Bulletin of the
Korean Mathematical Society BKMS

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