Wang, Yuying; Wang, Jinhuan; Yang, Hanchun Numerical solutions of Riemann problems in three pieces for two-dimensional nonconvex scalar conservation laws. (Chinese. English summary) Zbl 1240.65261 J. Yunnan Univ., Nat. Sci. 32, No. 6, 633-638 (2010). 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 Keywords:two-dimensional nonconvex scalar conservation laws; Riemann problems; Guckenheimer structure; Runge-Kutta; weighted essentially nonoscillatory (WENO); numerical results; shock waves PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Yunnan Univ., Nat. Sci. 32, No. 6, 633--638 (2010; Zbl 1240.65261)