Construction of solutions of the Riemann problem for a two-dimensional Keyfitz-Kranzer type model governing a thin film flow

Abstract

This article is concerned with constructing solutions involving nonlinear waves to a three-constant two-dimensional Riemann problem for a reduced hyperbolic model describing a thin film flow of a perfectly soluble anti-surfactant solution. Here, we solve the Riemann problem without the limitation that each jump of the initial data emanates exactly one planar elementary wave. We obtain ten topologically distinct solutions using the generalized characteristic analysis. Our analysis explores the intricate interaction between classical and non-classical waves. Furthermore, in order to validate our solutions we thoroughly compare the obtained analytical solutions with numerical results through the second-order Local Lax Friedrichs scheme which is implemented in numerical simulation.