A FORMULATION OF THE DIFFERENTIAL CONSTITUTIVE EQUATION OF OLDROYD-B FLUID AND WRITING PROGRAMMING CODE IN FREEFEM++ TO SOLVE IT BASED ON FINITE ELEMENT METHOD CONSIDERING TWO AUXILIARY NAVIER-STOKES AND TRANSPORT PROBLEMS
Keywords:
Oldroyd-B model, Navier-Stokes equations, transport equation, finite element method, FreeFemAbstract
In this paper we study the formulation of the constitutive relation of non-Newtonian visco-elastic fluid flow obeying an Oldroyd-B differential model and decoupling it into two auxiliary problems namely Navier-stokes and transport problem, we write the program in FreeFem++ to solve this model using the finite element method(FEM). We first give the general form of constitutive equations for visco-elastic Oldroyd-B fluid. The unknowns of these equations are the visco-elastic part of the extra stress tensor, the velocity and the pressure. We solve alternatively a transport equation for the stress and a Navier-Stokes like problem for velocity and pressure. We find the variational formulation of the two auxiliary problems and then we present the programs in FreeFem++ based on finite element method to solve them. We approximate the extra stress, velocity and pressure via P1 continuous, P2 continuous and P1 continuous finite element respectively.
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