Seminar 15 June

This week’s seminar will be held by Mats Brun at 1pm.

Title: Upscaling and discretization of coupled geomechanics, flow and heat in a poro-elastic medium in the quasi-static situation

Motivated by geothermal energy storage in the subsurface, we undertake the formal derivation of Biot’s law for a poro-elastic medium completely saturated by a fluid, coupled with heat conduction laws for both the fluid and solid phase. We assume small displacements of the solid structure (i.e. linear strain), a fully connected void and grain space, that the fluid flow is incompressible, and that the fluid/solid interface coupling conditions may be linearized. We start with the microscale model, and apply the technique of homogenization in order to derive the upscaled model, in the case of periodically distributed pores. Assuming the homogenization ansatz holds true, we obtain a fully coupled system of equations on the macro-scale accounting for the effects of geomechanics, heat conduction, and fluid flow within a porous material.

Benchmarking workshop

This Thursday and Friday, the  PMG hosted a workshop on modeling and benchmarking of porous media. The event was highly enjoyable and interesting with an abundance of excellent contributions, and we are sure it will inspire future work and collaboration. We are very grateful to Bernd Flemisch for initiating the benchmarking article whence the workshop originated and to our own Alessio Fumagalli and the rest of the organizing committee. We thank all the presenters and guests for joining us in Bergen, and last but not least our sponsors: The Norwegian Research Council, SRP NUPUS, VISTA and Politecnico di Milano.

Workshop on fracture flow

The group is currently making the last preparations for the upcoming workshop Modeling and Benchmarking of Fractured Porous Media which is to take place Thursday and Friday of this week. We are very happy for this opportunity to invite collaborators and colleagues to Bergen for what we are sure will be a most exciting, interesting and productive convention!

Two vacancies in the group

We are now announcing two vacancies for PhD students in the Porous Media Group. The project is in cooperation with Uni-CIPR and deals with developing mathematical techniques for upscaling for enhanced oil recovery processes from lab to field scale. The application deadline is 5 June, and further details may be found at the official announcements:

Vacancy – work package 1

Vacancy – work package 4

Seminar 20 April

This week’s seminar will be given by Ingeborg Gåseby Gjerde.

Title: Mixed methods for the Poisson equation with a Dirac right-hand side
Abstract: In this talk, we will investigate the use of mixed methods for the Poisson equation with a Dirac right-hand side. The solution to this problem does not lie in H1, leading to suboptimal convergence rates for finite element solutions. We will start by discussing numerical results obtained from primal and dual mixed methods. Weighted Sobolev spaces will then be introduced, and we will discuss their use in existence proofs for equations with singular solutions. Finally, we will examine the results obtained from solving a rescaled Poisson’s equation.

Researcher position

There is a new position in the PMG related to the TheMSES project. The researcher project concerns the understanding of how fractures can be created and opened as a consequence of change in flow and temperature in the subsurface when hot fluids are pumped down at elevated pressures and later produced. We warmly encourage interested parties to acquiant themselves further with the position through this announcement.

PhD position

Professor Antonella Zanna has just announced a vacant PhD position related to a project on modeling, simulation and image processing related to flow in human organs has just been announced at the department. For futher details, see the announcement of the position.

Guest lectures and seminar

This week, we are very pleased to have Prof. Peter Knabner from University of Erlangen-Nuremberg visiting. During his stay, Prof. Knabner will give some lectures on the topic “Flow, Transport and Multicomponent Reaction in Porous Media: Mathematical Modelling, Analysis and Simulation”, taking place

Tuesday, 28.03, 14:15-16:00, Hjørnet, Natural science building

Wednesday, 29.03, 14:15-16:00, Pi 4, Natural science building

As usual, there will also be a seminar on Thursday, this week given by Jakub Both.

Title: Minimization principles for Biot’s equations
Abstract: In this talk, we investigate Biot’s equations from a minimization point of view, modeling coupled flow and mechanical deformation of fully saturated porous media. We recall the model for the coupled problem written in a minimization formulation and apply a block coordinate descending method in order to decouple the mechanics and flow subproblems iteratively. The resulting scheme equals the classical and widely used undrained splitting scheme. We conclude, although considered from an alternative perspective, the same powerful splitting schemes can be derived mathematically as previously done from an physical point of view. We discuss briefly the potential of the framework to derive splitting algorithms for nonlinear Biot’s equations.

Seminar 23 Mars

This week’s seminar will be given by Florian List and will take place at 1pm on Thursday, as usual.

Title: Iterative methods for solving Richards’ equation
Abstract: This presentation concerns linearization methods for efficiently solving the Richards’ equation, a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media. The discretization of Richards’ equation is based on backward Euler in time and Galerkin finite elements in space. The most valuable linearization schemes for Richards’ equation, i.e. the Newton method, the Picard method, the Picard/Newton method and the L-scheme are presented and their performance is comparatively studied. The convergence, the computational time and the condition numbers for the underlying linear systems are recorded. The proof of the convergence of the L-scheme is presented and the convergence of the other methods is discussed. A new scheme is proposed, the L-scheme/Newton method which is more robust and quadratically convergent. The linearization methods are tested on illustrative numerical examples.

SIAM prize to Kundan Kumar

It is with great pleasure that we announce that Kundan Kumar, who has been with the group since 2014, was recently awarded the SIAG/Geosciences Early Career Prize. His current work concerns various coupled problems in porous media, such as geomechanics and flow, reactive transport and flow and multiphase flow problems. The prize was duly celebrated with cake and a presentation given by the recipient in yesterday’s porous media seminar.