多介质大变形扩散问题的一种简单高精度算法

A Simple and High Accurate Algorithm for Diffusion Problem in Multi-material on Large Distortion Meshes

在扩散方程基于单元中心量的大变形网格离散方法中,大部分算法都直接或者间接用到了单元节点量,其中更有一些方法的成败直接决定于单元节点量计算的好坏,如在实际中应用非常广泛的九点格式等.本文利用孪生逼近方法在处理间断扩散系数问题上的优势,发展了一种基于三角形子网格的简单高精度节点量计算方法,并应用该方法于九点格式.数值算例表明,新九点格式在大变形网格上和间断扩散系数处的精度与常系数扩散方程在正方形网格上的五点格式相当,近似二阶精度.

Among the methods with cell-centered unknowns on large distortion meshes, most adopt the vertex unknowns directly or indirectly, and the accuracy of some methods such as the nine-point scheme is ultimately determined by the approximation to the vertex unknowns. In this paper, taking advantage of the high-order accuracy of the ＂twin-fitting＂ method especially on discontinuous diffusion coefficients, a new treatment for the vertex unknowns is developed to apply to a nine-point scheme. Numerical experiments show that the new nine-point scheme has almost second order accuracy on distorted meshes and on discontinuous diffusion coefficients.