Research On Simpler Algorithm In Non-staggered Grids And Its Application To The Numerical Simulation Of Flow And Sedimentation

With the growth of numerical method and the fast development of computer science,people have paid more attention to numerical simulation. Computational Fluid Dynam-ics(CFD) and its numerical simulation has already become a powerful research method in?uid mechanics. It is as important as the other two traditional research methods; experi-mental method and theoretical method. This thesis is devoted to study a typical algorithm-SIMPLER algorithm and its applications in the simulation of incompressible viscous ?owand in the sediment trasportation of Yellow River in Ningxia. The main work is as follows:1. We analyze the algebraic method and the partial differential equation method indetail. The Poisson equation combing algebraic method controlled the boundary mesh sizeis constructed. Some numerical tests are reported. The test results show that this method isreliable and reasonable.2.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 schemeis constructed, and some numerical tests are reported.3.Analyze SIMPLE and SIMPLER. Improvements on non-staggered grids stuation isintroduced. Some numerical tests proved that the program is right.4.A plane 2-D ?ow and sedimentation governing equation is discussed. Applyingsome known in river dynamics results, we use the SIMPLER method to simulate the ?owand sedimant in Yellow River in Ningxia Shapotou area, and compare two Flow fields.A new hybrid method by combing algebraic and differential methods is constructed. Thetests results show that this method is reliable and reasonable. A new higher order scheme isconstructed, and some numerical tests are reported. The new scheme and SIMPLER methodis applied to the ?ow and sediment in the real Yellow River, and get good results.