Arguments of implicit divergence-term

chubb87 · October 30, 2014, 12:11

Hi all,

I need to implement an equation (which approximates the Jacobian in a Newton method) containing the following terms:

Code:

fvm::ddt(rho) + 1/eps*(fvc::div(phi_old) - fvm::div(phi_old+eps*(phi-phi_old),rho)

But the last fvm-term is a problem. I want to solve that term for rho. That means the specified flux "phi_old + eps*(phi-phi_old)" will be multiplied by rho. But only the second part (current phi) contains (the current) rho.

I already tried something like

Code:

fvm::ddt(rho) + 1/eps*(fvc::div(phi_old) - fvm::div(phi_old/phi_rho+eps*(phiU-phi_old/phi_rho)),rho)

but that does not seem to work.
Any ideas? Do I have to approximate the second divergence term?

Thanks in advance.

chriss85 · October 31, 2014, 07:19

The variable which is solved for always appears in the second argument of the fvm operators.
You should maybe think about using the linearity of the divergence operator to separate the terms, and use an explicit divergence (fvc::div) for phi_old ?

chubb87 · November 1, 2014, 08:33

Okay, that's what I tried as well. I was unsure if this is valid though, since this would lead to cancellation of most terms (even epsilon drops out!) and thus would not make sense.
If I use linearity but keep those terms the calculation might still be valid (I guess). It does not work as expected yet (density increases), but the problem may be somewhere else.

October 30, 2014, 12:11	Arguments of implicit divergence-term	#1
chubb87 New Member chubb87 Join Date: May 2011 Posts: 21 Rep Power: 14	Hi all, I need to implement an equation (which approximates the Jacobian in a Newton method) containing the following terms: Code: fvm::ddt(rho) + 1/eps(fvc::div(phi_old) - fvm::div(phi_old+eps(phi-phi_old),rho) But the last fvm-term is a problem. I want to solve that term for rho. That means the specified flux "phi_old + eps(phi-phi_old)" will be multiplied by rho. But only the second part (current phi) contains (the current) rho. I already tried something like Code: fvm::ddt(rho) + 1/eps(fvc::div(phi_old) - fvm::div(phi_old/phi_rho+eps*(phiU-phi_old/phi_rho)),rho) but that does not seem to work. Any ideas? Do I have to approximate the second divergence term? Thanks in advance.

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October 31, 2014, 07:19		#2
chriss85 Senior Member Join Date: Oct 2013 Posts: 397 Rep Power: 18	The variable which is solved for always appears in the second argument of the fvm operators. You should maybe think about using the linearity of the divergence operator to separate the terms, and use an explicit divergence (fvc::div) for phi_old ?

November 1, 2014, 08:33		#3
chubb87 New Member chubb87 Join Date: May 2011 Posts: 21 Rep Power: 14	Okay, that's what I tried as well. I was unsure if this is valid though, since this would lead to cancellation of most terms (even epsilon drops out!) and thus would not make sense. If I use linearity but keep those terms the calculation might still be valid (I guess). It does not work as expected yet (density increases), but the problem may be somewhere else.