高阶半离散中心迎风方法的研究与应用

Research and Application of a Semi-discrete Central-upwind Scheme

结合四阶Central Weighted Essentially Non-Oscillatory格式、三阶Central-Upwind格式构造了一种新的四阶半离散中心迎风差分方法求解双曲守恒律、浅水波方程及有关问题.而且由于数值粘性与时间步长无关,从而在涉及到对流扩散方程的求解时时间步长可根据稳定性需要尽可能的小.

A new fourth-order semi-discrete central-upwind scheme was constructed for hyperbolic system of conservation laws, convection-diffnsion equations and shallow water equations. The integration over the Riemann fans by more accurate information about one-sided local speed of wave propagation was augmented. By using the fourth-order CWEN0 reconstruction, the new scheme has the properties of higher order accuracy and higher resolution for discontinuities. Because the new scheme has less dissipation, which is＂ independent of time-steps, than the staggered central scheme, it can be efficiently used with time-steps as small as the requirement of the numerical stability.