleur compromis entre stabilité d’une part, et précision et efficacité d’autre part
Numerical simulations in the field of energetics often present sharp gradients or discontinuities, as well as strong disparity of spatial and temporal scales. This is typical of simulations runned with Cedre software, developed by ONERA’s Multi-physics department for energetics. All these features involve the development of accurate, robust and efficient numerical methods. In this framework, variable reconstruction is one of the key aspects of the resolution of hyperbolic conservation laws in finite volume methods. These reconstructions improve the accuracy of the numerical fluxes, which has a direct impact on the spatial accuracy of the scheme. Moreover, it is well known that a linear reconstruction is not sufficient to ensure the scheme stability. Thus, non-linear reconstructions are required. While scalar variables reconstructions have been intensively studied during the last decades, very few studies have been conducted on vectorial variable reconstructions. In industrial codes like Cedre, each component of vectorial variables is usually treated independently as a scalar variable. However, such an approach reveals to be frame-dependent : the solution is dependent on the frame, leading to conservation and accuracy problems on periodical meshes. This thesis therefore focuses on two aspects. Firstly, it aims to study theoretically the accuracy and stability of vectorial reconstructions, and secondly to develop a vectorial reconstruction method designed for the multislope MUSCL scheme, being efficient, accurate and robust. To do so, we introduce limited κ-schemes, allowing to obtain a second-order accurate frame-invariant reconstruction, easily adaptable to any monotone condition chosen. We also introduce fictitious reconstructions, allowing to get a formulation of the scheme highlighting its stability properties. We deduce from it two monotonicity definitions suitable for vectors, that we then run on different numerical test-cases. Lastly, we present a third approach, based on the direct extension of the scalar monotonicity condition to the vectorial case. Even if no stability proof has been written, this approach presents the best compromise between stability and accuracy
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Georges, Gabriel. "Développement d’un schéma aux volumes finis centré lagrangien pour la résolution 3D des équations de l’hydrodynamique et de l’hyperélasticité". Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0130/document.

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La Physique des Hautes Densités d’Énergies (HEDP) est caractérisée par desécoulements multi-matériaux fortement compressibles. Le domaine contenant l’écoulementsubit de grandes variations de taille et est le siège d’ondes de chocs et dedétente intenses. La représentation Lagrangienne est bien adaptée à la descriptionde ce type d’écoulements. Elle permet en effet une très bonne description deschocs ainsi qu’un suivit naturel des interfaces multi-matériaux et des surfaces libres.En particulier, les schémas Volumes Finis centrés Lagrangiens GLACE (GodunovtypeLAgrangian scheme Conservative for total Energy) et EUCCLHYD (ExplicitUnstructured Cell-Centered Lagrangian HYDrodynamics) ont prouvé leur efficacitépour la modélisation des équations de la dynamique des gaz ainsi que de l’élastoplasticité.Le travail de cette thèse s’inscrit dans la continuité des travaux de Maireet Nkonga [JCP, 2009] pour la modélisation de l’hydrodynamique et des travauxde Kluth et Després [JCP, 2010] pour l’hyperelasticité. Plus précisément, cettethèse propose le développement de méthodes robustes et précises pour l’extension3D du schéma EUCCLHYD avec une extension d’ordre deux basée sur les méthodesMUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) et GRP(Generalized Riemann Problem). Une attention particulière est portée sur la préservationdes symétries et la monotonie des solutions. La robustesse et la précision duschéma seront validées sur de nombreux cas tests Lagrangiens dont l’extension 3Dest particulièrement difficile
High Energy Density Physics (HEDP) flows are multi-material flows characterizedby strong shock waves and large changes in the domain shape due to rarefactionwaves. Numerical schemes based on the Lagrangian formalism are good candidatesto model this kind of flows since the computational grid follows the fluid motion.This provides accurate results around the shocks as well as a natural tracking ofmulti-material interfaces and free-surfaces. In particular, cell-centered Finite VolumeLagrangian schemes such as GLACE (Godunov-type LAgrangian scheme Conservativefor total Energy) and EUCCLHYD (Explicit Unstructured Cell-CenteredLagrangian HYDrodynamics) provide good results on both the modeling of gas dynamicsand elastic-plastic equations. The work produced during this PhD thesisis in continuity with the work of Maire and Nkonga [JCP, 2009] for the hydrodynamicpart and the work of Kluth and Després [JCP, 2010] for the hyperelasticitypart. More precisely, the aim of this thesis is to develop robust and accurate methodsfor the 3D extension of the EUCCLHYD scheme with a second-order extensionbased on MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws)and GRP (Generalized Riemann Problem) procedures. A particular care is taken onthe preservation of symmetries and the monotonicity of the solutions. The schemerobustness and accuracy are assessed on numerous Lagrangian test cases for whichthe 3D extensions are very challenging
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Hung, Jui-Chi, i 洪瑞祺. "Solving Laplace’s Equation by Cell-Centered Finite Volume Method on Unstructured Grids". Thesis, 2009. http://ndltd.ncl.edu.tw/handle/54845486365317191748.

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碩士
國立高雄海洋科技大學
輪機工程研究所
97
In this study a cell-centered finite volume method on unstructured grids is used to solve Laplace’s equation. The two- dimensional and three-dimensional heat conduction problems in steady and unsteady states are analyzed. First, Laplace’s equation is discretized to obtain differential equations with first-order and hyper-order accuracy. Then, the converged solution is determined within specific iterative times using the conjugate gradient iterative method (P-CG). This study compares the calculated results of first-order accuracy with those of hyper-order accuracy in steady and unsteady states. The experiment indicates that the results of first-order accuracy are consistent with those of hyper-order accuracy on unstructured grids in steady state. Moreover, applying the cell-centered finite volume method on problems in unsteady state will reduce the number of iterative times, and converges much faster.
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Lu, Tsung-Yi, i 陸宗儀. "A MATLAB Code to Solve Heat Conduction Problem by Cell-Centered Finite Volume Method on Unstructured Grids". Thesis, 2010. http://ndltd.ncl.edu.tw/handle/90594286564328855688.

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碩士
國立高雄海洋科技大學
輪機工程研究所
98
A MATLAB code is developed for solving Laplacian like equations such as heat conduction and concentration diffusion. The algorithm is based on the unstructured grids and the problems solving use conjugate gradient method to speed up the calculation. Two and three dimensional problems in heat conduction are examined in very good agreement with analytic solution.
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Części książek na temat "Cell-Centered Finite-Volume Methods"

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Feng, Xueshang. "Cell-Centered Finite Volume Methods". W Magnetohydrodynamic Modeling of the Solar Corona and Heliosphere, 125–337. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9081-4_2.

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Fořt, J., J. Fürst, J. Halama, M. Hrušová i K. Kozel. "Comparisons of Cell Centered and Cell Vertex Finite Volume Methods for Internal Flow Problems". W Hyperbolic Problems: Theory, Numerics, Applications, 325–32. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8720-5_35.

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Caucao, Sergio, Tongtong Li i Ivan Yotov. "A Cell-Centered Finite Volume Method for the Navier–Stokes/Biot Model". W Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 325–33. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43651-3_29.

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Hahn, Jooyoung, Karol Mikula, Peter Frolkovič, Martin Balažovjech i Branislav Basara. "Cell-Centered Finite Volume Method for Regularized Mean Curvature Flow on Polyhedral Meshes". W Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 755–63. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43651-3_72.

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Santugini, Kévin. "A Discontinuous Coarse Space (DCS) Algorithm for Cell Centered Finite Volume Based Domain Decomposition Methods: The DCS-RJMin Algorithm". W Lecture Notes in Computational Science and Engineering, 379–87. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-18827-0_38.

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Zarrouk, M. Mustapha. "Optimized Schwarz and Finite Volume Cell-Centered Method for Heterogeneous Problems". W Lecture Notes in Networks and Systems, 434–39. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-48465-0_57.

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Coudière, Yves, i Gianmarco Manzini. "Benchmark 3D: The Cell-Centered Finite Volume Method Using Least Squares Vertex Reconstruction (“Diamond Scheme”)". W Finite Volumes for Complex Applications VI Problems & Perspectives, 985–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_96.

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Benkhaldoun, Fayssal, Amadou Mahamane i Mohammed Seaïd. "Adaptive cell-centered finite volume method for non-homogeneous diffusion problems: Application to transport in porous media". W Finite Volumes for Complex Applications VI Problems & Perspectives, 79–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20671-9_9.

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Koren, Barry. "Iterative defect correction and multigrid accelerated explicit time stepping for the steady Euler equations". W Numerical Methods for Fluid Dynamics, 207–20. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198536963.003.0013.

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Abstract The computational grid is obtained by a hybrid finite element - finite volume partition. A (possibly unstructured) finite-element triangularization is used as the basic partition. A cell-centered finite-volume partition is derived from the finite-element partition by connecting the centers of the triangle sides in the manner illustrated in Figure 1. The finite-volume grid gives us the easy possibility of grouping together the nodes associated with contiguous finite volumes.
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Streszczenia konferencji na temat "Cell-Centered Finite-Volume Methods"

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Zhang, W., i M. Al Kobaisi. "Discrete Fracture-Matrix Simulations Using Cell-Centered Nonlinear Finite Volume Methods". W ECMOR XVII. European Association of Geoscientists & Engineers, 2020. http://dx.doi.org/10.3997/2214-4609.202035010.

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Zangeneh, Reza, i Carl F. Ollivier Gooch. "Reconstruction Map Stability Analysis for Cell Centered Finite Volume Methods on Unstructured Meshes". W 55th AIAA Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2017. http://dx.doi.org/10.2514/6.2017-0734.

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Nishikawa, Hiroaki, i Jeffery A. White. "A Simplified FANG Cell-Centered Finite-Volume Method and Comparison with Other Methods for Trouble-Prone Grids". W AIAA AVIATION 2021 FORUM. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-2720.

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Contreras, Fernando, Marcio Souza, Paulo Lyra i Darlan Carvalho. "Numerical Simulation of Fluid Flows in Petroleum Reservoirs Using a Cell Centered Non-Linear Finite Volume Method in Unstructured Polygonal Meshes". W XXXVI Iberian Latin American Congress on Computational Methods in Engineering. Rio de Janeiro, Brazil: ABMEC Brazilian Association of Computational Methods in Engineering, 2015. http://dx.doi.org/10.20906/cps/cilamce2015-0630.

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White, Jeffery A., Hiroaki Nishikawa i Robert A. Baurle. "Weighted Least-squares Cell-Average Gradient Construction Methods For The VULCAN-CFD Second-Order Accurate Unstructured Grid Cell-Centered Finite-Volume Solver". W AIAA Scitech 2019 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-0127.

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White, Jeffery A., Hiroaki Nishikawa i Robert A. Baurle. "A 3-D Nodal-Averaged Gradient Approach For Unstructured-Grid Cell-Centered Finite-Volume Methods For Application to Turbulent Hypersonic Flow". W AIAA Scitech 2020 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2020. http://dx.doi.org/10.2514/6.2020-0652.

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Lee, Hyungro, Einkeun Kwak i Seungsoo Lee. "Artificial Compressibility Method and Preconditioning Method for Solving Two Dimensional Incompressibile Flow". W ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-01007.

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In this study, two commonly used numerical methods for the analysis of incompressible flows (or low Mach number flows), Chorins’ artificial compressibility method and Wiess and Smith’s preconditioning method are compared. Also, the convergence characteristics of two methods are numerically investigated for two-dimensional laminar and turbulent flows. Although the two methods have similar governing equations, the eigensystems and other details are very different. The eigensystems of the artificial compressibility method and the preconditioning method are analytically examined. An artificial compressibility code that solves the incompressible RANS (Reynolds Averaged Navier-Stokes) equations is newly developed for the study. An artificial compressibility code and a well-verified existing low Mach number code uses Roe’s approximate Riemann solver in conjunction with a cell centered finite volume method. Using MUSCL extrapolation with nonlinear limiters, 2nd order spatial accuracy is achieved while maintaining TVD (total variation diminishing) property. AF-ADI (approximate factorization-alternate direction implicit) method is used to get the steady solution for both codes. Menter’s k–ω SST turbulence model is used for the analysis of turbulent flows. Navier-Stokes equations and the turbulence model equations are solved in a loosely coupled manner.
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Mathur, Sanjay R., i Jayathi Y. Murthy. "A Multigrid Method for the Solution of Ion Transport Using the Poisson Nernst Planck Equations". W ASME 2007 InterPACK Conference collocated with the ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ipack2007-33410.

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Recently there has been much interest in simulating ion transport in biological and synthetic ion channels using the Poisson-Nernst-Planck (PNP) equations. However, many published methods exhibit poor convergence rates, particularly at high driving voltages, and for long-aspect ratio channels. The paper addresses the development of a fast and efficient coupled multigrid method for the solution of the PNP equations. An unstructured cell-centered finite volume method is used to discretize the governing equations. An iterative procedure, based on a Newton-Raphson linearization accounting for the non-linear coupling between the Poisson and charge transport equations, is employed. The resulting linear system of equations is solved using an algebraic multigrid method, with coarse level systems being created by agglomerating finer-level equations based on the largest coefficients of the Poisson equation. A block Gauss-Seidel update is used as the relaxation method. The method is shown to perform well for ion transport in a synthetic channel for aspect ratios ranging from 16.67 to 1667 for a range of operating parameters.
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Shan, Hua, i Sung-Eun Kim. "Numerical Study of Advection Schemes for Interface Capturing in a Volume of Fluid Method on Unstructured Meshes". W ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-04029.

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In solving naval hydrodynamics problems using computational fluid dynamics (CFD), the moving free surface between air and water introduces extra difficulties to numerical methods, since the material property jumps across the interface and the time-dependent free surface position becomes part of the solution. Engineering applications often require a flexible and robust solver for incompressible multi-phase viscous flows with the capability of capturing the interface. In the volume of fluid (VOF) method, the interface is captured by directly solving the convection transport equation of volume fraction. In this case, the numerical dissipation of the advection scheme smears the sharp interface and the numerical dispersion causes unphysical oscillations near the interface. Utilizing the guidance of boundedness criteria, many limited higher-order non-liner advection schemes have been developed in an attempt to balance numerical dissipation and dispersion. Though it is well-known that these non-linear advection schemes can lead to solutions combining boundednesss and accuracy, users are often overwhelmed by the wide variety of available schemes. Also, these schemes are developed with the assumption of a uniform Cartesian-type mesh. Thus, a thorough investigation and comparison of the performance of these interface-capturing advection schemes are necessary, especially for naval hydrodynamics problems solved on unstructured meshes. In this study, a systematic comparison and evaluation of several existing and new bounded, higher-order advection schemes has been conducted within the framework of NavyFOAM, which is developed based on OpenFOAM — an object orientated C++ toolbox for the customization and extension of numerical solvers for continuum mechanics problems, including CFD, where the governing equations are discretized using the cell-centered finite volume method on unstructured mesh. The flexible infrastructure of the code enables us to implement and test the selected advection schemes very quickly. The test cases include advection of hollow cylinders, Zalesak’s rotating slotted disk, traveling solitary wave, dam breaking problem.
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Raif, Markus, Jürgen F. Mayer i Heinz Stetter. "Comparison of a TVD-Upwind Scheme and a Central Difference Scheme for Navier-Stokes Turbine Stage Flow Calculation". W ASME 1996 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-gt-031.

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The differences of two distinct numerical schemes implemented in one code called ITSM3D are presented for a turbine stage test case. Thus both schemes are used with exactly the same computational infrastructure, e. g, same grids, boundary conditions, acceleration strategies, time-stepping, turbulence model etc. The two methods are based on an explicit Runge-Kutta-type finite volume scheme expressed in cylindrical coordinates and have been developed at the Institut für Thermische Strömungsmaschinen und Maschinenlaboratorium of the University of Stuttgart. One scheme is a node centered 3rd order TVD scheme according to Osher and the other belongs to the cell vertex central difference type with the concept of artificial viscosity. The model of Baldwin-Lomax is used in order to simulate turbulent effects. Non-reflective boundary conditions are taken at stator inlet and rotor outlet to avoid non-physical reflections. A multigrid technique in combination with implicit residual smoothing and local time-stepping is employed to accelerate the computation. The test case for this comparison is the last stage of a low-pressure turbine. The computational results obtained are discussed and compared to each other as well as to experimental data. They are presented as pressure and Mach number isoline contours and diagrams of circumferential averaged quantities at inlet and outlet planes of stator and rotor versus radial position.
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