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work on the tutorial description for the coupled models

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doc/handbook/tutorial-coupled.tex
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@ -1,14 +1,16 @@
\section[Fully-coupled model]{Solving a problem using a Fully-Coupled Model}\label{tutorial-coupled} \section[Fully-coupled model]{Solving a problem using a Fully-Coupled Model}\label{tutorial-coupled}
The process of solving a problem using \Dumux can be roughly divided into four parts: The process of setting up a problem using \Dumux can be roughly divided into four parts:
\begin{enumerate} \begin{enumerate}
\item A suitable model has to be chosen.
\item The geometry of the 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 selected. \item Material properties and constitutive relationships have to be selected.
\item Boundary conditions as well as initial conditions have to be defined. \item Boundary conditions and as initial conditions have to be specified.
\item A suitable model has to be chosen.
\end{enumerate} \end{enumerate}
The problem being solved in this tutorial is illustrated in Figure \ref{tutorial-coupled:problemfigure}. A rectangular domain with no flow boundaries on the top and on the bottom, which is initially saturated with oil, is considered. Water infiltrates from the left side into the domain. Gravity effects are neglected. The problem being solved in this tutorial is illustrated in Figure \ref{tutorial-coupled:problemfigure}.
A rectangular domain with no flow boundaries on the top and on the bottom, which is initially saturated with oil, is considered.
Water infiltrates from the left side into the domain and replaces the oil. Gravity effects are neglected here.
\begin{figure}[ht] \begin{figure}[ht]
\psfrag{x}{x} \psfrag{x}{x}
@ -27,8 +29,7 @@ The problem being solved in this tutorial is illustrated in Figure \ref{tutorial
\caption{Geometry of the tutorial problem with initial and boundary conditions.}\label{tutorial-coupled:problemfigure} \caption{Geometry of the tutorial problem with initial and boundary conditions.}\label{tutorial-coupled:problemfigure}
\end{figure} \end{figure}
The equations solved here are the mass balances of oil and The solved equations are the mass balances of water and oil:
water:
\begin{align} \begin{align}
\label{massbalancewater} \label{massbalancewater}
\frac {\partial (\phi \, S_{w}\, \varrho_{w})}{\partial t} \frac {\partial (\phi \, S_{w}\, \varrho_{w})}{\partial t}
@ -50,9 +51,9 @@ water:
\subsection{The main file} \subsection{The main file}
Listing \ref{tutorial-coupled:mainfile} shows the main file Listing \ref{tutorial-coupled:mainfile} shows the main application file
\texttt{tutorial/tutorial\_coupled.cc} for the coupled two-phase \texttt{tutorial/tutorial\_coupled.cc} for the coupled two-phase
model. This file needs to be executed in order to solve the problem described model. This file has to be compiled and executed in order to solve the problem described
above. above.
\begin{lst}[File tutorial/tutorial\_coupled.cc]\label{tutorial-coupled:mainfile} \mbox{} \begin{lst}[File tutorial/tutorial\_coupled.cc]\label{tutorial-coupled:mainfile} \mbox{}
@ -61,12 +62,12 @@ above.
\end{lst} \end{lst}
From line \ref{tutorial-coupled:include-begin} to line From line \ref{tutorial-coupled:include-begin} to line
\ref{tutorial-coupled:include-end} the \Dune and \Dumux files which \ref{tutorial-coupled:include-end} the \Dune and \Dumux files, which
contain the needed functions and classes are included. contain some required functions and classes, and the problem file are included.
At line \ref{tutorial-coupled:set-type-tag} the type tag of the At line \ref{tutorial-coupled:set-type-tag} the type tag of the
problem which is going to be simulated is set. All other data types problem, which is going to be simulated, is set. All other data types
can be retrieved by the \Dumux property system and only depend on this can be retrieved via the \Dumux property system and only depend on this
single type tag. Retrieving them is done between line single type tag. Retrieving them is done between line
\ref{tutorial-coupled:retrieve-types-begin} and \ref{tutorial-coupled:retrieve-types-begin} and
\ref{tutorial-coupled:retrieve-types-end}. For an introduction to the \ref{tutorial-coupled:retrieve-types-end}. For an introduction to the
@ -75,12 +76,12 @@ property system, see section \ref{sec:propertysystem}.
The first thing which should be done at run time is to initialize the The first thing which should be done at run time is to initialize the
message passing interface using \Dune's \texttt{MPIHelper} class. Line message passing interface using \Dune's \texttt{MPIHelper} class. Line
\ref{tutorial-coupled:init-mpi} is essential if the simulation is \ref{tutorial-coupled:init-mpi} is essential if the simulation is
intended to be run on more than one processor at the same time. Next, intended to be run on more than one processor at the same time using MPI. Next,
the command line arguments are parsed starting at line the command-line arguments are parsed starting at line
\ref{tutorial-coupled:parse-args-begin} down to line \ref{tutorial-coupled:parse-args-begin} down to line
\ref{tutorial-coupled:parse-args-end}. In this example, it is checked if and \ref{tutorial-coupled:parse-args-end}. In this example, it is checked if and
from which time on a previous run of the simulation should be restarted. Furthermore, we from which time on a previous run of the simulation should be restarted. Furthermore, we
parse the time when the simulation ends and the initial time step size. parse the time when the simulation ends and the initial time-step size.
After this, a grid is created in line After this, a grid is created in line
\ref{tutorial-coupled:create-grid} and the problem is instantiated for \ref{tutorial-coupled:create-grid} and the problem is instantiated for
@ -106,48 +107,52 @@ numberstyle=\tiny, numbersep=5pt, firstline=27]{../../tutorial/tutorialproblem_c
First, a new type tag is created for the problem in line First, a new type tag is created for the problem in line
\ref{tutorial-coupled:create-type-tag}. In this case, the new type \ref{tutorial-coupled:create-type-tag}. In this case, the new type
tag inherits all properties defined for the \texttt{BoxTwoP} type tag, tag inherits all properties from the \texttt{BoxTwoP} type tag,
which means that for this problem the two-phase box model is chosen as which means that for this problem the two-phase box model is chosen as
discretization scheme. Further, it inherits from the spatial parameters type tag which is defined in the problem dependent saptial parameters file (line \ref{tutorial-coupled:define-spatialparameters-typetag}). On line \ref{tutorial-coupled:set-problem}, a discretization scheme. Further, it inherits from the spatial parameters type tag,
which is defined in the problem-dependent spatial parameters file (line \ref{tutorial-coupled:define-spatialparameters-typetag}).
On line \ref{tutorial-coupled:set-problem}, a
problem class is attached to the new type tag, while the grid which problem class is attached to the new type tag, while the grid which
is going to be used is defined in line \ref{tutorial-coupled:set-grid} -- is going to be used is defined in line \ref{tutorial-coupled:set-grid} --
in this case that is \texttt{SGrid}. Since there's no uniform in this case that is \texttt{SGrid}. Since there's no uniform
mechanism to allocate grids in \Dune, the \texttt{Grid} property also contains mechanism to allocate grids in \Dune, the \texttt{Grid} property also contains
a static \texttt{create()} method which provides just that. Therein, the three variables of a static \texttt{create()} method which provides just that. The \texttt{SGrid} uses three variables of
Type \texttt{Dune::FieldVector} define the lower left corner of the domain Type \texttt{Dune::FieldVector} to define the lower left corner of the domain
(\texttt{L}), the upper right corner of the domain (\texttt{H}) and the number (\texttt{L}), the upper right corner of the domain (\texttt{H}) and the number
of cells in $x$ and $y$ direction (\texttt{N}). Next, of cells in $x$ and $y$ direction (\texttt{N}).
the appropriate fluid system, which specifies both information about
Next, the appropriate fluid system, which specifies both, information about
the fluid mixture as well as about the pure substances, has to be chosen. the fluid mixture as well as about the pure substances, has to be chosen.
The two-phase model defaults to the \texttt{FluidSystem2P} which assumes The two-phase model uses by default the \texttt{FluidSystem2P}, which assumes
immiscibility of the phases, but requires the wetting and non-wetting phases immiscibility of the phases, but requires the wetting and non-wetting phases
to be explicitly set. In this case, liquid water which uses the relations from to be explicitly set. In this case, liquid water which uses the relations from
IAPWS'97~\cite{IAPWS1997} is chosen as the wetting phase on line IAPWS'97~\cite{IAPWS1997} is chosen as the wetting phase on line
\ref{tutorial-coupled:wettingPhase} and a liquid model oil is chosen as the \ref{tutorial-coupled:wettingPhase} and liquid oil is chosen as the
non-wetting phase on line \ref{tutorial-coupled:nonwettingPhase}. non-wetting phase on line \ref{tutorial-coupled:nonwettingPhase}.
The last property, which is set in line
The final property, which is set in line
\ref{tutorial-coupled:gravity}, is optional and tells the model not to \ref{tutorial-coupled:gravity}, is optional and tells the model not to
use gravity. use gravity.
Parameters which are specific to a set-up -- like boundary and initial Parameters which are specific to a set-up, such as boundary and initial
conditions, source terms or temperature within the domain -- but are conditions, source terms or temperature within the domain, and which are
required to solve the differential equations of the models are required to solve the differential equations of the models are
specified via a \textit{problem} class. If the two-phase box model is specified via a \textit{problem} class. If the two-phase box model is
used, this class must be derived from \texttt{TwoPBoxProblem} as done used, this class should be derived from \texttt{TwoPBoxProblem} as done
in line \ref{tutorial-coupled:def-problem}. in line \ref{tutorial-coupled:def-problem}.
The problem class always has at least five methods: The problem class always has at least five methods:
\begin{itemize} \begin{itemize}
\item A method \texttt{boundaryTypes()} specifying the kind of \item A method \texttt{boundaryTypes()} specifying the type of
boundary conditions to be used for a boundary segment boundary conditions at each vertex.
\item A method \texttt{dirichlet()} specifying the actual values for \item A method \texttt{dirichlet()} specifying the actual values for
the Dirichlet conditions on a boundary segment the Dirichlet conditions at each Dirichlet vertex.
\item A method \texttt{neumann()} specifying the actual values for \item A method \texttt{neumann()} specifying the actual values for
the Neumann conditions on a boundary segment the Neumann conditions, which are usually evaluated at the
\item A method for source or sink terms called \texttt{source()} integration points of the Neumann boundary faces.
\item A method for source or sink terms called \texttt{source()}, usually evaluated at
the center of a sub-control volume.
\item A method called \texttt{initial()} for specifying the initial \item A method called \texttt{initial()} for specifying the initial
condition. conditions at each vertex.
\end{itemize} \end{itemize}
For the definition of the the boundary condition types and of the values of the Dirichlet boundaries, For the definition of the the boundary condition types and of the values of the Dirichlet boundaries,
@ -157,12 +162,12 @@ two parameters are required:
the values in this vector mean is dependent on the method: For the values in this vector mean is dependent on the method: For
\texttt{dirichlet()} it contains the actual values of the primary \texttt{dirichlet()} it contains the actual values of the primary
variables, for \texttt{boundaryTypes()} it contains the boundary variables, for \texttt{boundaryTypes()} it contains the boundary
condition type. It has as many entries as the model has primary variables / equations. condition types. It has as many entries as the model has primary variables / equations.
For the typical case in which all equations have the same boundary For the typical case, in which all equations have the same boundary
condition at a certain position, there are two methods that set the appropriate conditions condition type at a certain position, there are two methods that set the appropriate conditions
for all primary variables / equations: Either \texttt{setAllDirichlet()} or \texttt{setAllNeumann()} for all primary variables / equations: Either \texttt{setAllDirichlet()} or \texttt{setAllNeumann()}.
\item [vertex:] The boundary condition and the Dirichlet values are specified at the vertex, which represents a \item [vertex:] The boundary condition and the Dirichlet values are specified at the vertex, which represents a
subcontrol volume. This avoids to specify two different boundary condition types at one subcontrol volume. sub-control volume. This avoids the specification of two different boundary condition types for one equation at one sub-control volume.
Be aware that the second parameter is a Dune grid entity with the codimension dim. Be aware that the second parameter is a Dune grid entity with the codimension dim.
\end{description} \end{description}
@ -180,8 +185,7 @@ Methods which make statements about boundary segments of the grid (i.e.
is located. is located.
\item[fvElemGeometry:] The finite-volume geometry induced on the \item[fvElemGeometry:] The finite-volume geometry induced on the
finite element by the box scheme. finite element by the box scheme.
\item[isIt:] The \texttt{Intersection} of the boundary \item[isIt:] The \texttt{Intersection} of the boundary segment as given by the grid.
segment as given by the grid.
\item[scvIdx:] The index of the sub-control volume in \item[scvIdx:] The index of the sub-control volume in
\texttt{fvElementGeometry} adjacent to the boundary segment. \texttt{fvElementGeometry} adjacent to the boundary segment.
\item[boundaryFaceIdx:] The index of the boundary face in \item[boundaryFaceIdx:] The index of the boundary face in
@ -207,15 +211,15 @@ can be found in the base class \texttt{Dumux::BoxProblem<TypeTag>}.
\subsection{Defining fluid properties}\label{tutorial-coupled:description-fluid-class} \subsection{Defining fluid properties}\label{tutorial-coupled:description-fluid-class}
The \Dumux distribution includes some common substances which can be used The \Dumux distribution includes some common substances which can be used
out of the box. The properties of the pure substances (such as the component out of the box. The properties of the pure substances (such as the components
nitrogen, water, or pseudo-component air) are stored in header files in nitrogen, water, or the pseudo-component air) are stored in header files in
the folder \verb+dumux/material/components+. Each of these files the folder \verb+dumux/material/components+. Each of these files
defines a class with the same name as the component but starting with a capital defines a class with the same name as the component but starting with a capital
letter, e.g. \texttt{Water}, and are derived from \texttt{Component}. letter, e.g. \texttt{Water}, and are derived from \texttt{Component}.
Most often, when two or more components are considered, fluid interactions Most often, when two or more components are considered, fluid interactions
such as solubility effects come into play and properties of mixtures such as such as solubility effects come into play and properties of mixtures such as
density are of interest. These interactions are defined in density or enthalpy are of interest. These interactions are defined in
a specific \verb+fluidsystem+ in the folder \verb+dumux/material/fluidsystems+. a specific \verb+fluidsystem+ in the folder \verb+dumux/material/fluidsystems+.
It features methods returning fluid properties like density, enthalpy, viscosity, It features methods returning fluid properties like density, enthalpy, viscosity,
etc. by accessing the pure components as well as binary coefficients such as etc. by accessing the pure components as well as binary coefficients such as
@ -234,9 +238,9 @@ well as the \textit{heat conductivity} can be defined in space using a
so-called \texttt{spatial parameters} class. However, because the soil so-called \texttt{spatial parameters} class. However, because the soil
also has an effect on the material laws of the fluids (e.g. \textit{capillarity}), also has an effect on the material laws of the fluids (e.g. \textit{capillarity}),
their selection and the definition of their attributes (e.g. \textit{residual their selection and the definition of their attributes (e.g. \textit{residual
saturations}) are also accomplished in the spatial parameters. saturations} or \textit{van Genuchten parameters}) are also accomplished in the spatial parameters.
The base class \texttt{Dumux::BoxSpatialParameters<TypeTag>} holds a general The base class \texttt{Dumux::BoxSpatialParameters<TypeTag>} contains a general
averaging procedure for vertex-centered box-methods. averaging procedure for vertex-centered box-methods.
Listing \ref{tutorial-coupled:spatialparametersfile} shows the file Listing \ref{tutorial-coupled:spatialparametersfile} shows the file
@ -247,13 +251,16 @@ Listing \ref{tutorial-coupled:spatialparametersfile} shows the file
numberstyle=\tiny, numbersep=5pt, firstline=27]{../../tutorial/tutorialspatialparameters_coupled.hh} numberstyle=\tiny, numbersep=5pt, firstline=27]{../../tutorial/tutorialspatialparameters_coupled.hh}
\end{lst} \end{lst}
First, a spatial parameters type tag has to be defined (line \ref{tutorial-coupled:define-spatialparameters-typetag}), from which the problem type tag inherits the properties, which can be classified as spatial parameter properties (problem file line \ref{tutorial-coupled:create-type-tag}). These are e.g. the spatial parameters class itself (line \ref{tutorial-coupled:set-spatialparameters}) or a certain material law (line \ref{tutorial-coupled:rawlaw} \label{tutorial-coupled:materialLaw}). First, the spatial parameters type tag has to be created (line \ref{tutorial-coupled:define-spatialparameters-typetag}),
from which the problem type tag inherits its properties and which can be classified as spatial parameter properties
(problem file line \ref{tutorial-coupled:create-type-tag}). These are e.g. the spatial parameters class itself (line \ref{tutorial-coupled:set-spatialparameters})
or a certain material law (line \ref{tutorial-coupled:rawlaw} \label{tutorial-coupled:materialLaw}).
\Dumux provides several material laws in the folder \Dumux provides several material laws in the folder
\verb+dumux/material/fluidmatrixinteractions+. \verb+dumux/material/fluidmatrixinteractions+.
The selected one -- here it is a relation according to a regularized version of Brooks \& Corey -- is included The selected one -- here it is a relation according to a regularized version of Brooks \& Corey -- is included
in line \ref{tutorial-coupled:rawLawInclude}. After the selection, in line \ref{tutorial-coupled:rawLawInclude}. After the selection,
an adapter in line \ref{tutorial-coupled:eff2abs} translates between the law an adapter in line \ref{tutorial-coupled:eff2abs} translates between effective saturations, which are employed in the Brooks \& Corey parameterization
for effective values (the Brooks \& Corey model) and the saturations generated as simulations results, i.e. residual saturations are considered. and which deduce the residual saturations, and the simulated saturations.
As the applied raw law knows best which kind of parameters are necessary, As the applied raw law knows best which kind of parameters are necessary,
it provides a parameter class \texttt{RegularizedBrooksCoreyParams} that is it provides a parameter class \texttt{RegularizedBrooksCoreyParams} that is
accessible via the member \texttt{Params} and defined in line accessible via the member \texttt{Params} and defined in line
@ -261,29 +268,28 @@ accessible via the member \texttt{Params} and defined in line
is now instantiated correctly as a private object is now instantiated correctly as a private object
in line \ref{tutorial-coupled:matParamsObject}. in line \ref{tutorial-coupled:matParamsObject}.
In line \ref{tutorial-coupled:permeability} the function returning the In line \ref{tutorial-coupled:permeability} a method returning the
intrinsic permeability can be found. As can be seen, the function has intrinsic permeability can be found. As can be seen, the method has
to be called with three different arguments. to be called with three arguments:
(\texttt{Element}) is again the current element, which also holds information (\texttt{Element}) is again the considered element, which also holds information
about its geometry and position, the second argument about its geometry and position, the second argument
(\texttt{fvElemGeom}) holds information about the finite-volume geometry induced (\texttt{fvElemGeom}) holds information about the finite-volume geometry induced
by the box-method, and the third defines the index of the current sub-control by the box-method, and the third defines the local index of the current sub-control
volume. The intrinsic permeability is a tensor and is thus returned in form of volume. The intrinsic permeability is a tensor and is thus returned in form of
a $\texttt{dim} \times \texttt{dim}$-matrix where \texttt{dim} is the dimension a $\texttt{dim} \times \texttt{dim}$-matrix where \texttt{dim} is the dimension
of the problem. of the problem.
The function \texttt{porosity()} defined in line The method \texttt{porosity()} defined in line
\ref{tutorial-coupled:porosity} is called with the same arguments as \ref{tutorial-coupled:porosity} is called with the same arguments as
the permeability function described before and returns the porosity the permeability function described before and returns the porosity
dependent on the position in the domain. dependent on the position in the domain.
Next, the method \texttt{materialLawParams()} defines in line Next, the method \texttt{materialLawParams()} defines in line
\ref{tutorial-coupled:matLawParams} which \verb+materialLawParams+ object \ref{tutorial-coupled:matLawParams} which \verb+materialLawParams+ object
should be applied at this specific position. Although in this case only one objects is returned, should be applied at this specific position. Although in this case only one object is returned,
in general the problem may be heterogeneous, demanding for different objects at different positions in space. in general the problem may be heterogeneous, returning different objects at different positions in space.
While the selection of the type of this object was already explained (line \ref{tutorial-coupled:rawLawInclude}), While the selection of the type of this object was already explained (line \ref{tutorial-coupled:rawLawInclude}),
some specific parameter some specific parameter values of the applied material law, such as the Brooks \& Corey parameters, are still needed. This is
values of the applied material law are still needed. This is
done in the constructor body (line \ref{tutorial-coupled:setLawParams}). done in the constructor body (line \ref{tutorial-coupled:setLawParams}).
Depending on the type of the \texttt{materialLaw} object, the adequate \texttt{set}-methods Depending on the type of the \texttt{materialLaw} object, the adequate \texttt{set}-methods
are provided by the object to access all necessary parameters are provided by the object to access all necessary parameters
@ -298,13 +304,13 @@ can change soil parameters, boundary conditions and fluid properties
in \Dumux. in \Dumux.
\subsubsection{Exercise 1} \subsubsection{Exercise 1}
\renewcommand{\labelenumi}{\alph{enumi})} For Exercise 1 you only have \renewcommand{\labelenumi}{\alph{enumi})} For Exercise 1 you have
to make some small changes in the tutorial files. to make only some small changes in the tutorial files.
\begin{enumerate} \begin{enumerate}
\item \textbf{Run the Model} \\ \item \textbf{Run the Model} \\
To get an impression what the results should look like you can first run the original version of the coupled tutorial model by typing \texttt{./tutorial\_coupled 5e5 10}. The first number behind the simulation name defines the timespan of the simulation run in seconds, the second number defines the initial time step size. Note that the time step size is automatically optimized during the simulation. For the visualization with paraview please refer to \ref{quick-start-guide}.\\ To get an impression what the results should look like you can first run the original version of the coupled tutorial model by typing \texttt{./tutorial\_coupled 5e5 10}. The first number behind the simulation name defines the time span of the simulation run in seconds, the second number defines the initial time-step size. Note that the time-step size is automatically optimized during the simulation. For the visualization with paraview please refer to \ref{quick-start-guide}.\\
\item \textbf{Changing the Model Domain and the Boundary Conditions} \\ \item \textbf{Changing the Model Domain and the Boundary Conditions} \\
Change the size of the model domain so that you get a rectangle with Change the size of the model domain so that you get a rectangle with
@ -318,7 +324,7 @@ To get an impression what the results should look like you can first run the ori
left boundary should be closed for water and oil fluxes. left boundary should be closed for water and oil fluxes.
Compile the main file by typing \texttt{make tutorial\_coupled} and Compile the main file by typing \texttt{make tutorial\_coupled} and
run the model. run the model as explained above.
\item \textbf{Changing Fluids} \\ \item \textbf{Changing Fluids} \\
@ -332,7 +338,7 @@ If you want to take a closer look on how the fluid classes are defined and which
\item \textbf{Use the \Dumux fluid system} \\ \item \textbf{Use the \Dumux fluid system} \\
\Dumux usually organizes fluid mixtures via a \texttt{fluidsystem}. In order to include a fluidsystem you first have to comment the lines \ref{tutorial-coupled:2p-system-start} to \ref{tutorial-coupled:2p-system-end} in the problem file. If you use eclipse, this can easily be done by pressing \textit{str + shift + 7} -- the same as to cancel the comment later on.\\ \Dumux usually organizes fluid mixtures via a \texttt{fluidsystem}. In order to include a fluidsystem you first have to comment the lines \ref{tutorial-coupled:2p-system-start} to \ref{tutorial-coupled:2p-system-end} in the problem file. If you use eclipse, this can easily be done by pressing \textit{str + shift + 7} -- the same as to cancel the comment later on.\\
Now include the file \texttt{fluidsystems/h2o\_n2\_system.hh} in the material folder, and set a property \texttt{FluidSystem} with the appropriate type, \texttt{Dumux::H2O\_N2\_System<TypeTag>}. However, the complicated fluidsystem uses tabularized fluid data, which need to be initialized in the constructor body of the current problem by adding \texttt{GET\_PROP\_TYPE(TypeTag, PTAG(FluidSystem))::init();}, hence using the initialization function of the applied fluidsystem. As water flow replacing a gas is much faster, test your simulation only until 2e3 seconds and start with a time step of 1 second.\\ Now include the file \texttt{fluidsystems/h2o\_n2\_system.hh} in the material folder, and set a property \texttt{FluidSystem} with the appropriate type, \texttt{Dumux::H2O\_N2\_System<TypeTag>}. However, the complicated fluidsystem uses tabularized fluid data, which need to be initialized in the constructor body of the current problem by adding \texttt{GET\_PROP\_TYPE(TypeTag, FluidSystem)::init();}, hence using the initialization function of the applied fluidsystem. As water flow replacing a gas is much faster, test your simulation only until 2e3 seconds and start with a time step of 1 second.\\
Please reverse the changes of this example, as we still use bulk phases and hence do not need such an extensive fluid system. Please reverse the changes of this example, as we still use bulk phases and hence do not need such an extensive fluid system.
\item \textbf{Changing Constitutive Relations} \\ \item \textbf{Changing Constitutive Relations} \\
@ -363,7 +369,7 @@ of the linear law and the respective \texttt{set}-functions can be found
\end{figure} \end{figure}
domain. You can use the fluids of exercise 1c).\\ domain. You can use the fluids of exercise 1c).\\
Hint: The current position of the element can be obtained via \texttt{element.geometry().center();}.\\ Hint: The current position of the element can be obtained via \texttt{element.geometry().center();}.\\
When does the front cross the material border? In paraview, the option \textit{View} $\rightarrow$ \textit{Animation View} is nice to get a rough feeling of the timestep sizes. When does the front cross the material border? In paraview, the option \textit{View} $\rightarrow$ \textit{Animation View} is nice to get a rough feeling of the time-step sizes.
\end{enumerate} \end{enumerate}
\subsubsection{Exercise 2} \subsubsection{Exercise 2}
@ -439,7 +445,7 @@ compile the program.
Create a new file for benzene called \texttt{benzene.hh} and implement Create a new file for benzene called \texttt{benzene.hh} and implement
a new fluid system. (You may get a hint by looking at existing fluid a new fluid system. (You may get a hint by looking at existing fluid
systems in the directory \verb+/dumux/material/fluidsystems+.) \\ systems in the directory \verb+/dumux/material/fluidsystems+). \\
Use benzene as a new fluid and run the model of Exercise 2 with water Use benzene as a new fluid and run the model of Exercise 2 with water
and benzene. Benzene has a density of $889.51 \, \text{kg} / \text{m}^3$ and benzene. Benzene has a density of $889.51 \, \text{kg} / \text{m}^3$
and a viscosity of $0.00112 \, \text{Pa} \; \text{s}$. and a viscosity of $0.00112 \, \text{Pa} \; \text{s}$.

6
doc/handbook/tutorial.tex
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@ -1,10 +1,10 @@
\chapter[Tutorial]{Tutorial}\label{chp:tutorial} \chapter[Tutorial]{Tutorial}\label{chp:tutorial}
In \Dumux two sorts of models are implemented: Fully-coupled models and decoupled models. In the fully-coupled models a flow system is described by a system of strongly coupled equations, which can be mass balance equations, balance equations of components, energy balance equations, etc. In contrast, a decoupled model consists of a pressure equation which is iteratively coupled to a saturation equation, concentration equations, energy balance equations, etc. In \Dumux two sorts of models are implemented: Fully-coupled models and decoupled models. In the fully-coupled models a flow system is described by a system of strongly coupled equations, which can be for example mass balance equations for phases, mass balance equations for components or energy balance equations. In contrast, a decoupled model consists of a pressure equation, which is iteratively coupled to a saturation equation, concentration equations, energy balance equations, etc.
Examples for different kinds of both coupled and decoupled models are isothermal two-phase models, isothermal two-phase two-component models, non-isothermal two-phase models, non-isothermal two-phase two-component models, etc. Examples for different kinds of both, coupled and decoupled models, are isothermal two-phase models, isothermal two-phase two-component models, non-isothermal two-phase models and non-isothermal two-phase two-component models.
In section \ref{box} a short introduction about the box method is given. The box method is used for the spatial discretization of the system of equations. The other two sections of the tutorial demonstrate how to solve problems using, first, a coupled model (section \ref{tutorial-coupled}) and, second, using a decoupled model (section \ref{tutorial-decoupled}). Being the easiest case, an isothermal two-phase system (two fluid phases, one solid phase) will be considered. In section \ref{box} a short introduction to the box method is given. The box method is used in the fully-coupled models for the spatial discretization of the system of equations. The decoupled models employ usually a cell-centered finite volume scheme. The following two sections of the tutorial demonstrate how to solve problems using, first, a fully-coupled model (section \ref{tutorial-coupled}) and, second, using a decoupled model (section \ref{tutorial-decoupled}). Being the easiest case, an isothermal two-phase system (two fluid phases, one solid phase) will be considered.
\input{tutorial-coupled} \input{tutorial-coupled}
\input{tutorial-decoupled} \input{tutorial-decoupled}
%\input{tutorial-newmodel} %\input{tutorial-newmodel}