In many technical applications, in particular in the field of fluid dynamics, comparably thin physical interfaces can have a large impact on the overall behavior of a modeled system. For instance, interfaces occur as separating layer between fluid phases in multiphase flows, in fluid- structure interaction and fluid-solid phase change. Even fractures in porous media can be modeled by lower-dimensional surfaces. Oftentimes, these interfaces move over time and the processes become a kind of free-boundary value problems.

The grid implementation Dune-MMesh aims at providing numerical capabilities for grid based methods to model interface-driven processes within the DUNE framework. Essentially, it consists of two things:

  1. A triangulation based on CGAL where a set of facets is considered as interface and

  2. the possibility to re-mesh the triangulation when necessary.

These two ingredients enable many new possibilities within the DUNE framework. First, the representation of some grid facets as an interface makes Dune-MMesh a useful tool for the implementation of mixed-dimensional models. Second, the inevitable non-hierarchical adaptation complements the existing grid implementations within the DUNE framework and allows for unprecedent flexibility of grid adaptation.

More details about the concepts behind Dune-MMesh are described in Concepts. The procedure to install and use Dune-MMesh is specified in Installation. You can find a collection of examples of what can be done with Dune-MMesh based on the discretization module Dune-Fem in Examples. The programming interface is described in the sections Python and C++.