Multigrid Method For A Class Of Viscoelastic Fluids And It's Convergence Analysis

Non-newtonian fluids are widely used in physics,chemistry,industry and other fields,our daily life is filled with non-newtonian fluids.Because the partial differential equations of non-newtonian fluids flow problem are very complex,the constitutive equation has some special properties,for example,hyperbolic,this makes the numerical simulation of non-newtonian fluid become very difficult.this paper is to establish a stable and efficient numerical algorithm to solve a class of Phan-Thien-Tanner viscoelastic fluids flow problem.In this paper,multigrid method and finite element method are used to solve a class of Phan-Thien-Tanner viscoelastic fluids problem.Considering the non-linearity of Phan-Thien-Tanner viscoelastic fluids constitutive equation,linearization is first performed,then the linearized fluids model is analyzed.The finite element method is used to discretize the time,and the finite element discretization equation is obtained.The basic idea of multiple grid methods is to create a set of coarse meshes to solve the same problem on different grids.For iterative solution to get on fine grid,and eliminate the residual amount of high frequency part,using the projection operator to transfer the residual amount to the coarse grid,elimination residual amount of low frequency part,by way of correction,we get the solution of the original equation.This paper is divided into four chapters,as follows:The first chapter is the introduction,which mainly introduces the research background and research status of this paper,and briefly introduces the multigrid method and non-newtonian fluids.The second chapter mainly introduces Phan-Thien-Tanner viscoelastic fluids model and related symbol.The third chapter mainly researches the convergence of Phan-Thien-Tanner viscoelastic fluids v-cycle multigrid format,and proves the existence and uniqueness of the iterative solution.Chapter four is conclusion and prospect.