Dumux and Dune

DuMux aims to be a generic framework for the simulation of multiphase fluid flow and transport processes in porous media using continuum mechanical approaches. At the same time, DuMux aims to deliver top-notch computational performance, high flexibility, sound software architecture and the ability to run on anything from single processor systems to highly parallel supercomputers with specialized hardware architectures.

The means to achieve these somewhat contradictory goals are the thorough use of object-oriented design in conjunction with template programming. These requirements call for C++ as the implementation language.

One of the more complex issues when dealing with parallel continuum models is managing the grids used for the spatial discretization of the physical model. To date, no generic and efficient approach exists for all possible cases, so DuMux is built on top of Dune, the Distributed and Unified Numerics Environment. Dune provides a generic interface to many existing grid management libraries such as Dune::UGGrid Dune::ALUGrid [7], and a few more. Dune also extensively uses template programming in order to achieve minimal overhead when accessing the underlying grid libraries. In fact, the performance penalty resulting from the use of Dune's grid interface is usually negligible [19].

Dune's grid interface is independent of the spatial dimension of the underlying grid. For this purpose, it uses the concept of co-dimensional entities. Roughly speaking, an entity of co-dimension $0$ constitutes a cell, co-dimension $1$ entities are faces between cells, co-dimension $2$ are edges, and so on until co-dimension $n$ which are the cell's vertices. The Dune grid interface generally assumes that all entities are convex polytopes, which means that it must be possible to express each entity as the convex hull of a set of vertices. For the sake of efficiency, all entities are further expressed in terms of so-called reference elements, which are transformed to the actual spatial incarnation within the grid by a so-called geometry function. Here, a reference element for an entity can be thought of as a prototype for the actual grid entity. For example, if we used a grid that applied hexahedrons as cells, the reference element for each cell would be the unit cube $[0,1{]}^3$, and the geometry function would scale and translate the cube so that it matches the grid's cell. A quick overview of reference elements and the related numbering can be obtained from the Dune cheat sheet. For a more thorough description of Dune's grid definition, see [11].

In addition to the grid interface, Dune also provides quite a few additional modules. dune-localfunctions provides a set of generic finite element shape functions, while dune-istl is the Iterative Solver Template Library and provides generic, highly optimized linear algebra routines for solving the generated systems.

DuMux comes in the form of an additional module dumux. It depends on the Dune core modules dune-common,dune-geometry, dune-grid, dune-istl, and dune-localfunctions. The main intention of DuMux is to provide a framework for easy and efficient implementation of new physical models for porous media flow problems, ranging from problem formulation and the selection of spatial and temporal discretization schemes as well as nonlinear solvers, to general concepts for model coupling. Moreover, DuMux includes ready-to-use numerical models and a few example applications.

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