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June 6, 2013, 14:14 
meaning of HbyA

#1 
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Tobias Holzmann
Join Date: Oct 2010
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Hi all,
I am not clear about the variable HbyA Code:
volVectorField HbyA("HbyA", U); HbyA = rAU*UEqn().H(); In the 1.6ext version I found the same declaration: Code:
U = rUA*UEqn().h(); Thanks in advance Tobi 

June 6, 2013, 16:07 

#2 
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Cyprien
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Location: Stanford University
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Dear Toby,
As you noticed, both lines are similiar. Actually, the notation HbyA has been spread over all the solvers since the latest OF version (OF 2.2.0) for a sake of clarity. Keep in mind that for the computation of NaviersStokes equation, OF uses either PISO or SIMPLE algorithms. The semidiscretized form of the momentum is : where is the diagonal coefficients of the matrix resulting from the discretization of the momentum equation. stands for the nondiagonal coefficient (mainly composed by convective and diffusive terms) and the source terms (the source part of the transient term and other source that appear in UEqn) apart from the pressure gradient. Once this equation has been implicitly solved (the momentum predictor step), the predicted velocity does not satisfy the continuity equation. Moreover, in the previous equation, the pressure field result from the previous time step. Therefore, we are looking for (U,p) that obeys and Assembling this two equations, you can form the pressure equation: and then you reconstruct the velocity with: You clearly remark in this procedure that you use H divided by A or.. HbyA ;) PS: in OF, rAU is the notation for the diagonal coeff of the matrix Best regards, Cyp 

June 6, 2013, 16:23 

#3 
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Cyprien
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I made slides some times ago to explain the PISO loops in OpenFOAM : http://fr.scribd.com/doc/143414962/P...oninOpenFOAM
They are in French but understandable. It uses old OpenFOAM version, that means without the HbyA notation. 

July 5, 2013, 02:45 

#4 
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Dongyue Li
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July 5, 2013, 06:24 

#5 
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Tobias Holzmann
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Hi all,
as I understand from Cyp 's comment: So your last line should be: Code:
fvScalarMatrix pEqn ( xxx == fvc::div(HbyA) ); Last edited by Tobi; July 6, 2013 at 05:41. 

November 15, 2013, 16:30 

#6 
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Cyprien
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December 24, 2013, 03:41 
thx

#7  
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enzhen zhang
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Quote:


March 14, 2014, 16:26 

#8 
Member
Join Date: Feb 2012
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Dear Guys,
I'm using the 3step rungekutta scheme to solve Navier Stokes equation. There are some differences in the equations must be solved, but the main equations are same.you can see the equations in the attachment(those equations are put in a for loop, from k=1 to k=3) Also, below you can see my summarized code to solve that, but i don't know how to use coefficients(same as piso loop of icoFoam) ! I would appreciate any idea on how to change my code to something like the piso loop of icoFoam : Code:
while (runTime.loop()) { for (int i = 1 ; i<=3 ; ++i) { U = U + runTime.deltaT() * ( + 2*alpha*fvc::laplacian(nu,U)  2*alpha*fvc::grad(p)  gamma*fvc::div(phi, U)  zeta*fvc::div(phiOld2, UOld2) ); solve(alpha*runTime.deltaT()*fvm::laplacian(nu,Unew)  fvm::Sp(1.,Unew) == //(alpha*runTime.deltaT()) == (1.)*(U) + alpha*runTime.deltaT()*fvc::laplacian(nu,U) ); solve (fvm::laplacian(pPhi) == fvc::div(U)/(2.*alpha*runTime.deltaT()));// pPhi is a pseudo pressure without physical meaning U = Unew  (2.*alpha*runTime.deltaT()*fvc::grad(pPhi)); p += pPhi  alpha*runTime.deltaT()*nu*(fvc::laplacian(pPhi)); adjustPhi(phi, U, p); U.correctBoundaryConditions(); } } //alpha,gamma and zeta change in each of those 3 steps 

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