流體力學數(shù)值方法及并行策略研究.pdf

1、南京航空航天大學博士學位論文流體力學數(shù)值方法及并行策略研究姓名：朱君申請學位級別：博士專業(yè)：流體力學指導教師：趙寧;戴嘉尊20060401南京航空航天大學博士學位論文 v ABSTRACT The aims of this thesis are trying to construct high order accuracy numerical schemes and study parallel comp

2、utational 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

3、 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- Weight

4、ed 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

5、 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

6、 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 pr

7、opose anew 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 co

8、nstruct 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

9、meshes According 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

10、 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