Wave interactions in pressureless Cargo–LeRoux model with flux perturbation

Abstract

In this article, we discuss the wave interactions in pressureless Cargo-LeRoux model with flux perturbation. The corresponding Riemann solution in terms of a one-parameter family of curves is presented. We prove the existence and uniqueness of the solution to the Riemann problem and construct estimates for the components of the solution. Relevant amplitudes are determined while presenting the interactions of weak discontinuity with contact discontinuity and shock waves. Further, we discuss the interaction of weak shocks in detail. Finally, some test cases are treated to understand the effect of initial data and strength of the shock on the transmitted, reflected amplitudes, and jump in the acceleration of the shock.