Research On Numerical Methods Of Fluid Dynamics And Parallel Computational Algorithms

The aims of this thesis are trying to construct high order accuracy numerical schemes and study parallel computational algorithms on CFD (Computational Fluid Dynamics). The main contents are as follows:1. A series of high order accurate finite difference schemes on uniform meshes Based on the idea of DWENO (Double Weighted Essentially Non-Oscillatory) schemes, through a new algorithm of calculating the multi-stencil sets' weights, we propose a new 5th order accurate MWENO5 (Multi-Weighted Essentially Non-Oscillatory) scheme and 7th order accurate MWENO7 scheme. Then we make use of the idea of combining multi-stencil sets into sub-stencil sets to construct a new 11th order accurate MPWENO11 (Monotonicity Preserving Weighted Essentially Non-Oscillatory) scheme.2. A series of high order accurate finite volume schemes on uniform meshes We use the least square sense to construct FVWENO4 (Finite Volume Weighted Essentially Non-Oscillatory) scheme and FVWENO5 scheme.3. The generation of unstructured meshes and finite volume schemes on unstructured meshes We propose a new generation algorithm of unstructured meshes, which combines the advancing front type algorithm and Delaunay triangulation algorithm. Then we use least square sense and ENO sense to construct FVENO scheme. And combining least square sense and DWENO sense, we construct FVDWENO scheme.4. Steady state and dynamic parallel computing algorithms with AMR techniques on unstructured meshesAccording to requirements of parallel computations, we propose a new projective relation between the former mesh and the background mesh to build a kind of parallel computating algorithms with AMR techniques to deal with steady state and dynamic fluid problems on unstructured meshes, which can efficiently keep load balance on the parallel systems and reduce the cost resulting from boundary condition communications.