Study On Finite Point Method For Solving Convection Diffusion Equation

Meshless Method as a newly developed numerical method,its application in engineering and mathematics have always been the hot content among scholars of computational mathematics.The main idea of Meshless Method is to adopt interpolation technology,by using intra-domain dissociation nodal data to structure the shape of local function,thus to process the whole approximate solution.Approximate function constructed by this method does not rely on mesh,therefore;it can avoid the difficulties of mesh division commendably,and to eliminate the impact of computational accuracy that caused by mesh distortion or mesh moving.Compared with finite element this method has many strengths and development potentials in many aspects.The finite point method in this article is a kind of meshless method that developed in recent years.The convection diffusion equation apply to hydromechanics,aerodynamics,environment and financial engineering etc,its main research contents is the changes of certain physical quantities that contained during the process of fluid flow.The finite point method used in this article is focus on the discussion and research of convection-diffusion model.It's mainly include the following aspects:Firstly,an overall description of fundamental and implement plan of finite point method is given,including adding the process of stability,structuring approximate function by moving least square method,the selection of the weighting functions,The impact of interpolation precision of approximate function caused by the size of support region,and discretization of equation etc.Additionally,this thesis contrapose the convection-diffusion model produced from practical physical background,using finite point method to infer the numerical scheme of one-dimensional and two-dimensional problem respectively.Finally,the numerical simulation of the one-dimensional convection-dominated diffusion equations,two-dimensional stability and unsteady convection-dominated diffusion equation is made,and fully discusses the links between numerical result and characteristic length,size of support region,time step.The numerical result shows: the method used in this thesis is simple,efficient and stable.Compared with traditional finite element method and finite difference method,the accuracies are the same or higher.As a result it is an effective numerical method to solve convection diffusion equation.