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Transport Theory and Statistical Physics Volume 37, 2008 - Issue 2-4
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Original Articles

A Finite Volume Scheme for Diffusion Equations on Distorted Quadrilateral Meshes

Zhiqiang Sheng Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China
&
Guangwei Yuan Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China
Pages 171-207 | Received 05 Sep 2007, Accepted 22 Apr 2008, Published online: 22 Dec 2008

Citations (11)

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Jian Wu & Philippe Traoré. (2013) Similarity and Comparison of Three Finite-Volume Methods for Diffusive Fluxes Computation on Nonorthogonal Meshes. Numerical Heat Transfer, Part B: Fundamentals 64:2, pages 118-146.
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Articles from other publishers (10)

Ali Daher & Stephen Payne. (2023) A dynamic multiscale model of cerebral blood flow and autoregulation in the microvasculature. Applied Mathematical Modelling 123, pages 213-240.
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Xavier Blanc, Francois Hermeline, Emmanuel Labourasse & Julie Patela. (2023) Arbitrary-order monotonic finite-volume schemes for 1D elliptic problems. Computational and Applied Mathematics 42:4.
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Pierre Anguill, Patricia Cargo, Cedric Énaux, Philippe Hoch, Emmanuel Labourasse & Gerald Samba. (2022) An asymptotic preserving method for the linear transport equation on general meshes. Journal of Computational Physics 450, pages 110859.
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Gung-Min Gie, Chang-Yeol Jung & Thien Binh Nguyen. (2019) Validation of a 2D cell-centered Finite Volume method for elliptic equations. Mathematics and Computers in Simulation 165, pages 119-138.
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Mouhamadou A. M. T. Baldé & Diaraf Seck. 2018. Shape Optimization, Homogenization and Optimal Control. Shape Optimization, Homogenization and Optimal Control 165 190 .
Zhiqiang Sheng & Guangwei Yuan. (2016) A new nonlinear finite volume scheme preserving positivity for diffusion equations. Journal of Computational Physics 315, pages 182-193.
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Hamidreza Shirkhani, Abdolmajid Mohammadian, Ousmane Seidou & Alexander Kurganov. (2016) A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids. Computers & Fluids 126, pages 25-40.
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Ricardo Costa, Stéphane Clain & Gaspar J. Machado. (2014) New cell–vertex reconstruction for finite volume scheme: Application to the convection–diffusion–reaction equation. Computers & Mathematics with Applications 68:10, pages 1229-1249.
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Zhiqiang Sheng & Guangwei Yuan. (2012) An improved monotone finite volume scheme for diffusion equation on polygonal meshes. Journal of Computational Physics 231:9, pages 3739-3754.
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Zhiqiang Sheng & Guangwei Yuan. (2011) The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes. Journal of Computational Physics 230:7, pages 2588-2604.
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