Algorithm of radiation hydrodynamics with nonorthogonal mesh for 3D implosion problem

Abstract

It is crucial to understand the degradation of implosion performance caused by three-dimensional physics and the implementation of 3-D spherical mesh is challenging. In this paper a mesh generation method based on the cube spherical projection is proposed for 3D implosion problem in Inertial Confinement Fusion (ICF). This kind of mesh has the advantage of good quality, convenient adding radiation source and adaptive moving in the radial direction. Together, a mathematical model of radiation hydrodynamics with ion-electron non-equilibrium is present. The equations of radiation hydrodynamics are solved with the operator splitting method, such that the hydrodynamics equations are solved explicitly making use of the capability of well understood explicit schemes while the radiation diffusion and electron/ion conduction parts are solved implicitly by an eleven-point scheme on the non-orthogonal mesh. We present results from several benchmark problems in order to validate our numerical scheme. And finally, we investigate the development of fourth-order modes and compute the disturbance growth process of hot spot boundary, which shown that it conforms to the physical law.