Operator-based preconditioning for the 2-D 3-T energy equations in radiation hydrodynamics simulations

Abstract Two-dimensional three-temperature (2-D 3-T) energy equations are a type of strongly nonlinear system that describe the energy diffusion and exchange between an electron and a photon or ion. In multi-physics simulations, the process of energy diffusion and exchange is coupled with some other physical processes, such as fluid dynamics. Typically, the Lagrangian method is employed in radiation hydrodynamics simulations. Consequently, the 3-T energy equations should be discretized on deforming meshes, which are moved with dynamics. In 2-D deforming meshes, a nine-point scheme must be employed to discretize the 3-T energy equations. Because the energy diffusion and swapping coefficients are strongly nonlinearly dependent on the temperature, and some physical parameters are discontinuous across the material interfaces, it is a challenge to solve the discretized nonlinear algebraic equations in multi-physics and multi-material applications. A Newton-Krylov method is used to solve the discretized 2-D 3-T energy equations. Based on the physical properties and the characteristics of the equations, four types of operator-based preconditioners are constructed. Numerical results show that all the preconditioning methods considered in this study are very effective.