TY - JOUR
T1 - An Interpolation-Free Cell-Centered Finite Volume Scheme for 3D Anisotropic Convection-Diffusion Equations on Arbitrary Polyhedral Meshes
AU - Miao , Shuai
AU - Wu , Jiming
AU - Yao , Yanzhong
JO - Communications in Computational Physics
VL - 5
SP - 1277
EP - 1305
PY - 2023
DA - 2023/12
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0136
UR - https://global-sci.org/intro/article_detail/cicp/22214.html
KW - Interpolation-free, finite volume scheme, convection-diffusion, polyhedral mesh.
AB - <p style="text-align: justify;">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.</p>