Robust And Effective Numerical Methods For The Multi-material Transfer Problems

Transfer problem plays a key role in many significant fields, such as Inertial Confinement Fusion (ICF) and weapon theory research. These equations are multi-scale, multi-physics, and the fundamental unknown can be a function of seven independent variables (in 3D), therefore, they offer an great challenge for their robust and accurate solution. In real application problem, there are several difficulties to solve the transfer equations:1) The numerical solution has non-physical oscillation and negative flux; 2) For the highly distorted mesh from the Lagrangian hydrodynamic flow, the accuracy decreases and even the simulation breaks down; 3) Expensive computational cost for the high-dimension problem. Aiming at the above issues, the thesis will explore the robust and effective numerical methods for the transfer problems. The main results in this thesis are following:1) We proved the stability and convergence of the simple corner balance (SCB) scheme for solv-ing the one dimension particle transfer equations. Furthermore, two new schemes are constructed basing on the nested mesh. Numerical examples are included to demonstrated the performance of the schemes in terms of accuracy and non-oscillatory. The new schemes can restrain numerical oscillation which existed in the diamond difference scheme and the SCB scheme.2) The transport algorithm is not accurate on the highly distorted mesh and even breaks down once a concave cell appears in spatial meshes. To deal with this issue a local h-refinement for the SCB scheme of Sn transport equation on arbitrary quadrilateral meshes is presented by using a new subcell partition. It follows that a hybrid mesh with both triangle and quadrilateral cells is generated. Combining with the original SCB scheme, an adaptive transfer algorithm based on the hybrid mesh is constructed. Numerical experiments are presented to verify the utility and accuracy of the new algorithm, The results show that it performs well on extremely distorted meshes with concave cells, on which the original SCB scheme doesn't work.3) We have developed the numerical method of the coupling models for the different-level physical models describing radiative transfer problems, The two specified coupling models:multi-group and single-group radiation diffusion equations, multi-group radiation diffusion and heat conduction equation, are considered. Based the domain decomposition method, the new coupling interface boundary condition according to the coupling model is designed in order to accomplish the simulation. The numerical results demonstrate the effect of the coupling simulation on the computing efficiency as well as accuracy.4) We have presented a block-centered finite difference domain decomposition scheme with unconditional stability and the second-order accuracy for the two dimensional diffusion equation. The constructed scheme doesn't need the predictor or correction step and satisfies the discrete mass conservation. The unconditional stability and second-order accuracy to both solution values and fluxes are proved. Numerical results show the good performance of the parallel difference method.