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49 lines
2.2 KiB
TeX
49 lines
2.2 KiB
TeX
\chapter[Tutorial]{Tutorial}\label{chp:tutorial}
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\eWoms provides two sorts of models: Models which use a fully-implicit
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discretization in space and time and models that use a
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semi-implicit space and an explicit time discretization.
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The semi-implicit models work by first implicitly solving a mass
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balance equation for all conservation quaintites combined. This
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procedire yields a pressure field. Then, the conserved quantities are
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transported using an explicit post-processing procedure based on of
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the pressure field obtained in the implicit step. These models are
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usually refered to be based on the IMPES approach (\textbf{i}mplicit
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\textbf{p}ressure \textbf{e}xplicit \textbf{s}aturation) or, more
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generally, on the IMPET approach (\textbf{i}mplicit \textbf{p}ressure
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\textbf{e}xplicit \textbf{t}ransport).
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In contrast, the fully-implicit models describe the conservation
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quantities of a flow system as a system of strongly coupled partial
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differential equations which is directly using a non-linear
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solver. Physically, these conservation quantities are mass, momentum
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and energy; Although the momentum is usually not explicitly conserved
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in the context of flow models for porous media.
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In section \ref{box} a short introduction to the vertex centered
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finite volume scheme (VCFV or box method) used by \eWoms as the
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spatial discretization of the fully-implicit models is given. The
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decoupled models usually employ a cell-centered finite volume scheme
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which is quite similar to the VCFV discretization, except that this
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scheme does not require to construct a dual grid centered around the
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primary grid's vertices.
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This chapter, first introduce how to solve flow problems using a
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fully-implicit model (section \ref{tutorial-coupled}) and then how to
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solve the same problem using a semi-implicit model (section
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\ref{tutorial-decoupled}). Being simple but representative case, an
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isothermal two-phase problem (i.e. two fluid phases, one solid phase)
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will be considered. The source code of these tutorials is shipped with
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the \eWoms source package and can be found in the \texttt{tutorial}
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directory.
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\input{tutorial-coupled}
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\input{tutorial-decoupled}
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%\input{tutorial-newmodel}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "ewoms-handbook"
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%%% End:
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