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.

To improve accuracy of entropy consistent schemes,we proposed high resolution entropy consistent schemes by inserting a new flux limiter into entropy consistent schemes. It uses limiter mechanism to construct high resolution schemes. In constructing high resolution entropy consistent schemes of Euler equations,we improve resolution of contact discontinuity by adjusting parameters of corresponding entropy consistent schemes. Several numerical experiments illustrate robustness and essentially non-oscillations of the schemes.

A semi-discrete central-upwind scheme for multi-class Lighthill-Whitham-Richards (LWR) traffic flow model is presented. It combines improved fifth-order weighted essentially non-oscillatory (WENO) reconstruction called WENO-Z with semi-discrete central-upwind numerical flux. WENO-Z reconstruction improves accuracy of solution with non-oscillatory property. Time integration is carried out with strong stability preserving Runge-Kutta method. Numerical results demonstrate the scheme is efficient.

Entropy stable schemes based on physical concepts guarantee the dissipation of total entropy.They are unnecessarily entropy-fixed and effectively avoid unphysical phenomena such as expansion shock and negative pressure.By inserting limiters and using high order reconstructions at cell interfaces,a high resolution entropy stable scheme is proposed.Several numerical experiments demonstrate that the scheme is robust,accurate and essentially non-oscillations.

A fifth-order semi-discrete central-upwind scheme for hyperbolic conservation laws is proposed. In one dimension, the scheme is based on a fifth-order central weighted essentially non-oscillatory(WENO) reconstruction:In two dimensions, the reconstruction is generalized by a dimension-by-dimension approach. A Runge-Kutta method is employed in time integration. The method requires neither Riemann solvers nor characteristic decomposition and therefore enjoys main advantage of the central schemes. The present scheme is verified by one and two dimensional Euler equations of gas dynamics and shows high resolution and high accuracy.