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

Abstract

Abstract 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 Burger 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.