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How to implement equation of mixture fraction and variance of mixture fraction? 

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April 23, 2012, 05:13 
How to implement equation of mixture fraction and variance of mixture fraction?

#1 
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Tobias Holzmann
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Hi all,
I am using OF for two years now and wanna get deeper into the code and wanna make a new solver using an old one and transform the steady equations into the time dependent equations. Okay my problem for now is, that I am not sure if I interpret the *Eqn.H files correct. I read a few threats here in the forum which helped me a lot but now I need your help. I added an attachment with my problem. There you can see my solving equations. I just wanna have a look at the differential equations but I think that I transformed them not right, or? Further more I do not know what "Sp" means. Thx in advance. Regards Tobi 

April 23, 2012, 09:17 

#2 
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Anton Kidess
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fvm::Sp denotes an implicit source term. You can ignore it when translating code into equations, it's purely related to numerics.
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April 23, 2012, 10:32 

#3 
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Niklas Nordin
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suppose you want to solve this equation
dU/dt = A + BU implemented like fvm:ddt(U) == A + B*U using euler scheme, this results in U^n  U^{n1} = dt*A + dt*B*U^{n1} => U^n = dt*A + (dt*B + 1)*U_{n1} implemented like this fvm::ddt(U) == A + fvm::Sp(B, U) this results in U^n  U^{n1} = dt*A + dt*B*U^n => (1  dt*B)*U^n = dt*A + U^{n1} so the first implementation is explicit treatment of the B*U term, while the other is implicit treatment. Hope this makes it clearer This also makes it possible to do some 'cheating' of large explicit sourceterms by linearizing them again... dU/dt = A + B*U = A*1 + B*U + A*(U/U) + B*U which can be implemented like fvm::ddt(U) = fvm:Sp(A/U, U) + B*U which in turn is treated numerically like U^{n}  U ^{n1} = dt*(A*U^n / U^{n1} + B*U^{n1}) so you see now that A is no longer multiplied by 1, but by something else, which for the converged solution hopefully is 1 and have a stabilizing effect on the solver. 

April 24, 2012, 05:24 

#4 
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Tobias Holzmann
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Hi nicklas,
thanks for your good explanation! I used your statement and generated a file (attachment). can you have a look at the file? I am interessted in the last line I added. Thats my understanding of your post. The second file is a transformation from openfoam equation code into scalar equation. Is that correct? Its a while ago that I used grad, div and laplacian. thx in advance tobi 

December 19, 2019, 00:55 
fvc and Sp

#6 
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Deepak J
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Sorry for bumping into this old thread. I am a beginner in CFD and OpenFoam and i am trying to implement mixture fraction and mixture fraction variance equations.
Can anyone help me understand why we need fvc apart from the fact that it is an explicit equation? I have seen that for calculating gradient or with source terms (Sp), it is always accompanied with fvc. Why is it so? Also what is happening when the Sp term is introduced. Thanks in advance Last edited by dj18deepak; December 19, 2019 at 10:28. 

December 26, 2019, 06:41 

#7 
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Deepak J
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Hi all,
I am trying to implement mixture fraction and mixture fraction variance conserved transport equations to simulate a simple propane non reacting jet flame. The simulation is well and running with slight amount of deviations from experimental data while using small value of grading in the x and y directions (8 and 8 resp). The problem i am facing is that with higher values of grading (12 in xdirection and 15 in ydirection), even though the velocity, temperature and all profiles are evolving, the mixture fraction and mixture fraction variance variables are having very low values of the order of 10^70 (for mixture fraction). What might be the possible causes of the error. Kindly help me. I am a beginner. Code fvScalarMatrix mifEqn ( fvm::ddt(rho, mif) + fvm::div(phi, mif)  fvm::laplacian(turbulence>mut()/0.7, mif) ); mifEqn.relax(); mifEqn.solve(); fvScalarMatrix mifvarEqn ( fvm::ddt(rho, mifvar) + fvm::div(phi, mifvar)  fvm::laplacian(turbulence>mut()/0.7, mifvar)  2.86*turbulence>mut()*magSqr(fvc::grad(mif)) + 2*rho*(turbulence>epsilon()/(turbulence>k()+k_small))*mifvar ); mifvarEqn.relax(); mifvarEqn.solve(mesh.solver("mifvar")); fvSchemes dictionary ddtSchemes { default Euler; } gradSchemes { default cellLimited Gauss linear 1; } divSchemes { default none; div(phi,U) Gauss limitedLinearV 1; div(phiU,p) Gauss limitedLinear 1; div(phi,epsilon) Gauss limitedLinear 1; div(phi,K) Gauss limitedLinear 1; div(phi,k) Gauss limitedLinear 1; div(phi,H) Gauss limitedLinear 1; div(phi,Yi_h) Gauss limitedLinear 1; div(phi,mif) Gauss limitedLinear 1; div(phi,mifvar) Gauss limitedLinear 1; div(((rho*nuEff)*dev2(T(grad(U))))) Gauss linear; } laplacianSchemes { default Gauss linear corrected; } interpolationSchemes { default linear; } fluxRequired { p; } fvSolution dictionary solvers { "rho.*" { solver diagonal; } p { solver PCG; preconditioner DIC; tolerance 1e6; relTol 0.1; } pFinal { $p; tolerance 1e6; relTol 0.1; } "(Uhkepsilon)" { solver PBiCGStab; preconditioner DILU; tolerance 1e6; relTol 0.1; } "(Uhkepsilonmif)Final" { $U; relTol 0.1; } "(mifmifvar)" { solver PBiCG; preconditioner DILU; tolerance 1e07; relTol 0.; } Yi { $hFinal; } } relaxationFactors { fields { p 0.4; rho 0.5; } equations { U 0.4; k 0.5; epsilon 0.5; //H 0.5; mif 0.5; mifvar 0.2; } } PIMPLE { momentumPredictor no; nOuterCorrectors 1; nCorrectors 2; nNonOrthogonalCorrectors 0; } Kindly note: mif is mixture fraction and mifvar is mixture fraction variance Thanks and regards Deepak J 

December 26, 2019, 10:47 

#9 
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Deepak J
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Hi Tobi,
Thanks for the reply. Will definitely check the same. Thanks and regards Deepak 

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