Finite volume discretization for Biot's equations
This package implements a discretization of poro-mechanics by cell centered
finite volume methods.
The package provides discretization of three different equations:
Examples of usage for the three options can be found in mpfa_ex, mpsa_ex and biot_ex, respectively.
Further information on the methods implemented herein, in particular the discretization of elasticity and poro-mechanics, can be found in the following papers (all open access):
J. M. Nordbotten: Stable cell-center finite volume disrcetizaiton for
Biot equations - SIAM J. Numer. Anal. 54(2) 942-968.
J. M. Nordbotten: Convergence of a cell-centered finite volume discretization
for linear elasticity - SIAM J. Numer. Anal. 53(2) 2605-2625.
E. Keilegavlen, J. M. Nordbotten: Finite volume methods for elasticity with weak
symmetry - Int. J. Num. Meth. Eng, 2017, doi: 10.1002/nme.5538.
The implementation of elasticity is based on the forumlation described in the latter.
For information on the MPFA discretizations for the flow equation, see
I. Aavatsmark: An introduction to multipoint flux approximations for quadrilateral grids, Comput. Geosci. 6(3-4) 405-432.
The is compatible with the (freely available) Matlab Reservoir Simulation
Toolbox (MRST) provided by SINTEF ICT, see http://www.sintef.no/projectweb/mrst/
In particular, the grid data structure is that of MRST, and it is assumed that
MRST is in the matlab path.
The code has been tested with Matlab R2015b, and mrst-2016a.