对流占优问题的非线性QUICK格式

A Nonlinear QUICK Scheme for Convection-Dominated Equations

本文构造了一种新的非线性加权格式,利用这种加权格式对对流项进行离散,在加权系数中构造了新的间断阈值来判断光滑与间断,使得此格式在间断的时候利用一阶迎风格式,这样可以避免振荡,而在光滑解部分用三阶QUICK格式保证了三阶精度,然后利用三阶Runge-Kutta方法对时间进行离散,进而保证整体精度,使得数值解达到比较好的逼近效果。

This paper constructed a nonlinear weighted scheme. The convective term is discretized by this new nonlinear weighted scheme. A new discontinuous threshold in the weighted coefficient is constructed to judge the smoothness and discontinuity, so that the scheme uses the first-order upwind scheme near the discontinuity which the oscillation can be avoided, and the third-order QUICK scheme is used to ensure the third-order accuracy in the smooth region. Time discretization is fulfilled by using the third order Runge-Kutta scheme. The new scheme achieves optimal order accuracy. It makes the numerical solution achieve a better approximation effect.