discretizing void fraction transport equation
I am having a really hard time for discretizing the transport equation for void fraction in OpenFOAM. The equation is as following:
and J is a function of alpha. I appreciate it if you help me to write it in OpenFOAM format.
What did you try up until now? Where are you stuck exactly? Have a look at $FOAM_SOLVERS/basic/scalarTransportFoam
Thanks for your response. I describe for you the whole story. The equation that I have put in my first post d(alpha)/dt+U.Δ(alpha)=Δ.J is the governing equation for the transport of particles in a suspension due to normal stresses (Δ is the divergence operator here). The normal stress is the J term in the right hand side.
The process that I have done to reach the J equation is:
Here, etha0 and ethaN are viscosity, gamma is the magnitude of the strain rate and Q is a tensor. In OpenFOAM format it is :
volTensorField SP = -1.0*etha0*sqrt(magSqr(symm(fvc::grad(U))))*ethan*Q
To find J, i have done:
volVectorField divSP = fvc::div(SP);
volVectorField J= (-2.0*aa*aa/9.0/etha0)*fphi*divSP;
As you see J is a vector which is calculated based on a divergence process on a tensor field. I do not know if the divergence calculation is correct or not. Having the J vector field, I have written the transport equation of void fraction:
+ fvm::div(phic, alpha, scheme)
As you see another divergence is applied to J. So now I do not know
first: if the two divergence process that I have done are written correctly in OpenFOAM format or not,
second: is my transport equation which is the discretized form of the equation presented in my first post correct or not?
I appreciate if any body can help me.
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