\chapter[Tutorial]{Tutorial}\label{chp:tutorial}

\eWoms provides two sorts of models: Models which use a fully-implicit
discretization in space and time and models that are
semi-implicit. 

The semi-implicit solve the combined mass balance equation for all
phases implicitly -- which yields a pressure -- and then transport the
conserved quantities in an explicit step based on the result of the
(implicit) pressure step. For this reason these models are also called
to be based on the IMPES approach (\textbf{i}mplicit \textbf{p}ressure
\textbf{e}xplicit \textbf{s}aturation) or, more generally, on the
IMPET approach (IMPES (\textbf{i}mplicit \textbf{p}ressure
\textbf{e}xplicit \textbf{t}ransport).

The fully-implicit models, describe the conservation quantities of a
flow system as a system of strongly coupled partial differential
equations. Physically, these conservation quantities are mass,
momentum and energy; Although the momentum is usually not explicitly
conserved in the context of flow models for porous media.

In section \ref{box} a short introduction to the vertex centered
finite volume scheme (VCFV or box method) used by \eWoms as the
spatial discretization of the fully-implicit models is given. The
decoupled models usually employ a cell-centered finite volume scheme
which is quite similar to the VCFV discretization, except that this
scheme does not require to construct a dual grid centered around the
primary grid's vertices.


The following two sections of the tutorial first introduce how to
solve flow problems using a fully-coupled model (section
\ref{tutorial-coupled}) and then how to solve the same problem using a
semi-implicit model (section \ref{tutorial-decoupled}). Being the
easiest case, an isothermal two-phase system (two fluid phases, one
solid phase) will be considered. The source code of these tutorials is
shipped with the \eWoms source package and can be found in the
\texttt{tutorial} directory.

\input{tutorial-coupled}
\input{tutorial-decoupled}
%\input{tutorial-newmodel}

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