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 jav1984 August 19, 2009 12:18

problems with simple algorithm(by patankar)

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)?
2-in coefficient aN there is Fb=rho*Vb,my outcome(guess)is:(vb 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?
3-how should I apply boundary condition for staggered grid?(for example
at enterance we know velocity for main point)
4-if 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 )

thanks

 francisco.angel November 3, 2017 21:57

Quote:
 Originally Posted by jav1984 (Post 226857) 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)?
Yes, that would be an approach, but the simple average approximation is not too good, due to that you use schemes like upwind for example, that Patankar discusses in a previous chapter.

[QUOTE=jav1984;226857]
2-in coefficient aN there is Fb=rho*Vb,my outcome(guess)is:(vb 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]
3-how 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' i-1)d to generate an equation for the pressure correction values adyacent to the boundary.

[QUOTE=jav1984;226857]
4-if 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.