Modifying the field matrix for BCs

celestial · April 29, 2022, 10:44

Hi

After more than 3 years, I still do not know how to solve for c in a domain with

solve
(
fvm::ddt(c) + fvm::div(V,c) - fvm::laplacian(D, c)
) ;

when the boundary condition

dc/dn = Kc + F

has also to be taken into consideration

(d/dn means derivative in the direction of the normal to the boundary and variables K, F can of course vary along the boundary and variables V and D can vary throughout the domain)

Regards to all

Tobermory · April 30, 2022, 05:37

I'm not surprised - that's a fairly unsual boundary condition. Have you tried a codedMixed boundary type? Seems to me that that would be a great place to start, although I have no idea how stable the boundary condition will be.

dlahaye · April 30, 2022, 06:30

This is a Robin boundary condition implememented in e.g.

https://www.openfoam.com/documentati...alarField.html

celestial · May 3, 2022, 11:58

I had already looked into a tutorial on BCs by Guerrero 3 years ago which discussed codedFixed and codedMixed at length but it had nothing to do with

dc/dn = Kc + F

On the other hand, I now realize that if I discretize

dc/dn = Kc + F

then, I can cast it into the form of a Robin boundary equation !

So that will probably solve the problem. Great thanks to you two for replying.

However my biggest problem is actually much worse: it involves solving a Poisson equation for the potential over two adjacent media of different dielectric constants where a charge can in addition build up on the interface between the two media. I wonder if I will have to become familiar with block-coupled solvers as discussed in the workshop by Ivor Clifford

April 29, 2022, 10:44	Modifying the field matrix for BCs	#1
celestial Member Join Date: Mar 2019 Posts: 86 Rep Power: 7	Hi After more than 3 years, I still do not know how to solve for c in a domain with solve ( fvm::ddt(c) + fvm::div(V,c) - fvm::laplacian(D, c) ) ; when the boundary condition dc/dn = Kc + F has also to be taken into consideration (d/dn means derivative in the direction of the normal to the boundary and variables K, F can of course vary along the boundary and variables V and D can vary throughout the domain) Regards to all

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April 30, 2022, 05:37		#2
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 670 Rep Power: 14	I'm not surprised - that's a fairly unsual boundary condition. Have you tried a codedMixed boundary type? Seems to me that that would be a great place to start, although I have no idea how stable the boundary condition will be.

April 30, 2022, 06:30		#3
dlahaye Senior Member Domenico Lahaye Join Date: Dec 2013 Posts: 736 Blog Entries: 1 Rep Power: 17	This is a Robin boundary condition implememented in e.g. https://www.openfoam.com/documentati...alarField.html

May 3, 2022, 11:58		#4
celestial Member Join Date: Mar 2019 Posts: 86 Rep Power: 7	I had already looked into a tutorial on BCs by Guerrero 3 years ago which discussed codedFixed and codedMixed at length but it had nothing to do with dc/dn = Kc + F On the other hand, I now realize that if I discretize dc/dn = Kc + F then, I can cast it into the form of a Robin boundary equation ! So that will probably solve the problem. Great thanks to you two for replying. However my biggest problem is actually much worse: it involves solving a Poisson equation for the potential over two adjacent media of different dielectric constants where a charge can in addition build up on the interface between the two media. I wonder if I will have to become familiar with block-coupled solvers as discussed in the workshop by Ivor Clifford