一类基于非均匀剖分的二维高精度差分格式

A kind of two-dimensional high-order accurate difference schemes based on non-uniformly partition

利用dimension-by-dimension方法,将求解一维非线性双曲型守恒律的一类基于非等距单元平均值重构的高效差分格式推广到二维标量双曲型守恒律方程,得到求解二维双曲型守恒律的一类二维高精度差分格式。证明了该类格式的无振荡特性。然后,将格式推广到二维双曲型守恒方程组情形。最后,给出了几个标准数值算例,验证了格式具有高阶精度、高效捕获激波等间断的能力。

Extending a class of high resolution difference schemes based on non - uniformly cell averaged - solution reconstruction for one dimensional nonlinear hyperbolic conservation laws to two - dimensional scalar hyperbolic conservation laws, a kind of two dimensional high - order accurate difference schemes is obtained by using dimension - by - dimension method for two - dimensional nonlinear hyperbolic conservation laws in this paper. Moreover, the non - oscillatory property of these schemes is proved. The extension to systems is carried out. Finally, several typical numerical experiments are given. The numerical results show that these schemes have high - order accuracy and high resolution for capturing shock waves.