A cell edge-based linearity-preserving scheme for diffusion problems on two-dimensional unstructured grids

作者：Luo Longshan; Gao Zhiming^*; Wu Jiming

来源：Mathematical Methods in the Applied Sciences, 2017, 40(15): 5423-5436.

DOI：10.1002/mma.4396

• anisotropic diffusion
• cell-centered scheme
• linearity-preserving criterion
• unstructured grid
• multipoint flux interpolation

We propose a new finite volume scheme for 2D anisotropic diffusion problems on general unstructured meshes. The main feature lies in the introduction of two auxiliary unknowns on each cell edge, and then the scheme has both cell-centered primary unknowns and cell edge-based auxiliary unknowns. The auxiliary unknowns are interpolated by the multipoint flux approximation technique, which reduces the scheme to a completely cell-centered one. The derivation of the scheme satisfies the linearity-preserving criterion that requires that a discretization scheme should be exact on linear solutions. The resulting new scheme is then called as a cell edge-based linearity-preserving scheme. The optimal convergence rates are numerically obtained on unstructured grids in case that the diffusion tensor is taken to be anisotropic and/or discontinuous.

• 出版日期2017-10
• 单位北京应用物理与计算数学研究所