Firstly, a review is given by classifying the existing fast algorithms for solving large-scale discrete linear systems arising from the Multi-Group Radiation Diffusion (MGRD) equations. Secondly, based on our recent work on parallel algebraic multigrid (AMG), two preconditioning algorithms and related theoretical frameworks are developed on a higher level. One is the approximate Schur complement type based on physical quantities and the other is the combined type based on physical and algebraic features, and the relevant components of these works are portrayed within these frameworks. Based on the above framework, a approximate Schur complement preconditioner with fundamental approximation property and low computational complexity is designed, and the corresponding spectral equivalence theory is established. Numerical experiments show that the new preconditioner has better robustness and computational efficiency. Finally, several issues that need to be further addressed are presented.

Based on a typical particle size distribution of conventional sandstone, we establish a three-dimensional porous media of unconsolidated sandstone reservoir with process method. By using phase field method(PFM), a two-phase flow model is established on the basis of two-dimensional porous media model, which is solved with finite element method. Influences of displacement velocity, fluid properties and wettability on remaining oil distribution and recovery are discussed. It shows that displacement speed increase and inviscosity ratio decrease lead to a higher capillary number, thereby facilitating enhancing oil recovery. As for wettability, capillary force is the driving force for displacement under-water wet condition and it is a resistance under oil-wet condition,which results in a higher oil recovery in water-wet core.Meanwhile, this study reveals mechanism of two-phase flow and remaining oil distribution in pore scale. It can be seen that due to complex pore structure, fluid exhibits various characteristics as flowing through pores,which have an important impact on pressure distribution and fluid velocity distribution of oil-water two-phase flow.