The Application Of Adaptive Discontinuous Finite Element Method In Neutron Transport Problem

The spatial variable is an important part of solving equation in the simulation of particle transport using deterministic method. The traditional finite difference method has limitations in dealing with complex geometry. Finite element method improves the adaptability of the geometry, but new problems are introduced, such as increased amount of calculation, difficulty in generating suitable meshes. An adaptive technology based on a posteriori error estimate can effectively remedy the above shortcomings. It can not only get optimized meshes which meet the error limits, but also make a proper evaluation of the calculation error.Combined with widely used discrete ordinate method and discontinuous finite element method, the three-dimensional particle transport problems are solved. The spatial discretization in tetrahedral mesh is derived in detail, so the solving of three-dimensional unstructured mesh using discontinuous finite element method can be realized. The code can deal with more complex geometries. A tetrahedral mesh subdivision technology is proposed, and two kind of posteriori error estimation method are introduced. Based on the above theory and methods, the three-dimensional discontinuous finite element and adaptive solution module of transport calculation code ARES are developed.To verify the feasibility of research method and correctness of code, a series of international benchmark and self-imposed problems are calculated. The results show that the code based on algorithm proposed in this thesis can well deal with complex geometries. The computing mesh can automatically adjust until a result which meets the error limits is obtained...