New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

Abstract

The Rienamm solution of the Cargo-LeRoux model has been recently introduced in [1] in which authors have found the exact solutions to the initial value problem. This work is the first attempt to apply numerical methods for the Cargo-LeRoux model. The higher-order flux limiter method applied in this paper holds the total variation diminishing property and gives smooth solutions in steep gradient regions. Various limiter functions that lead to different accuracy in numerical results are tested for the Riemann problem. The numerical investigations presented in this work can be used to review limiter-based TVD schemes extensively and to construct a class of highly efficient finite volume/ finite difference methods for such models.