Some new discretization and adaptation and multigrid methods for 2-D 3-T diffusion equations

In the simulation of laser-driven implosion of a fuel capsule in inertial confinement fusion experiments, a system of two-dimensional diffusion equations coupled with electron, iron and photon temperature are widely used to approximately describe the process of energy across multiple materials and the exchange of energy among electrons, irons and photons. The numerical solution of such equations is always challenging because of its strong nonlinear phenomena and strong discontinuous interfaces. In this article, we design a symmetric finite volume method, develop the corresponding preconditioning technique, and propose a mesh adaptation algorithm based on Hessian matrix and a two-grid method. Using these new methods, we demonstrate that the energy conservation error and computation efficiency of the integrated algorithm are much better than classical method.