Two-dimensional Riemann problem for Burgers' equation
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 191-205
Published online March 1, 2008
Daeki Yoon and Woonjae Hwang
Korea University
Abstract : In this paper, we construct the analytic solutions and numerical solutions for a two-dimensional Riemann problem for Burgers' equation. In order to construct the analytic solution, we use the characteristic analysis with the shock and rarefaction base points. We apply the composite scheme suggested by Liska and Wendroff to compute numerical solutions. The result is coincident with our analytic solution. This demonstrates that the composite scheme works pretty well for Burgers' equation despite of its simplicity.
Keywords : 2D Riemann problem, conservation laws, Burgers' equation, composite scheme
MSC numbers : Primary 35C05, 35L65, 65M06
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