结构网格MWENO-7格式的构造和应用

New MWENO-7 Scheme on Uniform Grids and Its Application

在结构网格上构造了一种多重加权实质无波动激波捕捉格式,命名为MWENO-7(Multi-weighted essen-tially non-oscillatory)格式。提出了一种新的模板集上权的计算策略:通过探测因子来判断模板集上间断出现的位置,调节相应模板上的线性权,再与光滑因子结合起来得到非线性权,以保证在不出现伪振荡的前提下尽可能利用原有的等距模板构造出尽可能高阶的格式。文中给出几个典型算例,验证了MWENO-7格式的有效性。

A new MWENO-7 （multi-weighted essentially non-oscillatory） scheme is constructed on uniform grids. This scheme is based on a new algorithm for calculating weights of stencil sets. By using detecting factors to search discontinuities, the associated linear weights can be modified. Combined with smooth indicators, new nonlinear weights can be obtained. For eliminating spurious oscillations, the original stencil sets are used to obtained proper higher order accuracy. Finally, some classical numerical examples are presented. Results show that the MWENO-7 scheme is effective.