An Interpolation-Free Cell-Centered Finite Volume Scheme for 3D Anisotropic Convection-Diffusion Equations on Arbitrary Polyhedral Meshes

An Interpolation-Free Cell-Centered Finite Volume Scheme for 3D Anisotropic Convection-Diffusion Equations on Arbitrary Polyhedral Meshes

Year:    2023

Author:    Shuai Miao, Jiming Wu, Yanzhong Yao

Communications in Computational Physics, Vol. 34 (2023), Iss. 5 : pp. 1277–1305

Abstract

Most existing cell-centered finite volume schemes need to introduce auxiliary unknowns in order to maintain the second-order accuracy when the mesh is distorted or the problem is discontinuous, so interpolation algorithms of auxiliary unknowns are required. Interpolation algorithms are not only difficult to construct, but also bring extra computation. In this paper, an interpolation-free cell-centered finite volume scheme is proposed for the heterogeneous and anisotropic convection-diffusion problems on arbitrary polyhedral meshes. We propose a new interpolation-free discretization method for diffusion term, and two new second-order upwind algorithms for convection term. Most interestingly, the scheme can be adapted to any mesh topology and can handle any discontinuity strictly. Numerical experiments show that this new scheme is robust, possesses a small stencil, and has approximately second-order accuracy for both diffusion-dominated and convection-dominated problems.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2023-0136

Communications in Computational Physics, Vol. 34 (2023), Iss. 5 : pp. 1277–1305

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Interpolation-free finite volume scheme convection-diffusion polyhedral mesh.

Author Details

Shuai Miao

Jiming Wu

Yanzhong Yao