非线性守恒方程的两种稳定化谱元方法

Two Stabilized Spectral Element Methods for Nonlinear Conservation Laws

考虑非线性守恒方程的高阶数值解法,介绍了基于谱元法的两种稳定性方法,一种是谱粘性消去法(SVV),另一种是过滤法.在SVV方法中,我们推广并分析了传统的基于单区域的SVV算子的定义.在过滤法中,我们分析了SVV-H elm holtz过滤算子的性质.文中从分析和计算两方面对两种方法进行了比较,建立了两者之间的关系.最后通过一系列数值试验说明方法的有效性.

This paper is aimed to develop efficient stabilization methods for the calculation of conservation laws by the spectral element method. We introduce two types of stabilization technique： spectral viscosity vanishing （SVV） and filtering. For the SW, we generalize the classical deifinition of the SW operator to the case of multi-domain. For the filtering technique, we introduce a SW-Helmholtz operator, and discuss its relationship with the classical spectral filters and SW-stabilization. Implementation technique of both methods are also given. Finally we present some numerical tests to confirm the efficiency of the proposed methods.