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January 23, 2010, 09:46 
Problems with SIMPLE

#1 
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Fabian
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Hello, for a little project I want to implement a really easy example for the SIMPLEalgorithm with matlab (speed doesn't matter and with matlab plotting is easy). I started with an example from a book (CFD from Versteeg et al., example 6.2) and I get every value right, but the example ends before the loop of SIMPLE is really starting and I cant find my errors. So I have a few general questions about SIMPLE:
1. There are two linear equations systems to solve: one to find the u* out of the p* with the momentum equations and one to find the p' with the contnuity. Am I correct, if I say that the matrices, lets call them A and P, are the same in every inner loop? And only the solutionvector differs? 2. Is there any difference from the first time to go thru the loop to the nth (with n>=2) time besides the fact that you dont have to guess the p* because you get it from the further looprun? 3. u* is always been calculated by the momentum equation and never guessed, right? 4. If I have got a steady and incompressible flow, is there any other variable beside the velocities and the pressure I have got to calculate? Thank you for any answers 

January 24, 2010, 17:44 

#2 
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Fabian
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Ok, let me simplify it: Do I have to calculate new coefficients (e.i. a_p, a_e, a_w) in every inner loop?


January 27, 2010, 13:03 
simple

#3  
Senior Member

Hi,
Let me try to find solutions to your problem. Quote:
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CFDtoy 

January 28, 2010, 15:21 

#4 
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Fabian
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Thank you for your answers, they helped me a lot. Yet another question: In almost every book about CFD you can read: You need SIMPLE to compute incompressible flows, because you dont have rho in the continuityeq, so you cant use p=rho*R*T for calculating p and the velocities are the dominant variables in the momentum eq, so you dont have got a eq for p.
But whats the problem? I have got 4 eq (3D): 3 momentum + conti and 4 variables (3 velocities + pressure), so i can solve the problem explicit or implicit... What's about this "dominant variables", why couldnt I compute one velocitie from the continuity? 

January 28, 2010, 16:57 

#5 
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Because the continuity equations acts like a boundary condition, and not like a real separate equation for velocities. In incompressible flows.
If you don't like the idea of using a pressure equation, you can use the full NS equations preconditioned for low speed flows, just like for a compressible flow. Or Chorin's method where you use a pseudodensity equation instead of a continuity without the density like you have for the incompressible case. 

January 28, 2010, 18:00 
Eqns

#6  
Senior Member

Hi there, (gautcho)
Let me try to get your questions straight. You have 4 eq (3 momentum + continuity) and 4 variablbes (3 vel and pressure)? Ok lets see. for incompressible part: (btw are you looking at incomp or comp?) continuity => rho*Area*vel = constant (without src) ok  eqn 1 Momentum eqns: u1 = dP/dx + ..  eqn 2 u2 = dP/dy + ..  eqn 3 u3 = dP/dz + ...  eqn 4 Now, you want to solve u from u1,u2,u3 right? ok..so what is your "good value" for p such that your u1, u2, u3 are good ? By saying good, when you solve u1,u2,u3 ...it should automatically give you Ai*ui = constnat (rho constant and no src) eqn 1 (Ai is the area vector) Can you make sure that del (dot) (A1u1+A2u2+A3u3 ) = 0 (divergence of this vector is zero) ? May be not. Somehow, your del (dot) (ui) gives some "extra value" on right side ..for the guessed P...so you correct p and try solving u1,u2,u3 again ...and check if del . aiui = 0 (or close to) ...this is basically SIMPLE method Basically, since you are guessing the initial p to get u and that divergence is not maintained..you correct it. ..this is an iterative process.. /CFDtoy Quote:
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CFDtoy 

January 29, 2010, 03:56 

#7 
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Fabian
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@DoHander: It have to use the SIMPLEalgorithm because it's the theme of my project. The question is: Why do I have to use it, if I want to compute incompressible flows. Maybe your first sentence give the right answer, but I'm not very experienced in CFD and FD and so it's a little bit too inexact for me. Why acts the continuity only like a BC? For me it's an equation in a system of equations and after discretisation I can solve this system...
@CFDtoy: I understand the method of SIMPLE, but it's the same question here: Why not solving it directly? And I'm looking at the incompressible part... 

February 2, 2010, 09:10 

#8 
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Simon Hubbard
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HI gautcho,
For incompressible flow you want to calculate four quantities for 3D flow  the three velocity components (u,v,w) and the pressure (p). You therefore need four equations  you've got the 3 NS equations, one for the velocity in each direction and you need another one to calculate the pressure. A common approach is to reformulate the continuity eqn into a correction to a guessed pressure field. This is what SIMPLE is. There is no point using continuity to get a velocity, that is what the NS eqns give you. 

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