An entropy stable scheme based on moving meshes is proposed for hyperbolic conservation laws. The method employs equidistribution principle to redistribute mesh points. Numerical solutions on new meshes are updated by using a conservative-interpolation formula. Entropy stable fluxes and third order strong stability-preserving Runge-Kutta time evolution method are employed to obtain numerical solutions at next time level. Several test problems are presented to demonstrate that the method not only improves resolution in discontinuous areas, but also reduces possible spurious oscillations.

A high resolution scheme is presented for shallow water equations. The scheme is based on entropy stable numerical flux with high order weighted essentially non-oscillatory (WENO) reconstruction at cell interfaces. A strong stability-preserving Runge-Kutta method is employed to advance in time. Several benchmark numerical examples demonstrate that the scheme is accurate and non-oscillatory.