Research On SIMPLE Algorithm In Non-staggered Grids And Its Application In The Numerical Simulation Of Water-Sediment Flow

With the growth of numerical method and the fast development of computer science, people have paid more attention to numerical simulation. Computational Fluid Dynamics(CFD) and its numerical simulation has already become a powerful research method in fluid mechanics. It is as important as the other two traditional research methods, experimental method and theoretical method. Research results given by numerical simulation can not only illustrate some complicated fluid theory, but also can provide very useful instructions for various engineering applications. This thesis is devoted to study a typical algorithm-SIMPLE algorithm and its application in the simulation of incompressible viscous flow and in the sediment transportation of Yellow River. The thesis is organized as follows:1. Firstly, the current state-of-art of CFD and water-sediment flow numerical simulation is reviewed and discussed. Some main problems are presented.2. Secondly, we analyze the partial differential equation mesh generation method in detail. Some improvement and a general mesh-generation program combing algebraic method is constructed.3. In the third chapter, the finite volume method for solving the convection-diffusion equation is studied. Special attention is paid to the treatment of the convective terms. A new higher order scheme, other than QUICK scheme, is constructed, and some numerical test results are reported.4. In chapter four, Some widely-used pressure-velocity linked methods for incompressible viscous flow are discussed. Improvements on non-staggered grids situation is introduced. Some numerical results comparing the methods on two kinds of grids are presented to illustrate the discussion.5. In chapter five, some applications are presented. A plane 2-D water-sediment flow governing equations together with the sediment transportation auxiliary equations are derived and discussed. By using this numerical model, numerical simulation for one-side sudden expand river and for the real Yellow River in Ningxia Shapotou area are presented.In this thesis, we have constructed a new scheme for the convetive term, and have done some improvements on mesh generation and on SIMPLE algorithm. Numerical tests shows that these improments are more reasonable and more effective.