Application Of PPMLR Scheme To The Numerical Simulation Of Fluid Instability In Inertial Confinement Fusion

Nuclear fusion energy will be important energy source which is clean and safe for people's survial and development in the future. Inertial Confinement Fusion(ICF) is an important approach for implementing nuclear fusion and a key technique problem to be settled urgently. Especially, after nuclear explosion has been forbidden, the development of software for the accurate numerical simulation has become pivotal content of weapon research and storage safety. Therefore the research of ICF and its numerical simulation are of significant meaning for promoting our national defence and modern construction. This paper is devoted to the study of high order Godunov scheme PPMLR and its application to the numerical simulation of fluid instability problems which appear frequently in ICF. At first, on the basis of theoretical analysis and a lot of numerical experiments, we improve the PPMLR scheme presented by Colella and Woodward in 1984 in two aspects: (1) the flattening algorithm for treating shocks is appropriately modified, (2) a new procedure for treating the dependent variables abtained from the remapping is given. These improvements are essential for getting more per-fact numerical results. Then we applied the improved PPMLR scheme to the numerical simulation of Richtmyer-Meshkov instability and Rayleigh-Taylor instability problems, satisfied results are obtained. Furthermore, the improved PPMLR scheme is also applied to the computation of compressible multicomponent large distortion flows, which is a well known very difficult project and has very important practical value in the research of ICF and many other high technique fields. Lots of numerical experiments indicate that the flexibility of the improved PPMLR scheme is very good, even if for high density ratio flow problems ,multicomponent strong shock problems and multicomponent large distortion vortex problems, the numerical results are satisfied. Another important job of this paper is that we have compared the PPMLR scheme, the fifth-order FD-WENO scheme and the MUSCL scheme quantitatively, and find that PPMLR scheme and fifth-order FD-WENO scheme both have their own advantages, are outstanding schemes and can be chosen for ICF numerical simulation, but the MUSCL scheme looks somewhat inferior, and we thus do not suggest it.