基于金字塔网格的高阶单调格式

流体力学许多问题都归结成解非线性双曲型偏微分方程(国外文献称为守恒律)。这类方程的基本困难是解出现了间断,当用高精度显式格式求解时,在间断处会产生振荡。文章基于金字塔网格,采用插值的方法,构造了2个二维对流方程的二阶显式格式,并给出了一个判断准则。在每一个网格点上,用这2个格式分别计算数值解,然后根据准则选取其中之一作为该点的最终数值解,最终的结果在非连续点具有单调性质,最后,将数值结果与有关方法进行了比较。

High-resolution scheme with monotone properties based on pyramidal stencil

Many problems in fluid mechanics end in the problems of nonlinear hyperbolic partial differential equations (also called conservation laws). The basic difficulty about those problems is that discontinuities occur in the solutions and oscillations arise near the discontinuities when the high-resolution explicit schemes are adopted. In this paper,two high-resolution explicit schemes are given by interpolation based on different pyramidal stencil for the nonlinear advection equation in two dimensional space. To construct the schemes with monotone properties around the discontinuities,one of the two schemes is chosen as the last numerical solution and the criterion is proposed. Finally,the results are compared with those of the related methods.