penalty-projection method for incompressible flows

Isabel

Dear CFD Forum, I have some problems when I try to implement a scheme to solve 3D Navier Stokes equations in a domain which has a boundary as an inflow and another one as an open boundary. Indeed, it is a rectangular tube whose dimensions are (0.002x0.04x0.002)=(x dimension ,y dimension,z dimension). As an inflow (in y=0.04) I put a constant inflow through (u,v,w)=(0,5.3,0) because the flow goes down the y axis. On the walls I put a non-slip boundary conditions through (u,v,w)=(0,0,0) and, finally, on the output I put Neumann boundary condition that says (viscosity* grad v- grad p)=0.

The scheme I am using is the one proposed by M. Jobelin, C.Lapuerta...in their interesting article called "A finite element penalty-projection method for incompressible flows". I am using FEM, first order in time and Q2/Q1 as elements for velocity and pressure respectively.

I solve the two systems consecutively: first velocity, second pressure. Later, I correct velocity components and pressure. I must say I control the outflow in each iteration so it is the same as the inflow, but when convergence is reached, the difference between inflow and outflow is of 5.3%, which is a lot since I don't stop until a residual of 1e-12 is got in both, velocity and pressure. Besides, on the output boundary I obtain a nearly Poiseuille flow, but not a perfect one because the velocity component has a small slope towards "y axis" and "x axis".

I don't know where the problem is, because I think I am following all the steps pointed out in the article; it is a penalty projection method.

I would be really grateful if anyone could give some advice.

Thanks for your time and best regards!

Isa