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I'm looking to solve the Richards' equation. This models water flow in porous media and is a nonlinear, possibly degenerative, parabolic differential equation that takes the form

$\partial_t \Theta(\psi) - \nabla \cdot (K(\Theta)\nabla(\psi+z))=0$

where $\psi$ is pressure head, $\Theta$ is the water content, $K$ is the conductivity and $z$ is a vertical height. Pressure is the primary unknown.

This is a 'famous' equation and further information can be found on scholar [1,2].

I would like to calculate a 3D solution, and I am looking into possible solvers.

  1. Is Clawpack applicable to this type of equation?

  2. Is it possible to use Clawpack with an 3D unstructured mesh such as those that are generated from CGAL (currently I have a surface mesh defined using CGAL).

Any insight is much appreciated.

[1] http://www.sciencedirect.com/science/article/pii/S037704270301001X

[2]http://onlinelibrary.wiley.com/doi/10.1029/WR026i007p01483/abstract

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No.

Clawpack is designed to solve systems of first-order hyperbolic PDEs on structured (logically quadrilateral or hexahedral) meshes. It is possible to incorporate parabolic terms, but the real advantage of using Clawpack is its capability for dealing with nonlinear hyperbolic terms that can lead to discontinuities in the solution.

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  • $\begingroup$ Ah ok. Thanks for the information. Also sorry about the extra tag, fat fingered it. $\endgroup$ – Chris Dec 9 '14 at 15:09

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