This paper studies numerical scheme and suppression method of wall heating error for elastic-plastic flow with cell-centered Lagrange Godunov method. Provide the viscosity correction equation of Godunov scheme, describe the procedure of a viscous shock formation and propagation with a jump type initial data, and analyze the relationship between the viscosity behavior of the correction equation and wall heating error. On this basis, a new HLLC-type approximate Riemann solver is proposed. In this solver, an adaptive heat conduction viscosity is introduced to suppress wall heating error of internal energy and density at the interface; What's more, an additional contact velocity is proposed to suppress the over-heating phenomenon of deviatoric stress.

A local discontinuous Petrov-Galerkin method is developed for nonlinear Schrödingerequations. Several kinds of solitons are simulated and related phenomena are discussed, such as the soliton propagation and collision, birth of solitons including standing soliton and mobile soliton, the bound state of N solitons. The algorithm simulates some narrow structures in soliton related phenomenon. Numerical examples show that the algorithm has high accuracy and can reach the optimal convergence order. Compared with local discontinuous Galerkin method, the local discontinuous Petrov-Galerkin method has high computational efficiency and simple computational formula.

We investigate entropy production in a cell centered Lagrangian method. The motivation is to reduce intrinsic entropy dissipation of a Godunov method in calculating isentropic flow problems. By implementing pressure modification to the original scheme, a flux fix approach is proposed based on the fully discrete entropy inequality. Numerical experiments show that for problems with expansion waves the modified flux algorithm has better solution behaviors than the original Lagrangian method.