高精度混合型格式的构造及数值模拟

在守恒变量形式的无波动无自由参数耗散(NND)格式的基础上,引入样条插值的思想,并采用具有一致二阶精度格式的限制器函数,构造了一个在光滑区具有四阶精度,在激波附近降为二阶精度的混合型格式。在计算中采用具有总变差减少(TVD)性质的四阶R unge-K u tta方法进行时间离散,通过对多个典型算例的计算,并与NND格式作了比较,分析结果表明:混合四阶格式引起的耗散和波动较小,并且能够高精度地分辨间断。

Structure and Numerical Simulation of High-Order Accuracy Hybrid Scheme

Based on a conservation variable non-oscillatory and non-free-parameter dissipation difference scheme(NND),a high-order accuracy hybrid scheme is constructed with spline interpolation and the flux limiter of uniformly second-order accuracy scheme.The scheme maintains the fourth-order accuracy in the smooth region and change into second-order accuracy in the region of the shock wave.The fourth-order TVD Runge-Kutta time discretization is used in solving many typical numerical experiments.Results are compared with that computed by the second-order NND scheme.The result shows that the new hybrid scheme is non-oscillatory high order accuracy and high resolution.