Two Projection Finite Element Methods For The Time-dependent Viscoelastic Oldroyd Flows

Viscoelastic Oldroyd fluid motion is one of the classical non Newtonian motion models,It is generally used to describe the fluid flow phenomena in polymer,biological fluids,suspensions and so on.Formally speaking,it can be considered as a perturbed Navier-Stokes problem by a integral term,it is this integral perturbation that makes the model different from the properties of non Newtonian fluids.The equations not only inherit lots of characteristics of the Navier-Stokes equations,but also contain the memory term,which designs the viscoelastic property.Compared with the NavierStokes equation,the model is more complicated,more diverse in nature,the study of it is still very limited,there is still great room for development.The theoretical study of projection methods has attracted more and more numerical analysis experts' attention and discussion,and its application in the Navier-Stokes equation is quite extensive,so it is difficult for us to make any other achievements in this respect.And for the study of viscoelastic Oldroyd flow problems is relatively small,so we can make an intensive study in this field.This paper mainly gives two projection methods for the time-dependent Viscoelastic Oldroyd flows: an incremental pressure correction projection finite element method and a projection finite element method based on a Possion equation.In the third chapter,we give the incremental pressure correction finite element method.And we also give stability analysis?error estimates and numerical experiments.In the fourth chapter,we give the projection finite element method based on a Possion equation.For similarly,we also give stability analysis?error estimates and numerical experiments.Although the two methods are very similar,numerical calculation is very different.