Jacobian-free Newton Krylov discontinuous Galerkin method and physics-based preconditioning for nuclear reactor simulations

摘要

We present a high-order-accurate spatiotemporal discretization of an all-speed flow solver using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. We use the fully conservative formulation of the Navier-Stokes equations, but precondition these equations in the primitive variable form, which allows for a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under fixed CFL conditions.