Differential Quadrature Method In The Simulation Of Incompressible Viscous Fluid

The objective of this study is to explore how the method of differential quadrature(DQmethod) can be used to solve the motion of incompressible viscous fluid in the complexflow passage. The main efforts of the thesis are as follows:Firstly, by reviewing a lot of literatures, the developing process and existing state ofthe numerical simulation in CFD are summarized, especially some common numerical andgrid generation methods are highlighted.Secondly, the basic principles of the DQ method and the algorithms of its weightingcoefficients are described, both the solution of two dimensional partial differential equation,and the simulation of three dimensional lid-driven cavity flow are joined together toillustrate the application of the DQ method. In addition, the pertinent results are gained byMatlab.Thirdly, DQ method has an obvious advantage that preciser solutions can be got by less grids in the simulation of incompressible fluid, but the method only suits to the simple flow passage, therefore the three dimensional fitted-body coordinates are induced to deal with the complex flow passage in this paper. The formulae that generate the fitted-body grids are respectively obtained and the original variable Navier-Stokes equations are transformed from Descartesian coordinates to fitted-body coordinates. By using the the polynomial—based differential quadrature method and SIMPLE algorithm, the discrete scheme of the N-S equations is established in the fitted-body coordinates based on the non-staggered gird.