适应强扭曲网格的扩散方程时空二阶精度计算

以全局支撑算子方法为基础，通过引入面通量，构造了具有局部模板点的时空二阶精度格式。对于大变形扭曲网格，格式采用法向修正技术和合理的单元角体积计算方法，可以保持通量的精确性。算例表明该格式在非凸网格上能够精确获得线性解; 在非光滑网格上可以达到时空二阶精度; 能够较好地保持对称性; 并适合于三维非结构网格上的求解。

Calculation of second-order spatial and temporal accuracy for diffusion equation on strongly distorted meshes

Numerical solution of the diffusion equation plays a key role in the study of inertial confinement fusion(ICF). In this paper, based on the global support operator method, a flux-based scheme is proposed. The scheme has local stencil with second-order accuracy both in space and time. For strongly distorted meshes, a procedure of normal direction fix is adopted with proper methods for the computation of corner volume weights, which obtains accurate discretization of the face flux. Numerical experiments show that the scheme can obtain accurate solution for linear problems on non-convex meshes. The method has second-order spatial and temporal accuracy on non-smooth meshes. The method can also preserve the symmetry well and can be extended to the three dimensional unstructured meshes.