# nonlinear time dependent example

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

- Last reply:
- 2013-02-27

Anders Logg (logg) said : | #1 |

On Wed, Feb 27, 2013 at 01:41:12PM -0000, Myles English wrote:

> New question #222964 on DOLFIN:

> https:/

>

> 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 : | #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

again about the basic equations.

Myles English (mylesenglish) said : | #3 |

Thanks Anders Logg, that solved my question.