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Energy equation in rhoCentralFoam (revisited) 

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May 31, 2016, 08:54 
Energy equation in rhoCentralFoam (revisited)

#1 
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Join Date: Sep 2015
Location: Singapore
Posts: 102
Rep Power: 9 
Hello everyone,
I am a bit confused about the energy equation implementation in rhoCentralFoam. Particularly, why does the viscous term 'sigmaDotU' appear in the (supposedly) Euler equation? Code:
surfaceScalarField sigmaDotU ( "sigmaDotU", ( fvc::interpolate(muEff)*mesh.magSf()*fvc::snGrad(U) + (mesh.Sf() & fvc::interpolate(tauMC)) ) & (a_pos*U_pos + a_neg*U_neg) ); solve ( fvm::ddt(rhoE) + fvc::div(phiEp)  fvc::div(sigmaDotU) );  Kuragnov flux scheme is derived for strictly hyperbolic equations which are the Euler equations in this case  'a_pos' and 'a_neg' are calculated using the eigenvalues of Euler equations and hence, the flux scheme should not be applied to the viscous term 'sigmaDotU' However, when I modified the solver by removing the viscous term from this equation and introducing it in the internal energy/enthalpy equation later, the results were not as good as the current solver (more diffusion, shocks were not sharp, unexpected flow separation). So, I am guessing that whatever the current solver is doing is correct but I can't seem to understand why. There are two other threads that I managed to find asking the exact question but both remain open: 1. Viscous terms in rhoCentralFoam 2. energy equation in rhoCentralFoam I am hoping that someone would point in the right direction. Thanks to all! 

May 2, 2018, 01:10 

#3 
Senior Member
Join Date: Sep 2015
Location: Singapore
Posts: 102
Rep Power: 9 
Hi Mary,
I am afraid that I do not have a complete answer but let me give my opinion and, hopefully, someone will confirm/correct it. The first thing to note is that if the case is inviscid, then muEff=0. So, the term 'sigmaDotU' does not have any effect on the results for inviscid flows. The second thing to note is that the energy equation is solved using a predictor step for rhoE: Code:
fvm::ddt(rhoE) + fvc::div(phiEp)  fvc::div(sigmaDotU) Code:
fvm::ddt(rho, e)  fvc::ddt(rho, e)  fvm::laplacian(turbulence>alphaEff(), e) a_pos and a_neg are essentially interpolation factors to compute an intermediate state at each face based on the pos and neg values obtained by TVD reconstruction. So, (a_pos*U_pos + a_neg*U_neg) can be seen as some intermediate velocity Ustar. This intermediate velocity is used in the calculation of 'sigmaDotU'. Code:
surfaceScalarField sigmaDotU ( "sigmaDotU", ( fvc::interpolate(muEff)*mesh.magSf()*fvc::snGrad(U) + (mesh.Sf() & fvc::interpolate(tauMC)) ) & (a_pos*U_pos + a_neg*U_neg) ); Cheers, USV 

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energy equation, openfoam, rhocentrafoam 
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