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August 19, 2009, 12:18 
problems with simple algorithm(by patankar)

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E jav
Join Date: Aug 2009
Posts: 3
Rep Power: 10 
I have some questions about SiMPLE algorithm based on Patankar's book.
on page 123 step 2 of algorithm:solving u* and v*(for 2D problem).to writing a fortran code for this algorithm I have a confusing problem.if we note at eq. 6.8 & 6.9 the nodes that are involved in two equations are not the same!(because the first eq is written for sataggerd grid at x direction,the second is at y directin) for example in the coefficient aE(for solving ue)there is FE=rho*uE(u*E) we konw that UE is velocity in main point that is not calculated in this eq.shoud I interpolate UE=0.5*(ue+uc)? 2in coefficient aN there is Fb=rho*Vb,my outcome(guess)isvb is unknwon which should be guessed at the first and after solving u*,we should enter the coefficient of anb based on calculated v*,then use these V* adgain for coeficeint u* and repete this to converge).is my guess(the sentence in pranteses) true? if it is true we know that the nodes that their velocity entered in these two eq are not the same! what shoud I do? 3how should I apply boundary condition for staggered grid?(for example at enterance we know velocity for main point) 4if we have a solid in our domain shoud we define gamma as an array or as a parameter? (we should attribute gamma=infinity for solid ) please help me thanks 

November 3, 2017, 21:57 

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Francisco Angel
Join Date: Dec 2012
Posts: 21
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Quote:
[QUOTE=jav1984;226857] 2in coefficient aN there is Fb=rho*Vb,my outcome(guess)isvb is unknwon which should be guessed at the first and after solving u*,we should enter the coefficient of anb based on calculated v*,then use these V* adgain for coeficeint u* and repete this to converge).is my guess(the sentence in pranteses) true? if it is true we know that the nodes that their velocity entered in these two eq are not the same! what shoud I do? [QUOTE] I didn't understand you quite well, but basically you have (rho*vn)*vn the vn inside the parenthesis is the guessed value that you ends up in the aN coefficient, the second vn is the unknown, the SIMPLE algorithm is an iterative procedure so you keep updating velocities and consequently a's (coefficients). Remember that all flow terms could require a scheme like SIMPLE. [QUOTE=jav1984;226857] 3how should I apply boundary condition for staggered grid?(for example at entrance we know velocity for main point) [QUOTE] It depends on the boundary condition, if you know the value of velocity you just use it like always in the momentum equations, in the continuity equation you use this correct value instead of u* + ( p'  p' i1)d to generate an equation for the pressure correction values adyacent to the boundary. [QUOTE=jav1984;226857] 4if we have a solid in our domain shoud we define gamma as an array or as a parameter? (we should attribute gamma=infinity for solid ) It's not so easy to to treat an inmersed solid, you can approximate the solid boundary to match some grid lines and apply the v=0 (no slip) boundary condition at those grid lines. please help me [QUOTE] thanks 

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