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.

Seminar 09 March

This weeks seminar, at 1pm in the “delta” room, will be given by Ivar Stefansson, who will present his master thesis.

Title: A comparison of two numerical methods for flow in fractured porous media and the impact of intersection cell removal

Abstract: A very brief description of a cell-centered finite volume method and a mixed finite element (mortar)  method will be followed by the comparison of the two methods. I will use the opportunity to mention and summarize
the benchmark study led by Bernd Flemisch. This part will be followed by an presentation of a procedure for   eliminating small discretization cells at the fracture intersections aimed at improving condition numbers and time step restrictions for flow and transport problems.

Seminar 02 March

The PMG organizes weekly seminars, which this semester take place on Thursdays at 1.15pm. This week, Runar Lie Berge will give the following talk:

Title: Ustructured gridding and consisten discretization for reservoirs with fractures and complex wells

This work consists of two parts. In the first part, we present new methods for generating unstructured polyhedral grids that align to prescribed geometric objects. Control-point alignment of cell  centroids is introduced to accurately represent horizontal and multilateral wells, but can also be used to create volumetric representations of fracture networks. Boundary alignment of cell faces is introduced to accurately preserve geological features such as layers, fractures, faults, and/or pinchouts. Prescribed geometric objects will often intersect each other. To handle such cases, we  propose a conflict-point handling scheme that creates conforming cells even at intersections. We also discuss how to generalize this method to 3D. Here, our method honors control-point alignment of cell centroids and boundary alignment of cell faces away from object intersections.
The predominant discretization method for multiphase flow in reservoir simulation is the two-point flux-approximation (TPFA) method. This finite-volume method is mass conservative, but only conditionally consistent and hence susceptible to grid-orientation effects. In the second part of the paper, we review a series of consistent methods and compare and contrast these methods both  with respect to accuracy and monotonicity. Our comparisons include a multipoint flux-approximation (MPFA-O) method, the nonlinear TPFA method, mimetic methods, and the more recent virtual  element methods. To limit the discussion, we focus on incompressible flow, for which we study the effects of deformed cell geometries, anisotropic permeability, and robustness with respect to  various approaches to grid near wells and adapt it to lower-dimensional objects like faults and fractures.

The Porous Media Group starts blogging!

We, the members of the porous media group at the University of Bergen, have decided to start a blog. The intention is to present the ongoing work and activities of the group in an accessible form. So, in the future you may expect to find updates on matters of the following nature:

  • Short presentations of the research of individual members or projects under the PMG kept in a moderately technical language.
  • Posts presenting the main projects of the group.
  • Descriptions and reminders of our weekly seminar.
  • Any events organized by the group and possibly events attended by our members.