1，A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws
摘要：A moving mesh discontinuous Galerkin method is developed for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the mesh movement strategy which is based on the moving mesh partial di_erential equation approach and moves the mesh continuously in time and orderly in space using a system of mesh partial di_erential equations. It not only can achieve the high order in smooth regions, but also capture shocks well in nonsmooth regions. For the same number of grid points, the numerical solution with the moving mesh method is much better than ones with the uniform mesh method. Numerical examples are presented to show the accuracy and shock-capturing features of the method.
2，A new hybrid WENO scheme for hyperbolic conservation laws
摘要：In this paper, a new hybrid weighted essentially non-oscillatory (WENO) scheme is designed in the finite difference framework for hyperbolic conservation laws. The main idea of the scheme is that if all extreme points of the big reconstruction polynomial for numerical flux are located outside of the big stencil, then reconstruct the numerical flux by upwind linear approximation directly, otherwise use a new WENO procedure. The scheme has advantages of its simplicity, higher efficiency and robustness. Extensive Numerical results show these good performance of the hybrid WENO schemes.