An Interpolation-Free Cell-Centered Finite Volume Scheme for 3D Anisotropic Convection-Diffusion Equations on Arbitrary Polyhedral Meshes (Communications in Computational Physics, 2023)
Most existing cell-centered finite volume schemes need to introduce auxiliary unknowns in order to maintain the second-order accuracy when the mesh isdistorted or the problem is discontinuous, so interpolation algorithms of auxiliaryunknowns 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 meshtopology and can handle any discontinuity strictly. Numerical experiments show thatthis new scheme is robust, possesses a small stencil, and has approximately second-order accuracy for both diffusion-dominated and convection-dominated problems.
Keywords: Interpolation-free; finite volume scheme; convection-diffusion; polyhedral mesh.