扩散方程保正的有限体积格式

在大变形网格上数值求解多介质扩散方程时, 如何构造具有保正性的扩散格式一直是人们关注的难题. 本文将简要综述与保正性相关的扩散格式的研究历史, 并为解决这一难题提出新的设计途径,构造出新的具有较高精度的单元中心型守恒保正格式, 它们可兼顾网格几何变形和物理量变化. 本文将给出数值实验结果, 验证新格式在变形的网格上保持非负性.

The finite volume scheme preserving the positivity for diffusion equation

It is a challenging problem to construct a finite volume scheme preserving positivity for diffusion equations with multimaterial on the distorted meshes. We review the works related with discrete schemes preserv- ing the positivity for diffusion equations, and construct some new cell-centered finite volume schemes to resolve this challenging problem. Both of the geometric deformation of mesh and the change of physical quantity are taken into account in the new schemes. Numerical results verify that the new scheme can preserve the positivity and obtain high accuracy on some distorted meshes.