opm-simulators/doc/handbook/intro.tex

\chapter{Introduction}

\eWoms~\cite{EWOMS-HP} a generic simulation framework using continuum
mechanical approaches with a focus on multi-phase fluid flow and
transport processes in porous media. \eWoms is also an integral part
of the open porous media initiative~\cite{OPM-HP} for which it
implements the fully-implicit discretization schemes. \eWoms is based
on the source code of the \Dumux~\cite{DUMUX-HP} simulation framework
and aims to be a proper superset of \Dumux when it comes to features,
while at the same time it delivers better performance and a
higher-quality code base. To ease porting features from \Dumux to
\eWoms, the \eWoms source code uses very similar naming and style
conventions as the one of \Dumux.

Besides being a generic simulation framework, \eWoms also aims to to
deliver top-notch computational performance, high flexibility, a 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 motivated
the decision to implement \eWoms using the \Cplusplus programming
language.

One of the more complex issues when dealing with parallel continuum
models for partial differential equations, is the management of the
grids used for the spatial discretization. To date, no generic and
efficient approach exists for all possible cases, which lead to \eWoms
being build on top of \Dune, the \textbf{D}istributed and
\textbf{U}nified \textbf{N}umerics
\textbf{E}nvironment~\cite{DUNE-HP}. Instead of trying to implement a
grid for everything, \Dune defines a generic \Cplusplus interface to
grids, and provides adapters to several existing grid management
libraries such as UG~\cite{UG-HP}, ALBERTA~\cite{ALBERTA-HP} or
ALUGrid~\cite{ALUGRID-HP}. DUNE also extensively uses template
programming in order to achieve minimal overhead when accessing the
underlying grid libraries\footnote{In fact, the performance penalty
  resulting from the use of \Dune's grid interface is usually
  negligible~\cite{BURRI2006}.}.
\begin{figure}[hbt]
  \centering 
  \includegraphics[width=.5\linewidth, keepaspectratio]{EPS/dunedesign}
  \caption{
    \label{fig:dune-design}
    A high-level overview of \Dune's design is available on the project's
    web site~\cite{DUNE-HP}.
  }
\end{figure}

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 $1$ 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 which 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. For a more thorough description of \Dune's
grid definition, see~\cite{BASTIAN2008}.

In addition to the grid interface, \Dune also provides quite a few
additional modules; In the context of this handbook the
\texttt{dune-localfunctions} and \texttt{dune-istl} modules are
probably the most relevant. \texttt{dune-localfunctions} provides a
set of generic finite element shape functions, while
\texttt{dune-istl} is the \textbf{I}terative \textbf{S}olver
\textbf{T}emplate \textbf{L}ibrary and provides generic, highly
optimized linear algebra routines for solving linear systems of
equations.

\eWoms comes in form of a module \Dune module '\texttt{ewoms}'.  It
depends on the \Dune core modules \texttt{dune-common},
\texttt{dune-grid}, \texttt{dune-istl}, and on
\texttt{dune-localfunctions}.  The main intention of \eWoms is to
provide a framework for an 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 and linear solvers, to general concepts
for model coupling.  Moreover, \eWoms includes ready-to-use numerical
models and a few example applications.

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