A Runge-Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxes

TL;DR

This paper introduces a hybrid Runge-Kutta discontinuous Galerkin scheme combined with a { extdelta}-mapping algorithm to effectively solve hyperbolic conservation laws with discontinuous fluxes, applicable to complex systems like nonlinear elasticity and traffic flow.

Contribution

It presents a novel hybrid numerical scheme that integrates { extdelta}-mapping with Runge-Kutta discontinuous Galerkin methods for discontinuous flux problems.

Findings

Efficiently resolves complex wave structures in heterogeneous media.

Applicable to nonlinear elasticity and multi-class traffic flow.

{ extdelta}-mapping can be combined with other classical methods.

Abstract

The paper proposes a scheme by combining the Runge-Kutta discontinuous Galerkin method with a {\delta}-mapping algorithm for solving hyperbolic conservation laws with discontinuous fluxes. This hybrid scheme is particularly applied to nonlinear elasticity in heterogeneous media and multi-class traffic flow with inhomogeneous road conditions. Numerical examples indicate the scheme's efficiency in resolving complex waves of the two systems. Moreover, the discussion implies that the so-called {\delta}-mapping algorithm can also be combined with any other classical methods for solving similar problems in general.