Application Of Multigrid Technology To The SIMPLE-family Algorithms For Solving The Incompressible Navier-Stokes Equations

Computational Fluid Dynamics(CFD)is more concerned in the research of Fluid Me-chanical. As important as the other two traditional research methods, experimental methodand theoretical methods.With the progress of computer technology, numerical method andits application in CFD have also obtained rapid progress in the past years.A number of nu-merical methods are created. Finite Volume Method (FVM)has clear concept, simple imple-mentation and good physical conservation property, so that it has obtained wide application.In FVM, SIMPLE is one of the most important algorithm. In order to improve the effi-ciency of algorithm, people proposed SIMPLER,SIMPLEC,SIMPLEX which are calledSIMPLE-family algorithms.Multigrid approach is a good technique to improve the efficiency for solving algebraicequation. However only few scholars have applied multigrid method to SIMPLE-familyalgorithms.The thesis is organized as following:1.The research of SIMPLE-family algorithms on collocated grid system. Some nu-merical results comparing the methods on two kinds of staggered and collocated grid arepresented to illustrate the discussion.2.Multigrid technique applied to the SIMPLE-family algorithms. By analysis,we cansee that this approach can accelerate considerably the convergence speed of SIMPLE-familyalgorithms. It is even better for the SIMPLE algorithm.3.Multigrid method method is used to speed up the SIMPLE-family algorithms.Thisapproach is also used to the two-dimensional water-sediment numerical simulation of a bendof Yellow River in Ningxia Shapotou area. We get a relatively better results.