NAOct 31, 2015
A Runge-Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxesDian-liang Qiao, Peng Zhang, Zhi-yang Lin et al.
The paper proposes a scheme by combining the Runge-Kutta discontinuous Galerkin method with a δ-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 δ-mapping algorithm can also be combined with any other classical methods for solving similar problems in general.