Radiation Hydrodynamics Precision Arbitrary Lagrangian - Eulerian Approach

The process of laser fusion can be described by the equations of radiation hydrodynamics with the heat diffusion and energy exchange terms. Numerical simulation is one of the most important approaches in the study of laser fusion. From the physical and mathematical points of view, numerical methods for the equations of radiation hydrodynamics should not only be adaptive to large distortion, but also better to model multi-material and multi-physics complicated processes. Arbitrary Lagrangian-Eulerian (ALE) methods with high order of accuracy have often been used in radiation hydrodynamics codes, because the ALE methods combine the advantageous features of both Lagrangian and Eulerian schemes.This thesis is focused on the study of ALE methods of radiation hydrodynamics. The aim of the thesis is to overcome some bottlenecks in ALE methods. The following aspects have been addressed in this thesis.Firstly, a new integrated gradient scheme IGTSP, which combines the advantages of the IGA and IGT schemes, is presented. A careful and detailed discussion on the features of the IGA (Integral Gradient Average), IGT (Integral Gradient Total ) and IGTSP(Integral Gradient Total Symmetry-Preserving) schemes is given: 1. For a planar problem and a cylindrically symmetric problem, the IGA scheme is equivalent to the IGT scheme if the boundary force between neighbouring cells is taken as the weighted mass average; 2. The IGT scheme can preserve the total momentum conservation; 3. The conservation is violated by the IGA scheme when there exists a large mass ratio between neighbouring cells; 4. The IGTSP scheme gives not only the spherical motion in a spherical problem with equal angular spacing in the cylindrical coordinate system, but also the reasonable fluid motion even if the initial cell masses are widely disparate, and the accuracy of the total momentum conservation is of order one. Numerical results demonstrate the advantages and disadvantages of the three schemes.Secondly, a nine-point rezone strategy which is adaptive to variation of the flow variables is presented. This rezone strategy improves geometric quality(smoothness and orthogonality) of the computational grids and keeps the rezoned grids as close as possible to the Lagrangian meshes. The rezone strategy is proved to approximate an elliptic equation with spherical symmetry. More forms of the nine-point rezone strategy are derived in order to meet with different needs in practical problems. Numerical examples demonstrate robustness and effectiveness of our scheme on benchmark examples.Thirdly, Kershaw's nine-point diffusion difference scheme is extended to general boundary conditions. When dealing with the black body radiation boundary condition, our difference scheme for the boundary cells is united with that for the inner cells. By introducing the pseudo-Cartesian coordinates, the difference scheme for the two-dimensional three-temperature energy equations in Cartesian and cylindrical coordinates is written in aunified form.Finally, the above algorithms are incorporated into our radiation hydrodynamics code. Consequently, the code is extended to the simulation of the physical processes of both hohlraum and disk irradiated by obliquely incident laser, and the reliability is improved on the numerical simulation of direct and indirect drivings in ICF.