一种高精度MWENO格式及在Riemann问题中的应用

A High Precision MWENO Scheme and Its Application in Riemann Problem

提出一种新的高精度激波捕捉MWENO(Multi-Weighted Essentially Non-Oscillatory)格式求解Riemann问题.通过将计算的模板集的模板再划分为尽可能小的子模板,由这些子模板组合出相应的高阶模板,在出现强间断时,通过非线性权值系数的调节来尽可能地避开采用包含强间断的子模板进行状态变量的插值,从而有效地控制了伪振荡的出现,且能达到预期的精度要求.通过几个经典数值算例的结果表明本格式具有较高的间断分辨率,能针对各种Riemann问题得到较好的数值模拟结果.

In this study,a new high precision shock capturing MWENO（Multi-Weighted Essentially Non-Oscillatory） scheme is proposed to solve Riemann problems.we firstly subdivide the stencil sets into sub-stencil sets,then adjust values of the nonlinear weights＇ factors of these sub-stencil sets to avoid the oscillations and at the same time obtain the proper numerical accuracy in the smooth regions.The several classic numerical tests presented here show that the MWENO scheme is successful and efficient in solving the various Riemann problems.