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.

First principles molecular dynamics calculation is used to study anharmonic effect of metallic hydrogen system. Lattice vibrations of metallic hydrogen are given, and temperature effect of phonon spectrum of metallic hydrogen is discussed. Phonon dispersions of FCC phases of protium, deuterium and tritium at non-zero temperature were given. Comparing phonon dispersions at different temperatures, we found that 3.6 TPa is the critical pressure of thermodynamic stability at zero temperature, while the critical pressure dropped to 2.8 TPa at a finite temperature (100 K). Anharmonic effect changes significantly stability and phonon dispersions of the system.