# Problems with pressure equation in SIMPLER algorithm

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June 17, 2013, 09:24
Problems with pressure equation in SIMPLER algorithm
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Hi,

short version of the questions:
• Can anybody give me a tip where to find the bug for the wrong solution of the pressure equation (poisson pressure equation withing the SIMPLER algorithm)? Used Neumann conditions at the farfield and simply broke the link at the wall (a_s = 0).
• Do I need correction terms (coordinate transformation) when using curvilinear coordinates in the finite volume method?
Thanks!

And here the "long" story:

Concerning CFD I am a real newbie. Within my research activities I want to investigate the applicability of a circulation control concept on aircraft design. The objective is to obtain trends and sensibilities of geometrical parameters and blowing rates at the trailing edge of an airfoil. As it is used for preliminary design activities, stability is more important than accuracy.

Therefore I wanted to set up a "simple" 2D-CFD code (incompressible in the first approach). As common turbulence models in commercial CFD-codes seem to have problems to predict the "Coanda flow" at the round trailing edge, I plan to introduce an empirical zero equation model that has already proven its applicability. At the end the comuter cluster at our university shall be used in order to evaluate thousands of geometrical variations and to explore the design space for aircraft design a bit.

I followed the finite volume approach and based the development of my CFD-tool on the introductory explanations of Versteeg and Malalasekera (Title: An Introduction to Computational Fluid Dynamics). As I plan to initialise the velocity field by an approximate solution coming from potential theory, I started to implement the SIMPLER algorithm for steady flows. I read that a "good" velocity guess is not completely destroyed inside this algorithm. I applied the hybrid discretisation scheme (upwind & central).

Moreover I chose a staggered O-grid because I thought that it would be most suitable for what is happening at the trailing edge (wall jet). The effectiveness of the concept highly depends on the separation point of the wall jet (imaginary aft stagnation point).

Unfortunately (but predictably) I got problems with the solution of the pressure equation where pseudo velocities are used to solve the pressure field. I attached an image of the static pressure where strong oscillations can be seen. I do not care about the absolute values yet. At the farfield I set Neumann conditions (with perpendicular gradients equal zero) everywhere. But the solution appears physically wrong to me. I am not familiar with the "solution path" of the algorithm (where intermediate unphysical solutions might be normal) but the high resulting pressure gradients result in a complete change of the velocity field afterwards (what is physically obvious) and diverges.

My question now is if there's somebody who could give me a tip where to continue my search for the bug? I can't exclude completely a mistake in the code but I revised the discretisations and the assembly of the matrix several times. I think that has something to do with the boundary conditions of the pressure equation. Did anybody have a similar problem?

A second question arose when I was reading about non-uniform finite volume grids. I read different and contradicting statements about coordinate transformations. Do I need to introduce any corrective terms when I follow the finite volume method? In my implementation the velocities are aligned with the grid lines (curvilinear).

Korbi
Attached Images
 static pressure.jpg (50.6 KB, 11 views) static pressure more detailed.jpg (45.0 KB, 10 views)

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