We are very satisfied with the group’s strong presence at the SIAM GS 2019. Through our numerous (excellent!) presentations, participation as organisers of minisymposia and sheer number of participants, we definitely made our mark on the conference. Also, Inga Berre was elected as a SIAM GS officer and secretary of the SIAG Geosciences committee.

SIAM GS - Part I

Some fifteen members of the PMG are going to the SIAM GS 2019 conference. We take part as organisers of the following minisymposia:

Verification Benchmarks for Single-phase Flow in Three-dimensional Fractured Porous Media: Inga Berre, Eirik Keilegavlen and Ivar Stefansson

Advances in Modeling of Non-linear Elasticity and Plasticity for Geomaterials: Inga Berre and Michele Starnoni

Also, we highly recommend attending the following talks:


9.45 Local and Semi-local Modeling and Discretization Principles for Fractured Porous Media by Jan M Nordbotten

11.00 Block Preconditioners for Mixed-dimensional Flow Problems in Fractured Porous Media by Ana Budisa

2.40 Numerical Modeling of Fracture Reactivation in a Three-dimensional Domain Based on a Coulomb Friction Law by Runar Lie Berge

3.05 The Mathematical Structure of Coupled 1D-3D Models by Ingeborg G Gjerde

4.50 Iterative Solvers for Poromechanics with Large Deformation by Manuel Borregales

5.30 A Pore-scale Study of the Transport of Inertial Particles in Porous Media by Max Endo Kokubun


2.15 Challenges in Modelling the Anisotropic Poroelastoplastic Behaviour of Fractured Rocks as Homogenized Media by Michele Starnoni


3.55 Mathematical Modelling of the Bio-plug Technology: Laboratory Experiments, Upscaling, and Numerical Simulations by David Landa Marban

5.50 Monolithic and Splitting Based Solution Schemes for Nonlinear Quasi-static Thermo-poroelasticity by Mats Kirksæther Brun

6.30 Gradient Flow Perspective on Poromechanics by Jakub Both


10.10 Numerical Methods for Flow in Fractured Porous Media in a Unified Implementation by Ivar Stefansson

11.00 Mixed-dimensional Discrete Fracture Matrix Models with Heterogeneous Discretizations and Non-matching Grids by Eirik Keilegavlen


An update will follow once the delegation is back from Houston!

Florin Radu in Stuttgart

Florin Radu recently visited the University of Stuttgart, where he gave a short course on solvers for nonlinear and coupled problems with the assistance of Erlend Storvik and Manuel Borregales. In addition to the students from the University of Stuttgart, the course was also attended by a delegation from the University of Hasselt. While in Stuttgart, Florin was also interviewed by Samuel Barbulla.

Magne Espedal Professor II-position

We are abolutely thrilled to announce that the PMG will be joined by Professor Rainer Helmig in a Professor II position in honour of Magne Espedal, the founder of the group. The position is funded by DEA Norge. The agreement between DEA and UoB was signed during a one-day workshop with presentations of ongoing work in the PMG. For more details, see this UoB page.

From the signing of the DEA-UoB agreement.


The interdisciplinary geothermal energy conference GeoEnergy2019 was held in Bergen this week. The PMG was well represented with five participants and three presentations. The picture is from Sæunn Halldórsdóttir’s presentation on supercritical and superheated geothermal systems in Iceland.

Sæunn presenting

New publication in microbial enhanced oil recovery

The paper A Pore-Scale Model for Permeable Biofilm: Numerical Simulations and Laboratory Experiments was published online on 08 December 2018 in the Journal Transport in Porous Media.

In this paper, we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided into two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substance (EPS), active bacteria, and dead bacteria. The flow of water is modeled by the Stokes equation, whereas a diffusion–convection equation is involved for the transport of nutrients. At the biofilm–water interface, nutrient transport and shear forces due to the water flux are considered. In the biofilm, the Brinkman equation for the water flow, transport of nutrients due to diffusion and convection, displacement of the biofilm components due to reproduction/death of bacteria, and production of EPS are considered. A segregated finite element algorithm is used to solve the mathematical equations. Numerical simulations are performed based on experimentally determined parameters. The stress coefficient is fitted to the experimental data. To identify the critical model parameters, a sensitivity analysis is performed. The Sobol sensitivity indices of the input parameters are computed based on uniform perturbation by ±10% of the nominal parameter values. The sensitivity analysis confirms that the variability or uncertainty in none of the parameters should be neglected which is a beautiful tragedy confirming the difficulty of this problem.

This work is part of the project IMMENS. In this project we aim to develop a numerical simulator for bio-plugging technology based on experiments from the pore to the core scale. In this publication we developed a pore-scale model for biofilm formation. A second publication is under review, where we upscaled this pore-scale model in two different pore geometries. Finally, a third paper is in preparation, where we aim to calibrate a core-scale model with laboratory results.


Water flux

Visiting Tufts University

This fall semester I had a chance to visit Computational and Applied Math group at Tufts University in Medford, USA. Together with Xiaozhe Hu, I have been studying preconditioning techniques for applications in fractured porous media to allow for efficient simulation of subsurface processes. For simulation, we combined the softwares of each research group – PorePy toolbox of PMG in Bergen and HAZMATH solver library developed by Xiaozhe Hu with James Alder (Tufts) and Ludmil Zikatanov (Penn State).


Our main focus was to develop robust solvers and preconditioners for single-phase flow problems in fractured porous media based on the mixed-dimensional modeling of the phenomenon. We investigated two approaches to the problem: one specifically designed for the flow model, and another more general approach resulting from the mathematical structure of related partial differential equations. It was very inspiring to learn and implement new solving strategies that may also be used in different applications, but also very exciting to see our research producing valuable results.


Apart from research, living in greater Boston area was a great new experience. Having many excellent universities close by, I had a lot of fun hanging out with students and academics from all over the US and the world. But, the highlights of my visit were definitely being there in time to enjoy the most of American culture, such as trick-or-treating on Halloween and having a big family dinner on Thanksgiving.


Ana Budiša


Four of the group members went to last week’s European Geothermal Workshop in Strasbourg, along with our good friend and collaborator Luisa Zuluaga, from the UiB geology department. The workshop attracted a diverse range of participants from working on all aspects of geothermal exploitation, from monitoring and characterisation to risk management and modelling. We congratulate Luisa most warmly with the workshop’s poster prize, awarded for her poster on studies of outcrops from Sotra.

Benchmark study

Members of the group have contributed to a paper with the title Call for participation: Verification benchmarks for single-phase flow in three-dimensional fractured porous media, which is now available at arXive. We strongly encourage interested researchers to participate. The UiB simulations are already available in the PorePy collection of published results, here.

Simulated matrix and fracture pressure from the fourth test case.

Associate professor position

We would like to draw attention to a call for applications to an associate professor position in applied and computational mathematics at UiB with deadline 15 September. For further details, please follow this link.