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 schemes 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.
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