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correction of the dumux tutorial (handbook)

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Markus Wolff 2008-09-22 09:00:30 +00:00 committed by Andreas Lauser
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doc/handbook/dumux-handbook.tex
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@ -18,7 +18,7 @@
\DeclareGraphicsExtensions{.eps, .jpg}
\newcommand{\Dune}{{\sf\bfseries DUNE}}
\newcommand{\Dumux}{DuMu$^\text{x}$}
\newcommand{\Dumux}{DuMu$^\text{x}$ }
%The theorems
\theorembodyfont{\upshape}

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doc/handbook/tutorial-decoupled.tex
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@ -3,7 +3,7 @@
The process of solving a problem using \Dumux can be roughly divided into four parts:
\begin{enumerate}
\item The geometry of problem and correspondingly a grid have to be defined.
\item The geometry of the problem and correspondingly a grid have to be defined.
\item Material properties and constitutive relationships have to be defined.
\item Boundary conditions as well as initial conditions have to be defined.
\item A suitable model has to be chosen.
@ -28,26 +28,26 @@ The problem which is solved in this tutorial is illustrated in figure \ref{tutor
\caption{Geometry of the tutorial problem with initial and boundary conditions.}\label{tutorial-decoupled:problemfigure}
\end{figure}
Listing \ref{tutorial-deoucpled:mainfile} shows how the main file, which has to be executed, has to be set up, if the problem described above shall be solved using a decoupled model. This main file can be found in the directory \texttt{/dune-mux/test/tutorial}.
Listing \ref{tutorial-deoucpled:mainfile} shows how the main file, which has to be executed, has to be set up, if the problem described above is to be solved using a decoupled model. This main file can be found in the directory \texttt{/dune-mux/test/tutorial}.
\begin{lst}[File dune-mux/test/tutorial/tutorial\_decoupled.cc]\label{tutorial-deoucpled:mainfile} \mbox{}
\lstinputlisting[basicstyle=\ttfamily\scriptsize,numbers=left,
numberstyle=\tiny, numbersep=5pt]{../../test/tutorial/tutorial_decoupled.cc}
\end{lst}
First, in line \ref{tutorial-decoupled:include-begin} to \ref{tutorial-decoupled:include-end} the Dune and the \Dumux\, files respectively which contain the functions and classes that are needed in the main loop are included into the main file.
First, in line \ref{tutorial-decoupled:include-begin} to \ref{tutorial-decoupled:include-end} the Dune and the \Dumux files respectively which contain the functions and classes that are needed in the main loop are included into the main file.
In line \ref{tutorial-decoupled:grid-begin} to \ref{tutorial-decoupled:grid-end} the geometry is defined and the grid is generated. The three variables of Type \texttt{Dune::FieldVector} define the lower left corner of the domain (\texttt{L}), the upper right corner of the domain (\texttt{H}) and the number of cells in $x$ and $y$ direction (\texttt{N}), where the dimensions are previously defined in line \ref{tutorial-decoupled:dim}. The grid of type \texttt{Dune::SGrid} is then generated in line \ref{tutorial-decoupled:grid-end}. For more information about the dune grid interface, the different grid types that are supported and the generation of different grids it is referred to the \textit{Dune Grid Interface HOWTO} (REFERENCE!!!).
The second point mentioned at the beginning of this section was the definition of material properties and constitutive relationships. The fluid properties of the two fluid phases considered here are defined in lines \ref{tutorial-decoupled:water} and \ref{tutorial-decoupled:oil}. The fluid classes including different kinds of fluids (here: \texttt{Dune::Water} and \texttt{Dune::Oil}) can be found in the file \texttt{phaseproperties2p.hh} in the directory \texttt{/dune-mux/dumux}-\texttt{/material/phaseproperties}. The properties of the solid matrix are defined in a special soil class. The \texttt{soil} object is generated in line \ref{tutorial-decoupled:soil}. As can be seen, the class type is \texttt{Dune::TutorialSoil}, which is defined in the file \texttt{tutorial\_soilproperties.hh} in the folder \texttt{/test/tutorial}. A description of this file and the definition of s soil class including the soil parameters can be found in section \ref{tutorial-decoupled:description-soil-class}. Finally, in line \ref{tutorial-decoupled:twophaserelations} the information included in the fluid and soil objects is used to generate an object of type \texttt{Dune::TwoPhaseRelations}, which includes the constitutive relationships (capillary pressure-saturation relation, relative permeability-saturation relation, etc.). The file \texttt{twophaserelations.hh} can be found in the directory \texttt{/dune-mux/dumux/material}.
The second point mentioned at the beginning of this section was the definition of material properties and constitutive relationships. The fluid properties of the two fluid phases considered here are defined in lines \ref{tutorial-decoupled:water} and \ref{tutorial-decoupled:oil}. The fluid classes including different kinds of fluids (here: \texttt{Dune::Water} and \texttt{Dune::Oil}) can be found in the file \texttt{phaseproperties2p.hh} in the directory \texttt{/dune-mux/dumux}-\texttt{/material/phaseproperties}. The properties of the solid matrix are defined in a special soil class. The \texttt{soil} object is generated in line \ref{tutorial-decoupled:soil}. As can be seen, the class type is \texttt{Dune::TutorialSoil}, which is defined in the file \texttt{tutorial\_soilproperties.hh} in the folder \texttt{/test/tutorial}. A description of this file and the definition of a soil class including the soil parameters can be found in section \ref{tutorial-decoupled:description-soil-class}. Finally, in line \ref{tutorial-decoupled:twophaserelations} the information included in the fluid and soil objects is used to generate an object of type \texttt{Dune::TwoPhaseRelations}, which includes the constitutive relationships (capillary pressure-saturation relation, relative permeability-saturation relation, etc.). The file \texttt{twophaserelations.hh} can be found in the directory \texttt{/dune-mux/dumux/material}.
The definition of boundary and initial conditions is done by definition of a so-called \textit{problem} class. In case of this tutorial the problem class is defined in the file \texttt{tutorialproblem\_decoupled.hh} in the texttt{/test/tutorial} folder. In the main file the problem object of type \texttt{Dune::TutorialProblemDecoupled} is then generated in line \ref{tutorial-decoupled:problem}. A further explanation of the definition of boundary and initial conditions and the structure of the problem class can be found in section \ref{tutorial-decoupled:description-bc-ic}. Besides the definition of the boundary and initial conditions the problem class is also a kind of interface containing all the objects generated before (geometry, fluids, soil, constitutive relationships, etc.). Thus, as can be seen in line \ref{tutorial-decoupled:problem} all this objects are given as arguments when calling the constructor of the problem class.
The definition of boundary and initial conditions as well as source of sink terms is done by definition of a so-called \textit{problem} class. In case of this tutorial the problem class is defined in the file \texttt{tutorialproblem\_decoupled.hh} in the \texttt{/test/tutorial} folder. In the main file the problem object of type \texttt{Dune::TutorialProblemDecoupled} is then generated in line \ref{tutorial-decoupled:problem}. A further explanation of the definition of boundary and initial conditions, source and sink terms and the structure of the problem class can be found in section \ref{tutorial-decoupled:description-bc-ic}. Besides the definition of the boundary and initial conditions the problem class is also a kind of interface containing all the objects generated before (geometry, fluids, soil, constitutive relationships, etc.). Thus, as can be seen in line \ref{tutorial-decoupled:problem} all this objects are given as arguments when calling the constructor of the problem class.
Following the steps listed at the beginning of this section, finally, a model has to be chosen. In case of this tutorial a decoupled isothermal two phase model is the choice. As explained before a decoupled model consists of a pressure equation which is decoupled or only weakly coupled to a saturation equation, concentration equations, energy balance equations, etc. In case of isothermal two phase flow one pressure equation and one saturation equation have to be solved.
The discretisation of the pressure equation is included in the object which is generated in line \ref{tutorial-decoupled:diffusion} of the main file. It is called \texttt{diffusion} and it is of type \texttt{Dune::FVDiffusionVelocity}. The definition of this class can be found in \texttt{/dune-mux/dumux/diffusion/fv} in the file \texttt{fvdiffusionvelocity.hh}. The \texttt{FV} in the class name indicates that a finite volume discretisation is used. For the pressure equation also other discretisation methods like finite elements or mimetic finite differences are available.
The discretisation of the pressure equation is included in the object which is generated in line \ref{tutorial-decoupled:diffusion} of the main file. It is called \texttt{diffusion} and it is of type \texttt{Dune::FVDiffusionVelocity}. The definition of this class can be found in \texttt{/dune-mux/dumux/diffusion/fv} in the file \texttt{fvdiffusionvelocity.hh}. The \texttt{FV} in the class name indicates that a \textit{finite volume} discretisation is used. For the pressure equation also other discretisation methods like \textit{finite elements} or \textit{mimetic finite differences} are available.
Similarly, an object containing the discretisation of the saturation equation is generated in line \ref{tutorial-decoupled:transport} of the main file. As can be seen, this object is called \texttt{transport}. The class \texttt{Dune::FVTransport} can be found in the directory \texttt{/dune-mux/dumux/transport/fv}. Again, the \texttt{FV} in the class name indicates a finite volume discretisation.
Similarly, an object containing the discretisation of the saturation equation is generated in line \ref{tutorial-decoupled:transport} of the main file. As can be seen, this object is called \texttt{transport}. The class \texttt{Dune::FVTransport} can be found in the directory \texttt{/dune-mux/dumux/transport/fv}. Again, the \texttt{FV} in the class name indicates a \textit{finite volume} discretisation.
For the decoupled model the so-called \textit{IMPES} (\textit{IM}plicit \textit{P}ressure \textit{E}xplicit \textit{S}aturation) algorithm is used. This means that the pressure equation is first solved using an implicit method. The resulting velocities are then used to solve the saturation equation explicitly. It is clear that depending on the non-linearity this is an iterative process within every timestep. The object \texttt{impes} of type \texttt{Dune::IMPES} which is generated in line \ref{tutorial-decoupled:impes} of the main file combines the objects \texttt{diffusion} and \texttt{transport} and proceeds the iterations of the IMPES algorithm within a timestep. The definition of the class \texttt{Dune::IMPES} can be found in the file \texttt{impes.hh} in the directory \texttt{/dune-mux/dumux/fractionalflow/impes}.
@ -63,7 +63,7 @@ It is important to mention, that existing fluid classes should not be changed. N
\subsection{The definition of the soil parameters}\label{tutorial-decoupled:description-soil-class}
Soil properties which can be defined in \Dumux\, are the \textit{intrinsic permeability}, the \textit{porosity} and the \textit{heat capacity} as well as the \textit{heat conductivity} of the solid matrix. Further the \textit{residual saturations} of the fluids, and the \textit{capillary pressures-saturation function} as well as the \textit{relative permeability-saturation functions} are depending on the soil.
Soil properties which can be defined in \Dumux are the \textit{intrinsic permeability}, the \textit{porosity} and the \textit{heat capacity} as well as the \textit{heat conductivity} of the solid matrix. Further the \textit{residual saturations} of the fluids, and the \textit{capillary pressures-saturation function} as well as the \textit{relative permeability-saturation functions} are depending on the soil.
The base class \texttt{Dune::Matrix2p} for the definition of the soil parameters can be found in the file \texttt{property\_baseclasses.hh} in the directory \texttt{/dune-mux/dumux/material}. Derived from this base class, there exist two standard soil type classes named \texttt{HomogeneousSoil} and \texttt{HeterogeneousSoil}. Both can be found in the file \texttt{matrixproperties.hh} in the \texttt{/material} folder. If one wants to use a soil that differs from this standard soil types, new soil classes can be derived either from the base class (\texttt{Dune::Matrix2p}) or from the two standard soil classes (\texttt{Dune::HomogeneousSoil} and \texttt{Dune::HeterogeneousSoil}).
@ -103,7 +103,7 @@ Listing \ref{tutorial-decoupled:tutorialproblem}) includes five types of functio
\end{itemize}
The second part of the function name indicates if the return value is used for the pressure equation (\textbf{Press}) or for the saturation equation (\textbf{Sat}).
All different function types have to be called with three different arguments. The first one (\texttt{x}) is a vector including the global coordinates of the current entity (can be an element, vertex, etc.), the second one (\texttt{e}) is the entity itself and the third one is a vector including the local coordinates of the current entity. Thus, the return of the functions, which can be a boundary value, an initial value, a source/sink, etc. , can be defined depending on the position in the domain.
All different function types have to be called with three different arguments. The first one (\texttt{x}) is a vector including the global coordinates of the current entity (can be an element, vertex, etc.), the second one (\texttt{e}) is the entity itself and the third one is a vector including the local coordinates of the current entity. Thus, the return of the functions, which can be a boundary value, an initial value, a source/sink, etc., can be defined depending on the position in the domain.
The first function defined in the problem class \texttt{TutorialProblemDecoupled} is the function \texttt{qPress} (line \ref{tutorial-decoupled:qpress}). It returns a source or a sink term for the pressure equation.
@ -113,4 +113,5 @@ In lines \ref{tutorial-decoupled:gpress} and \ref{tutorial-decoupled:gsat} the f
Finally, the function \texttt{initSat} is defined in line \ref{tutorial-decoupled:initsat}. This function returns the initial saturation distribution.
\subsection{Exercise}
\subsection{Exercise}
TODO: give some exercises