Outflow boundary Control Volume SIMPLE Help !!!
 

Hi guys,

I'm new to this forum community, but I have been a long time lurker so I'm really hoping I can access some of the great help you guys give.

I'm just a bit confused about how to implement the outflow boundary condition. I've been reading Versteeg's book on the control volume method and SIMPLE, and my code is based on the teachings of that book.

I've written a little program in C for 2D transient problems that works well with the lid-driven problem, but now I'm trying to calculate the flow around a circle obstacle and I can't seem to get the outflow boundary to work!

I have a rectangle region where the west wall is inflow and the other three walls are to be outflow. In the middle is the circular obstacle. At the inflow I've specified the velocity in the X direction and zero velocity in the Y direction.

I've read in Versteeg that I should take the boundary velocities at the outflows equal to the velocities of the adjacent outer-most layer of interior cells. It says I should then adjust the velocities perpendicular to the outflow boundaries by the ratio of total velocities per cell summed across the inflow divided by the total perpendicular-to-outflow velocities per cell summed across the outer-most layer of interior cells adjacent to the outflow boundaries.

That is as much info as Versteeg gives. I'm wondering how this all fits into the SIMPLE algorithm... Once these velocities have been extrapolated for for the outflow cells should I treat them as dirichlet boundary cells for velocity? I am really kinda in the dark here... Where in the SIMPLE algorithm do I extrapolate these outflow velocities?

Any hints would be great! Thank you!
Miz

you could reference peric's 2dc\pipe\pcol1.f code

C################################################# ############
SUBROUTINE OUTBC
C################################################# ############
C In this routine, zero-gradient condition is implemented
C at outlet and the velocity is corrected to satisfy the
C global mass conservation. In this way, one can treat the
C velocity at outlet boundary as prescribed for one SIMPLE
C step, i.e. in the pressure-corrcetion equation, the
C velocity is assumed given at all boundaries and will not
C corrected.
C-------------------------------------------------------------

this is a classic question
 

hi,

do not be upset, many people meet these kinds of people when they first start the CFD study...

as for the outflow boundary condition treatments, there are three main kinds of methods , there are some good references and you can have a search ....

according to the information you described, i think you select a good method,

in my opinion,

'there is a global correction of mass fluxes at the outlet boudary to make them satisfy the global mass conservation; before solving the pressure-correction equation'

'when this is done, one can assume in the pressure-correction that the mass fluxes are prescribed at all boundaries and therefore need not be corrected, leading to Neumann boundary conditions for pressure correction at all boundaries.'

in practice,

1. you solve discrete momentum equations

2. do the outflow velocities correction;

3. solve pressure - correction equations, still with full neumann boundary conditions;

4. update velocities and pressure , noting, at all boudaries, no correction ...

best wishes !

Thank you so much for this explanation ! I will try this for now and see how it works for me :D

I'm trying to implement it as suggested but I am unsure how to do the tri-diagonal method without a constant boundary value.

The way Versteeg has in his book is that the tri-diagonal method runs along a column of cells from cells 1 to N-1 where the values of cells 0 and N are defined boundary values. How do I do this algorithm without set boundary values like the outflow boundary?

Further I would like to ask how are the coefficients aE,aW,aN,aS calculated for cells adjacent to these outflow boundary cells?

Thanks so much!