# nonlinear time dependent example

Asked by Myles English on 2013-02-27

I am trying to make a time dependent model using the pressure form of the Richards' Equation for unsaturated flow through a porous medium. It is nonlinear in the conductivity term, in which the saturated conductivity is scaled by a relative permeability function of the saturation (or pressure).

This particular model is in the horizontal plane so a vertical component of flow can be ignored and it becomes the nonlinear heat equation.

The FEniCS book has examples of nonlinear problems and time dependent problems but not both together.

Is there an existing model I can have a look at, or an example of a nonlinear coefficient in a time dependent problem?

## Question information

Language:
English Edit question
Status:
Solved
For:
DOLFIN Edit question
Assignee:
No assignee Edit question
Solved by:
Anders Logg
Solved:
2013-02-27
Last query:
2013-02-27
2013-02-27
 Anders Logg (logg) said on 2013-02-27: #1

On Wed, Feb 27, 2013 at 01:41:12PM -0000, Myles English wrote:
> New question #222964 on DOLFIN:
>
> I am trying to make a time dependent model using the pressure form of the Richards' Equation for unsaturated flow through a porous medium. It is nonlinear in the conductivity term, in which the saturated conductivity is scaled by a relative permeability function of the saturation (or pressure).
>
> This particular model is in the horizontal plane so a vertical component of flow can be ignored and it becomes the nonlinear heat equation.
>
> The FEniCS book has examples of nonlinear problems and time dependent problems but not both together.
>
> Is there an existing model I can have a look at, or an example of a nonlinear coefficient in a time dependent problem?

Have you looked at the Cahn-Hilliard demo? It solves a time-dependent
nonlinear problem.

--
Anders

 Myles English (mylesenglish) said on 2013-02-27: #2

Ah yes thanks. I looked at it before but found it too compact for my needs.
I understand it a bit better now and it has made me realise I need to think

 Myles English (mylesenglish) said on 2013-02-27: #3

Thanks Anders Logg, that solved my question.