A symmetry preserving scheme for three-dimensional Lagrangian radiation hydrodynamic simulations of ICF capsule implosion

Abstract

A symmetry preserving scheme for three-dimensional (3D) Lagrangian radiation hydrodynamic simulations of an inertial confinement fusion (ICF) capsule implosion is presented. Violation of spherical symmetry exists in conventional scheme in 3D Cartesian coordinate system. Following the idea of Caramana et al. (E.J. Caramana, et al., A Compatible, Energy and Symmetry Preserving Lagrangian Hydrodynamics Algorithm in Three-Dimensional Cartesian Geometry, Journal of Computational Physics, 157 (2000) 89–119), a symmetry preserving scheme in 3D Cartesian coordinate system is extended to Lagrangian radiation hydrodynamics. This scheme is specially designed for spherical (radial) grids. Appropriate calculations of auxiliary points in the discretization of Lagrangian hydrodynamic equations are given. Small modification is applied to the flux-related Jacobian matrix in the diffusion scheme. The modified diffusion scheme can guarantee the symmetrical flux. The symmetry preserving properties of the developed scheme for Lagrangian radiation hydrodynamics are proved in theory. The developed symmetry preserving scheme is applied to the 3D simulations of an ICF capsule implosion. Numerical results show that the symmetry preserving scheme for Lagrangian radiation hydrodynamics helps to remove unphysical instability in the 3D simulations of ICF capsule implosion.