MRST - MATLAB Reservoir Simulation Toolbox

Multi-Point Stress Approximation (MPSA)
This module implements a discretization of poro-mechanics by cell centered finite volume methods.

The module provides discretization methods for three different equations:

  1. Scalar elliptic equations (Darcy flow), using multipoint flux approximations (this is more or less equivalent to the MPFA implementation in the MRST's mpfa module, although the implementation and data structures is slightly different).
  2. Linear elasticity, using Multipoint stress approximations.
  3. Poro-mechanics, e.g., coupling terms for the combined system of 1. and 2.

Examples of usage for the three options can be found in mpfa_ex, mpsa_ex, and biot_ex, respectively, see the examples folder. The code has been tested for 2D and 3D problems on Cartesian and simplex grids, see papers below for illustrations.

Displacements (upper and middle) and pressure increase under injection in a layered formation.


This implementation uses the weakly symmetric formulation used in [3] (specifically using vertex-based averaging).

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)



  1. J. M. Nordbotten: Stable cell-center finite volume disrcetizaiton for Biot equations - SIAM J. Numer. Anal. 54(2) 942-968.
  2. J. M. Nordbotten: Convergence of a cell-centered finite volume discretization for linear elasticity - SIAM J. Numer. Anal. 53(2) 2605-2625.
  3. E. Keilegavlen, J. M. Nordbotten: Finite volume methods for elasticity with weak symmetry, arXiv:1512.01042

Published November 25, 2016