五阶高分辨率熵稳定算法

针对双曲守恒律方程的数值求解问题,构造一种新型的熵稳定算法.新算法空间方向采用五阶中心加权基本无振荡(CWENO)重构格式,时间方向采用四阶强稳定龙格-库塔(Runge-Kutta)方法.将新算法应用于若干一维Burgers方程和Euler方程组问题数值算例的求解.结果表明:新算法精度高,有效抑制了伪振荡的产生,与理论分析的结果一致.

Fifth-order High-resolution Entropy Stable Algorithm

The new-type entropy stable schemes were proposed for the hyperbolic conservation systems. The Central Weighted Essentially Non-Oscillatory( CWENO) reconstruction was used in space and the strong stability-preserving Runge-Kutta( Runge-Kutta) method of fourth-order was utilized in time for the new algorithm. Some numerical examples of one-dimensional Burgers equation and Euler systems were solved by the new scheme. According to the results,the new method has higher-accuracy and can effectively inhibit spurious oscillations,which identifies with the theoretical analysis.