Biot theory, porous media

[Quanshu Li]

Hi all,

I am new to deal.ii.

I am wondering whether deal.ii can do a stress-flow coupling simulation by using Biot theory.

If so, how should I do it?

Furthermore, if I want to change some parameters in the flow domain based on the results in the deformation domain, or reversely, how should I do it?

Thank you.

Quanshu

[Thomas Wick]

Hi Quanshu,

On 10/25/2015 12:44 AM, Quanshu Li wrote:

Hi all,

I am new to deal.ii.

I am wondering whether deal.ii can do a stress-flow coupling simulation by using Biot theory.

Yes. This is no problem to solve coupled problems with deal.II.

If so, how should I do it?

This strongly depends on your algorithm:
if you use `monolithic' then you need to implement all equations into one system.
The starting point would be for example step-22 (replace Stokes by Darcy and add linear elasticity).

If you want to solve sequentielly, first pressure/flow and then geomechanics (elasticity)
as in `fixed-stress' then one possibility (there might be others) is to build two seperate problems
(two DoF handlers etc. ) and to couple them.

Furthermore, if I want to change some parameters in the flow domain based on the results in the deformation domain, or reversely, how should I do it?

See answer before: one famous method is `fixed-stress' iterative coupling.


Best Thomas

Thank you.

Quanshu

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[Uwe Köcher]

Hej Quanshu,

I'm currently working on the problem. This extends my research I've done in the last couple years

regarding in solving elasticity (and linear-elastic wave) problems and the diffusion equation separately.

The note given by Thomas are very correct and outline the current research on the problem, but

my approach will solve the problem in one system.

Firstly, good starting points are (for the "flow problem")

- step 20 (stationary diffusion problem with RT-DGQ)

- step 26 (heat equation)

combining both together leads to the well-known instationary diffusion equation, studied and implemented

further (for esp. higher-order time discretisations) in my thesis given here:

http://koecher.cc/uk/uk/papers.php

A reference code for a distributed-parallel solver of a special lower-order in time cG(1) together with the

outlined MFEM approach for the instationary diffusion equation can be found here:

  https://github.com/koecher/meat

Regarding the applied space-time discretisation, to documentation is given mostly by my thesis.

Secondly, you must solve the geomechanical problem, which is at least solving the

(quasi-static) elasticity problem. But this is a coupled-problem! cf. the current literature!

In the so-called "fully-coupled" (monolithic) approaches, you need to solve the complete system,

having at least the displacement and the pressure as independent variables together.

Since deal.II does not have to opportunity of solving finite-volume problems, you also need to

add the flux variable of the RT x DGQ approach of step-20 in the sense of step-26 (or meat),

to keep locally the mass conservation.

I prefer to research on a fully DoF system for the displacement, flux and pressure, since this

is easier in my point of view. (Having potentially different triangulations & boundary descriptions

are knocking to my head! Interpolations of different solutions also...)

The first approach of mine in solving the quasi-static Biot's equations will be on the fixed-stress

approach, since I think I have useful iterative solvers for both problems, but the time will show if they are

really useful.

Unfortunately, due to some research restrictions, the newly develop code of mine for the Biot's equations

will not be available soonly under a public release.

Anyhow, if you are willing to share ideas and cooperating in a shared research on the problem

you may contact me per email on koe...@hsu-hamburg.de directly.

Best

  Uwe

[Quanshu Li]

Thank you Thomas.

I feel like I want to start with thermal (step 26) and elasticity (step 8), to make a thermoelastic model first, then modify it into a poroelastic model. 

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