High-Order Accurate Flux-Splitting Scheme for Conservation Laws with Discontinuous Flux Function in Space

A new modified Engquist–Osher-type flux-splitting scheme is proposed to approximate the scalar conservation laws with discontinuous flux function in space. The fact that discontinuity of fluxes space results jump unknown may be reason why it difficult design a high-order solve this hyperbolic law. In order implement WENO reconstruction, we apply compensate for Together third-order TVD Runge–Kutta time discretization, can obtain accurate scheme, which keeps equilibrium state across space, function. Some examples are given demonstrate good performance scheme.