非线性双曲型守恒律的一类应用通量限制器的二步二阶格式

本文提出了计算非线性双曲型守恒律弱解的一类新的二步二阶精度有限差分格式,这类高精度非线性差分格式的构造应用了三点单调差分格式的数值通量和通量限制器。文章证明,在拟CFL条件限制下,格式为总变差衰减差分格式(TVD格式),因此不发生常用的诸如二步二阶Lax-Wendroff格式、Maccomark格式和其他古典二阶格式计算不连续解时在其周围出现的剧烈振荡现象。 为了减少Roe推广技术引起的计算复杂性,文中我们基于Davis,S.F.的思想,使用了Rusanov数值通量,把标量差分格式推广到方程组,构造了求解双曲型守恒律方程组的新的预测-修正格式,较之其他一般的预测-修正格式而言,仅增加了很少的计算复杂性,初步的数值试验表明,本文提出的格式无振荡和具有极好的激波分辨率。

A Class of Two-Step Second-Order Schemes Using Flux Limiters for Nonlinear Hyperbolic Conservation Laws

In this paper, a new class of explicit, two-step, second-order accurate, finite difference schemes for the computation of weak solutions of nonlinear hyperbolic conservation laws are presented. These highly accurate and nonlinear schemes are constructed by applying the numerical flux of three point monotonic schemes and the flux limiters. These new schems are total-variation-diminishing (TVD) under the the CFL-like restrictions, hence do not imply spurious oscillations, such as those generated by the two-step Lax-Wendroff scheme, the Maccom-ark scheme and other classical second-order accurate schemes near discontinuities of the solutions.In order to decrease the complexity of the computational algorithms, which are generated by Roe extended technique, we extend the scalar difference schemes to systems based on the thought from Davis,S.F.and using Rusanov numerical flux. A new class of predicter-corrector difference schemes for hyperbolic conservation laws, which are only slightly more complex than standard predictor-corrector finite difference schemes, are constructed. Preliminary numerical results obtained show that these schemes are nonoscillatory and have good shock resolution.