The Roe-type interface flux for conservation laws with discontinuous flux function

We consider the scalar conservation laws with discontinuous flux function (1−H(x))g(u)+H(x)f(u), where f and g are smooth nonlinear functions, and H(x) is the Heaviside function. By entropy solutions of type (A,B), which is defined by Bürger et al. (2009), we introduce a simple and efficient Roe-type interface flux, which is Lipschitz continuous and monotone. Riemann solvers are not involved at the interface x=0. In addition, some numerical results are presented to demonstrate the behavior of this interface flux.