Generalising 1D-equation

Dharoc · April 8, 2018, 06:17

Hello,

I am creating a custom solver that is based around the following equation:

$a v (\frac{\partial v}{\partial z}) + v/b = - \frac{\partial y}{\partial z} + c$

where a, b and c are constants. v and y are both scalars.
y is known and v is the variable I'm solving for.

My approach is to implement a generic solution (3D) and introduce the one-dimensional condition by defining all side patches as empty. As such I am trying to implement the following equation in my solver:

$a (V \cdot \nabla) V + V/b = - \nabla y + C$

Where V and C instead are vectors.

However I am struggling to do so.

Is this the recommended/correct approach to my problem?
How would I implement equation 2 in my Solver? Are there any resources describing this part of OpenFOAM-development?

Dharoc · April 21, 2018, 13:52

I've made an attempt to implement the equation

$a (V \cdot \nabla) V + V/b = - \nabla y + C$

based on icoFoam:

Code:

surfaceScalarField phi = fvc::interpolate(V) & mesh.Sf();
fvVectorMatrix VEqn
(
    a * fvm::div(phi, V)
    + fvm::Sp((1/b), V)
);
solve(VEqn == -fvc::grad(y) + C);

where V and C are volVectorField.

The solution produced are however non-physical. Is there something I've overlooked or misunderstood?

Thanks in advance,
Dharoc

babakflame · April 22, 2018, 15:49

Hello,

The main thing is that if you create an almost 1 dimensional grid with suitable boundary conditions. You can still run OpenFOAM codes in 1 dimensional. I mean there is no 1 dimensional coding approach.

The second thing that I wanted to mention and you might probably find it helpful is trying to adapt OpenFOAM momentum (UEqn.H) to your case by adding and excluding terms. Easily, you can make it compatible with your case.

Dharoc · April 26, 2018, 06:52

Hello babakflame, thank you for your reply. That is exactly how I've approached the problem so far, so it's nice to know I've taken the right approach.

I've also identified the issue I described in the second post i this thread. The problem was not my implementation of the equation, but rather with the boundary conditions for the y-field. So far now are things looking promising.

Dharoc · May 6, 2018, 14:15

Hello again!

I'm stuck with the same problem, albeit with another equation. I'm trying to implement:

$\nabla \cdot (a*V + \nabla a - \nabla b ) = 0$

where V is a volVectorField and a and b are volScalarFields.

Does anyone have any pointers?

Dharoc · May 12, 2018, 08:58

I've not made any progress. Just to clarify, I'm trying to implement the following one-dimensional equation, where a is the unknown I'm solvning for:

$\frac{\partial }{\partial z}(a * v + \frac{\partial a}{\partial z}- \frac{\partial b}{\partial z}=0$

By generalising it to the following three-dimensional equation and using empty boundary conditions to make it one-dimensional.

$\nabla \cdot (a*V + \nabla a - \nabla b ) = 0$

Is this not the correct approach in this case?

April 8, 2018, 06:17	Generalising 1D-equation	#1
Dharoc New Member Albin Lindskog Join Date: Dec 2017 Posts: 8 Rep Power: 8	Hello, I am creating a custom solver that is based around the following equation: $a v (\frac{\partial v}{\partial z}) + v/b = - \frac{\partial y}{\partial z} + c$ where a, b and c are constants. v and y are both scalars. y is known and v is the variable I'm solving for. My approach is to implement a generic solution (3D) and introduce the one-dimensional condition by defining all side patches as empty. As such I am trying to implement the following equation in my solver: $a (V \cdot \nabla) V + V/b = - \nabla y + C$ Where V and C instead are vectors. However I am struggling to do so. Is this the recommended/correct approach to my problem? How would I implement equation 2 in my Solver? Are there any resources describing this part of OpenFOAM-development?

April 21, 2018, 13:52		#2
Dharoc New Member Albin Lindskog Join Date: Dec 2017 Posts: 8 Rep Power: 8	I've made an attempt to implement the equation $a (V \cdot \nabla) V + V/b = - \nabla y + C$ based on icoFoam: Code: surfaceScalarField phi = fvc::interpolate(V) & mesh.Sf(); fvVectorMatrix VEqn ( a * fvm::div(phi, V) + fvm::Sp((1/b), V) ); solve(VEqn == -fvc::grad(y) + C); where V and C are volVectorField. The solution produced are however non-physical. Is there something I've overlooked or misunderstood? Thanks in advance, Dharoc

May 6, 2018, 14:15		#5
Dharoc New Member Albin Lindskog Join Date: Dec 2017 Posts: 8 Rep Power: 8	Hello again! I'm stuck with the same problem, albeit with another equation. I'm trying to implement: $\nabla \cdot (aV + \nabla a - \nabla b ) = 0$ where V is a volVectorField and a and b are volScalarFields. Does anyone have any pointers? Last edited by Dharoc; May 12, 2018 at 08:24.*

May 12, 2018, 08:58		#6
Dharoc New Member Albin Lindskog Join Date: Dec 2017 Posts: 8 Rep Power: 8	I've not made any progress. Just to clarify, I'm trying to implement the following one-dimensional equation, where a is the unknown I'm solvning for: $\frac{\partial }{\partial z}(a * v + \frac{\partial a}{\partial z}- \frac{\partial b}{\partial z}=0$ By generalising it to the following three-dimensional equation and using empty boundary conditions to make it one-dimensional. $\nabla \cdot (aV + \nabla a - \nabla b ) = 0$ Is this not the correct approach in this case? Last edited by Dharoc; May 12, 2018 at 10:56.*

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April 22, 2018, 15:49		#3
babakflame Senior Member Bobby Join Date: Oct 2012 Location: Michigan Posts: 454 Rep Power: 15	Hello, The main thing is that if you create an almost 1 dimensional grid with suitable boundary conditions. You can still run OpenFOAM codes in 1 dimensional. I mean there is no 1 dimensional coding approach. The second thing that I wanted to mention and you might probably find it helpful is trying to adapt OpenFOAM momentum (UEqn.H) to your case by adding and excluding terms. Easily, you can make it compatible with your case.

April 26, 2018, 06:52		#4
Dharoc New Member Albin Lindskog Join Date: Dec 2017 Posts: 8 Rep Power: 8	Hello babakflame, thank you for your reply. That is exactly how I've approached the problem so far, so it's nice to know I've taken the right approach. I've also identified the issue I described in the second post i this thread. The problem was not my implementation of the equation, but rather with the boundary conditions for the y-field. So far now are things looking promising.