The Efficient Adaptive Methods Of Two Dimension Three Temperature Radiation Heat Conduction Equations

Two dimension radiation heat conduction equations coupled with electron , iron and photon temperature is an important model which arises from laser-driven implosion of a fuel capsule with the goal of igniting a self-sustained reaction in inertial confinement fusion (ICF), and approximately describes the process of radiant energy broadcasting in the quiescent medium and energy exchange of electrons with photons and irons. This dissertation has developed some new efficient numerical methods for the equations on discretization, preconditioner and mesh adaptation. There are five achievements in the dissertation.Firstly, we propose an improved symmetric finite volume element method (SFVEM) on the triangulation, and prove that the corresponding discrete system of 2-D 3-T radiation heat conduction equations is symmetric.Secondly, we develop a new type of preconditioning technique for finite volume element method (FVEM) and SFVEM based on the preconditioning theoretics of finite element method(FEM) by studying the discrete system of FVEM, SFVEM and FEM.Thirdly, a two-grid discretization algorithm of nonlinear partial differential equations has been developed, which induce from 2-D 3-T radiation heat conduction equations by half-discretization of time. The estimate of error with || ? ||₁ norm is obtained.Fourthly, we propose a new mesh adaptation algorithm based on the Hessian matrix, which is suitable for 2-D 3-T radiation heat conduction equations.Finally, we develop a software RH3T-2D to solve the 2-D 3-T radiation heat conduction equations, which include the classical numerical methods of PDEs and new technologies proposed in this dissertation.A lot of numerical experiments has been done with RH3T-2D. The results of these examples indicate the conclusion as following:1. The discretization speed of SFVEM is faster than FVEM and FEM. When we use the different space discretization scheme to solving 2-D 3-T radiation heat conduction equations, the energy conservation error of SFVEM is lower than FVEM and FEM too . 2. when the dimension of finite element space become more bigger, the number of iteration of GMRES and PCG become steady, which preconditioned by AMG developed in the dissertation.3. The accuracy of two-grid method is validated. It demonstrates that the corresponding algorithm is suitable for 2-D 3-T radiation heat conduction equations.4. The new mesh adaptation can trace the abrupt domain of 2-D 3-T radiation heat conduction equations. It is very efficient to shorten the computation time and reduce the energy conservation error.