FEniCS Project

nonlinear source term

Asked by Abbas Shirinifard

hello, I am trying to solve (transient and steady state) a diffusion equ in a 3D geometry that has multiple domains. Each domain acts as source and/or sink. The equation looks like the following:
dC/dt=D*Lap(C)+S*C/(C0+C)-Q*C/(C1+C)
where S is 1 in some domains and zero elsewhere, similarly Q is 1 in some domains and zero elsewhere (Q and S can be both 1).
Does FEniCS handle this kinds of discontinuous nonlinear source and sink terms? How much coding should I expect to implement this using FEniCs and DOLFIN?
This kinds of problems are very common in modeling transport in a growing tumor where tumor cells consume nutrients coming out of blood vessels.
comments and suggestions are appreciated!

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Johan Hake
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Best Johan Hake (johan-hake) said : 		#1

DOLFIN handles both subdomain and nonlinear pdes very well so it should
be pretty straight forward to implement.

johan

On 11/19/2012 11:55 PM, Abbas Shirinifard wrote:
> New question #214668 on FEniCS Project:
> https://answers.launchpad.net/fenics/+question/214668
>
> hello, I am trying to solve (transient and steady state) a diffusion
> equ in a 3D geometry that has multiple domains. Each domain acts as
> source and/or sink. The equation looks like the following:
> dC/dt=D*Lap(C)+S*C/(C0+C)-Q*C/(C1+C) where S is 1 in some domains and
> zero elsewhere, similarly Q is 1 in some domains and zero elsewhere
> (Q and S can be both 1). Does FEniCS handle this kinds of
> discontinuous nonlinear source and sink terms? How much coding should
> I expect to implement this using FEniCs and DOLFIN? This kinds of
> problems are very common in modeling transport in a growing tumor
> where tumor cells consume nutrients coming out of blood vessels.
> comments and suggestions are appreciated!
>

Revision history for this message
Abbas Shirinifard (abbas-shirinifard) said : 		#2

Thanks Johan Hake, that solved my question.

Revision history for this message
Abbas Shirinifard (abbas-shirinifard) said : 		#3

thanks for the answer Johan. This is a really exciting opportunity to integrate FEniCS with CompuCell3D which is an open-source framework for multi-cell modeling of tissues. CompuCell3D is implemented in C++ and uses python for scripting which is a perfect fit with DOLFIN. I have a couple of more questions which I post them separately.