Dune-MMesh: The Dune Grid Module for Moving Interfaces

Abstract

In several physical and environmental processes that concern multiphase flows, biological systems, and geophysical phenomena, important physical processes occur along thin physical interfaces. These processes include effects that may alter the interface's position or topology over time creating a moving interface, which complicates traditional modeling techniques. Moving interface problems thus require advanced numerical tools with specific treatment of the interface and the simultaneous ability to implement complex physical effects, which this work seeks to create solutions for.

Flow in Porous Media with Fractures of Varying Aperture

“…The program code is openly available (see [18] and corresponding repository 1 ). Specifically, the implementation relies on DUNE-MMesh [9], a grid module tailored for applications with interfaces. In particular, DUNE-MMesh is a useful tool for mixed-dimensional models, such as the DG schemes (5.11) and (5.12), as it allows to export a predefined set of facets from the bulk grid as separate interface grid and provides coupled solution strategies to simultaneously solve bulk and interface schemes.…”