The Dune FoamGrid implementation for surface and network grids

TL;DR

FoamGrid is a versatile grid implementation for the DUNE framework, supporting complex, non-manifold, and adaptive grids in arbitrary dimensions, suitable for simulating foams, networks, and growth phenomena.

Contribution

It introduces FoamGrid, a novel grid data structure with support for non-manifold topology, adaptive refinement, and dynamic element addition/removal, expanding the capabilities of DUNE.

Findings

Supports non-manifold, curved, and high-dimensional grids

Enables adaptive non-conforming refinement and grid modification

Demonstrated through three numerical examples

Abstract

We present FoamGrid, a new implementation of the DUNE grid interface. FoamGrid implements one- and two-dimensional grids in a physical space of arbitrary dimension, which allows for grids for curved domains. Even more, the grids are not expected to have a manifold structure, i.e., more than two elements can share a common facet. This makes FoamGrid the grid data structure of choice for simulating structures such as foams, discrete fracture networks, or network flow problems. FoamGrid implements adaptive non-conforming refinement with element parametrizations. As an additional feature it allows removal and addition of elements in an existing grid, which makes FoamGrid suitable for network growth problems. We show how to use FoamGrid, with particular attention to the extensions of the grid interface needed to handle non-manifold topology and grid growth. Three numerical examples demonstrate the possibilities offered by FoamGrid.