一种MWENO谱体积(SVMWENO5)格式

A kind of MWENO spectral volume(SVMWENO5) scheme

构造一种新的谱体积(spectral volume)格式来求解双曲型守恒律,记为SVMWENO5(Spectral Volume method byMulti-Weighted Essentially Non-Oscillatory)格式。其主要思想是:第一步,将空间计算区域划分为一系列单元,称为谱体积,等分每个谱体积为一些子单元,称为控制体积(control volume)。第二步,在谱体积内部采用类似MWENO5(Multi-Weighted Essentially Non-Oscillatory)的格式进行重构,而在谱体积的边界处采用传统WENO5格式进行处理。第三步,利用Runge-Kutta TVD离散方法对半离散格式进行时间离散,得到时空一致高精度全离散格式。最后,在文中给出几个经典数值算例用以验证本格式的计算能力。

We construct a spectral volume method to solve hyperbolic conservation laws, which is termed as SVMWENO5 （Spectral Volume method by Multi- Weighted Essentially Non-Oscillatory） scheme. The main idea is as follows： Firstly, separate the calculating domain in different direction into intervals, named spectral volumes. Then divide the intervals into sub-intervals, named control volumes. Secondly, reconstruct flux in the spectral volume by using the cell averages over control volumes in the same spectral volume. Thirdly, use MWENOS-like scheme in these control volumes to eliminate oscillations without losing numerical accuracy. After that, use Runge-Kutta TVD time discrete method to obtain total discrete scheme. Several classic numerical tests show that the scheme here has capabilities to capture discontinuities in high resolution.