TY - JOUR
T1 - The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V
T2 - Multidimensional Systems
AU - Cockburn, Bernardo
AU - Shu, Chi Wang
PY - 1998/4/10
Y1 - 1998/4/10
N2 - 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.
AB - 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.
KW - Discontinuous Galerkin
KW - Euler equations
KW - Slope limiters
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U2 - 10.1006/jcph.1998.5892
DO - 10.1006/jcph.1998.5892
M3 - Article
AN - SCOPUS:0001690553
VL - 141
SP - 199
EP - 224
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
IS - 2
ER -