  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.
