A linearity-preserving finite volume scheme with a diamond stencil for the simulation of anisotropic and highly heterogeneous diffusion problems using tetrahedral meshes

Filho, Ricardo Jorge Morais de Lira; Santos, Sidicley R. dos; Cavalcante, Túlio de Moura; Contreras, Fernando Raul Licapa; Lyra, Paulo Roberto Maciel; Carvalho, Darlan Karlo Elisiário de

doi:10.1016/j.compstruc.2021.106510

Cited by 12 publications

(1 citation statement)

References 34 publications

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“…It is not easy to design interpolation methods such as Gao 22 in 3D, mainly due to 3D mesh geometry and topology complexity. Recently, some researchers 26 proposed an extension of the vertex interpolation method LPEW2 22 for 3D case, they are only applicable to tetrahedral meshes, not general meshes.…”

Section: Introductionmentioning

confidence: 99%

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

Yang

Gao

2022

Numerical Methods in Fluids

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Two kinds of nonlinear cell‐centered positivity‐preserving finite volume schemes are proposed for the anisotropic diffusion problems on general three‐dimensional polyhedral meshes. Firstly, the one‐sided flux on the cell‐faces is discretized using the fixed stencil of all vertices, then the cell‐centered discretization scheme is obtained using the nonlinear two‐point flux approximation. On this basis, a new explicit weighted second‐order vertex interpolation algorithm for arbitrary polyhedral meshes is designed to eliminate the vertex auxiliary unknowns in the scheme. In addition, an improved Anderson acceleration algorithm is adopted for nonlinear iteration. Finally, some benchmark examples are given to verify the convergence and positivity‐preserving property of the two schemes.

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Section: Introductionmentioning

confidence: 99%

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

Yang

Gao

2022

Numerical Methods in Fluids

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show abstract

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

Yang

Gao

2022

Numerical Methods in Fluids

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Two kinds of nonlinear cell-centered positivity-preserving finite volume schemes are proposed for the anisotropic diffusion problems on general three-dimensional polyhedral meshes. First, the one-sided flux on the cell-faces is discretized using the fixed stencil of all vertices, then the cell-centered discretization scheme is obtained using the nonlinear two-point flux approximation. On this basis, a new explicit weighted second-order vertex interpolation algorithm for arbitrary polyhedral meshes is designed to eliminate the vertex auxiliary unknowns in the scheme. In addition, an improved Anderson acceleration algorithm is adopted for nonlinear iteration. Finally, some benchmark examples are given to verify the convergence and positivity-preserving property of the two schemes.

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A Multipoint Flux Approximation with a Diamond Stencil and a Non-Linear Defect Correction Strategy for the Numerical Solution of Steady State Diffusion Problems in Heterogeneous and Anisotropic Media Satisfying the Discrete Maximum Principle

Cavalcante¹,

Filho²,

Souza³

et al. 2022

J Sci Comput

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A linearity-preserving finite volume scheme with a diamond stencil for the simulation of anisotropic and highly heterogeneous diffusion problems using tetrahedral meshes

Cited by 12 publications

References 34 publications

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

The positivity‐preserving finite volume scheme with fixed stencils for anisotropic diffusion problems on general polyhedral meshes

A Multipoint Flux Approximation with a Diamond Stencil and a Non-Linear Defect Correction Strategy for the Numerical Solution of Steady State Diffusion Problems in Heterogeneous and Anisotropic Media Satisfying the Discrete Maximum Principle

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