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May 2, 2010, 09:59 
what's the meaning of UEqn().A()

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wangle
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I'm a new user of OpenFOAM,now I'm analyzing a solver .But I don't know what's the meaning of UEqn().A() and UEqn().H().Can you help me translate them to mathematic form.Thank you!


May 2, 2010, 10:13 

#2 
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Cedric Van Holsbeke
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May 2, 2010, 10:25 

#3 
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wangle
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Thank you for your reply.Does it mean the matrix A in equntion AU=H?But it's expressed a volScalarField，what's the connection between the matrix and the "scalar"? Thank you!


May 3, 2010, 10:21 

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Matthew J. Churchfield
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In the solver you are analyzing, the equation system to be solved begins as CU = R where C is a matrix, U is the solution vector, and R is the right hand side. The C matrix can be split into a matrix with only the diagonal elements of C, which is called A, and a matrix that has only the offdiagonal elements of C, which is called H'. In other words C = A + H'.
Therefore, the linear system becomes (A + H')U = R, which is the same as AU = R  H'U. The right hand side is simply called H, so H = R  H'U. Therefore, we know have AU = H. So take a look at the code you are analyzing, and you'll see something similar to: Code:
fvVectorMatrix UEqn ( fvm::ddt(U) // time derivative + fvm::div(phi, U) // convection + turbulence>divDevReff(U) // viscous and turbulent deviatoric stresses ==  gradPd // specified mean pressure gradient ); It is important to note, though, that there will be a piece of code that forms an fv<Type>Matrix, like the piece of code I included above. Later, there will be a piece of code that says something like Code:
solve(UEqn ==  fvc::grad(pd)  fvc::grad(rhok) * gh); For more description of this go take at look at section 2 of my description of buoyantBoussinesqPisoFoam at http://openfoamwiki.net/index.php/Bu...sinesqPisoFoam 

May 4, 2010, 03:36 
Thank you very much to help me solve the problem!

#5  
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wangle
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Quote:
Thank you very much to help me solve the problem! 

May 6, 2010, 02:23 
need help

#6  
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Quote:
After reading your description of buoyantBoussinesPisoFoam, I am still puzzled about the meaning of the red line in the following code, which is in the UEqn of twophaseEulerFoam.I can not find the corresponding mathematical expression, can you help me? Thank you! UaEqn = ( (scalar(1) + Cvm*rhob*beta/rhoa)* ( fvm::ddt(Ua) + fvm::div(phia, Ua, "div(phia,Ua)")  fvm::Sp(fvc::div(phia), Ua) )  fvm::laplacian(nuEffa, Ua) + fvc::div(Rca) + fvm::div(phiRa, Ua, "div(phia,Ua)")  fvm::Sp(fvc::div(phiRa), Ua) + (fvc::grad(alpha)/(fvc::average(alpha) + scalar(0.001)) & Rca) ==  fvm::Sp(beta/rhoa*K, Ua)  beta/rhoa*(liftCoeff  Cvm*rhob*DDtUb) 

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