A high order conservative finite difference scheme for compressible two-medium flows.

• A high order finite difference scheme for compressible two-medium flows. • The scheme is conservative. • The new method can maintain high order accuracy when the solution is smooth. • WENO is applied to the primitive variables to maintain the equilibrium of velocity and pressure across the interface. In this paper, a high order finite difference conservative scheme is proposed to solve two-medium flows. Our scheme has four advantages: First, our scheme is conservative, which is important to ensure the numerical solution captures the main features properly. Second, our scheme directly applies the WENO interpolation method to the primitive variables so that it can maintain the equilibrium of velocity and pressure across the interface, which is very helpful to obtain a non-oscillatory solution. Third, the usage of nodal values enables us to manipulate algebraic functions easily. Fourth, the scheme can maintain high order accuracy when the solution is smooth. Extensive numerical experiments are performed to verify the high resolution and non-oscillatory performance of this new scheme. [ABSTRACT FROM AUTHOR]