求解双曲型方程的一致二阶守恒型差分格式的构造及数值实验

A KIND OF UNIFORMLY SECOND ORDER DIFFERENCE SCHEME FOR HYPERBOLIC CONSERVATION LAWS

由于TVD格式具有激波分辨率高与非物理振荡小的特点,在气体动力学问题的求解中得到了广泛的应用.但现有的TVD格式受其构造方式所限,在解的局部极值点附近只能达到一阶精度. 考虑以下单个双曲型方程:

Because of their high resolution and non-oscillation, TVD (Total Variation Decrease)schemes have been widely used in the calculation of gas-dynamical problems. But due to theirinherent mechanism, TVD schemes will deteriorate to first order schemes at the local extremepoints of the solution. To overcome this weakness, a new scheme is designed by modifyingthe flux limiter in the original TVD scheme. The new scheme has global second order accu-racy even at the local extreme points of the solution. Several numerical results testify that theperformance of the new scheme is much better than that of the original TVD scheme at localextreme points. The resulte of the Riemann problem show that the scheme is effective for shockcapturing.