Flux splitting schemes for the Euler equations
Flux splitting schemes for the Euler equations
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DOI：
10.1016/j.compfluid.2012.08.023
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发表时间：
2012-11
影响因子：
2.8
通讯作者：
E. Toro;M. Vázquez-Cendón
中科院分区：
文献类型：
--
作者：
E. Toro;M. Vázquez-Cendón
在本文中，我们考虑通量分裂的两个方面，一个是在微分方程的水平和另一个有关的数值方法来离散所产生的问题。在这个框架中，在偏微分方程的水平上的分裂有各种选择，并且它们的数值离散化有许多选择。一些现有的通量分裂方案属于这个框架。对于欧拉方程，我们提出了一个新的通量分裂和研究相关的两个系统的微分方程，称为平流系统和压力系统。对于每一个分裂研究，我们分析了由此产生的两个系统的微分方程，并提出离散化方案的Goddom型。这些计划是简单的，强大的和准确的与现有的方法相比。此外，他们享有一个最理想的属性：识别接触不连续性和剪切波。
In this paper we consider two aspects of flux splitting, one at the level of the differential equations and another concerned with numerical methods to discretize the resulting problems. In this framework there are various choices for the splitting at the level of the PDEs and many choices for their numerical discretization. Some of the existing flux splitting schemes fall within this framework. For the Euler equations we propose a new flux splitting and study the associated two systems of differential equations, called the advection system and the pressure system. For each of the splittings studied we analyse the resulting two systems of differential equations and propose discretization schemes of the Godunov type. These schemes are simple, robust and accurate when compared with existing methods. Moreover, they enjoy a most desirable property: recognition of contact discontinuities and shear waves.