How to add coupled euqations with coupled exponential term in a solver

Lann · November 4, 2019, 11:09

Hi, everyone.
I am new to OpenFoam and I feel so addicted when exploring.
The problem I need to solve is an equation system with the frame as below:

fvm::laplacian(a , X) = c*exp(X-Y)
fvm::laplacian(b , Y) = -c*exp(X-Y)

where
a, b and c are constant coefficients.
X and Y are two passive scalar fields to be solved.

I have no idea how to implement it in a solver (can be laplacianFoam).
My questions are:
1. How to deal with this coupled exponential equation? Should I treat it like what pisoFoam dose?
2. How to deal with the exponential source term. Should I use fvOptions? Since the second equation has the same source as equation but with negative sign.

Any suggestions and answers are welcome. Thanks in advance!

Lann · November 5, 2019, 11:13

I don't know if I should use fvOption or just coupled loop to solve this equation.
Any idea is super welcomed.

Thanks again

Lann · November 14, 2019, 10:24

Now I am more clear about the linearization of the exponential terms.
But still stumped on the coupling equations.

November 4, 2019, 11:09	How to add coupled euqations with coupled exponential term in a solver	#1
Lann New Member Xun Lan Join Date: Oct 2019 Posts: 21 Rep Power: 7	Hi, everyone. I am new to OpenFoam and I feel so addicted when exploring. The problem I need to solve is an equation system with the frame as below: fvm::laplacian(a , X) = cexp(X-Y) fvm::laplacian(b , Y) = -cexp(X-Y) where a, b and c are constant coefficients. X and Y are two passive scalar fields to be solved. I have no idea how to implement it in a solver (can be laplacianFoam). My questions are: 1. How to deal with this coupled exponential equation? Should I treat it like what pisoFoam dose? 2. How to deal with the exponential source term. Should I use fvOptions? Since the second equation has the same source as equation but with negative sign. Any suggestions and answers are welcome. Thanks in advance! Last edited by Lann; November 14, 2019 at 10:29.

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November 5, 2019, 11:13		#2
Lann New Member Xun Lan Join Date: Oct 2019 Posts: 21 Rep Power: 7	I don't know if I should use fvOption or just coupled loop to solve this equation. Any idea is super welcomed. Thanks again

November 14, 2019, 10:24		#3
Lann New Member Xun Lan Join Date: Oct 2019 Posts: 21 Rep Power: 7	Now I am more clear about the linearization of the exponential terms. But still stumped on the coupling equations.