The Runge-Kutta discontinuous Galerkin method for conservation laws V - Multidimensional systems
The Runge-Kutta discontinuous Galerkin method for conservation laws V - Multidimensional systems
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DOI：
10.1006/jcph.1998.5892
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发表时间：
1998-04-10
影响因子：
4.1
通讯作者：
Shu, CW
中科院分区：
文献类型：
--
作者：
Cockburn, B;Shu, CW
这是我们构造和研究数值求解双曲型守恒律的所谓Runge-Kutta间断Galerkin方法的系列文章中的第五篇。本文将该方法推广到多维非线性守恒律系统。对算法进行了描述和讨论，包括三角形单元和矩形单元的数值通量、求积规则、自由度和斜率限制器等算法的形成和实际实现问题。对可压缩气体动力学的二维欧拉方程进行了数值实验，结果表明精度的(形式)阶数和三角形或矩形的使用对近似的质量有影响。(C)1998年学术出版社。
This is the fifth paper in a series in which we construct and study the so-called Runge-Kutta discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are described and discussed, including algorithm formulation and practical implementation issues such as the numerical fluxes, quadrature rules, degrees of freedom, and the slope limiters, both in the triangular and the rectangular element cases. Numerical experiments for two-dimensional Euler equations of compressible gas dynamics are presented that show the effect of the (formal) order of accuracy and the use of triangles or rectangles on the quality of the approximation. (C) 1998 Academic Press.