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Numerical solutions of Riemann problems in three pieces for two-dimensional nonconvex scalar conservation laws. (Chinese. English summary) Zbl 1240.65261

Summary: The Riemann problems with three pieces of constants for two-dimensional nonconvex scalar conservation laws are considered. By using weighted essentially nonoscillatory (WENO) and Runge-Kutta schemes, a numerical analysis of solutions involving a Guckenheimer structure is presented. The numerical results clearly exhibit the mathematical mechanism of the Guckenheimer structure made up of global interactions among the shock waves. Thus, the important nonlinear phenomenon of the Guckenheimer structure of solutions in two dimensions is shown numerically.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
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