# InterPore2018 New Orleans

14-17 May 2018
New Orleans
US/Central timezone

## Robust numerical simulation of poromechanics

17 May 2018, 13:45
25m
New Orleans

#### New Orleans

No preference GS 2: Computational challenges in porous media simulation

### Description

In this work we consider robust iterative methods for the effective simulations of poromechanics, which has plenty of societal relevant applications like geothermal energy, $CO_2$ sequestration or oil recovery, to name a few. We will focus on the quasi-static linear Biot model and non-linear extensions.

We start with the well-recognized fixed stress method [1, 2] and present some recent convergence results for heterogeneous media [3] and higher order space-time elements [4]. Next, we introduce a new, parrallel-in-time fixed stress scheme [5]. Further, we consider a non-linear extension of the Biot model and study different (monolithical or splitting) iterative schemes for it [6]. The linearization will be based on Newton's method or a variant of it, the L-scheme, see e.g. [7]. Finally, we move to unsaturated/saturated flow and poromechanics. Now, also the coupling flow-mechanics term is non-linear, which makes the problem even more challenging. A fixed stress type method, combined with the Newton or L-scheme will be presented. Anderson acceleration will be used. Especially, we will show the general ability of the Anderson acceleration to effectively accelerate convergence and stabilize the underlying scheme, allowing even non-contractive fixed-point iterations to converge [8]. Both rigorous convergence results and illustrative numerical examples will be presented.

### References

1. J. Kim, H. Tchelepi, R. Juanes, Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits. Comput. Methods. Appl. Mech. Eng. (2011): 1591-1606.

2. A. Mikelic, M.F. Wheeler, Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17 (3) (2013): 455-461.

3. J. Both, M. Borregales, F.A. Radu, K. Kumar, J.M. Nordbotten, Robust fixed stress splitting for Biot's equations in heterogeneous media. Appl. Math. Letters 68 (2017): 101-108.

4. M. Bause, F. A. Radu, U. Koecher, Space-time finite element approximation of the Biot poroelasticity system with iterative coupling. Comput. Methods. Appl. Mech. Eng. 320 (2017): 745-768.

5. M. Borregales, K. Kumar, F.A. Radu, C. Rodrigo, F.J. Gaspar, A parallel-in-time fixed-stress splitting method for Biot's consolidation model. arXiv: 1802.00949, 2018.

6. M. Borregales, F.A. Radu, K. Kumar, J.M. Nordbotten, Robust iterative schemes for non-linear poromechanics. Comput. Geosci. (also arXiv:1702.00328), 2018, to appear.

7. F. List, F.A. Radu, A study on iterative methods for Richards' equation. Comput. Geosci. 20 (2016): 341-353.

8. J. Both, K. Kumar, J.M. Nordbotten, F.A. Radu, Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media, submitted, 2018.