diff --git a/doc/handbook/tutorial-coupled.tex b/doc/handbook/tutorial-coupled.tex
index 27dc0f1b21b34efb29a6133c4cbe69b21157a16a..8baa6370df76b2ac2f01b74a381916ce8b824c6a 100644
--- a/doc/handbook/tutorial-coupled.tex
+++ b/doc/handbook/tutorial-coupled.tex
@@ -265,7 +265,7 @@ the \textit{relative permeability}, the \textit{porosity}, the
parameters are defined using a so-called \textit{spatial parameters}
class.
-If the box discretization is to used, the spatial parameters class
+If the box discretization is used, the spatial parameters class
should be derived from the base class
\texttt{Dumux::BoxSpatialParams<TypeTag>}. Listing
\ref{tutorial-coupled:spatialparametersfile} shows the file \\
@@ -371,8 +371,8 @@ For the visualization of the results using paraview please refer to section \ref
edge lengths of $\text{x} = \unit[400]{m}$ and $\text{y} = \unit[500]{m}$ and with
discretization lengths of $\Delta \text{x} = \unit[20]{m}$ and $\Delta
\text{y} = \unit[20]{m}$. For this you have to edit the parameter file (\texttt{tutorialproblem\_coupled.input})
- and run the programme again.\\
- Note, that you do not have to recompile the programme if you make changes to the parameter file.
+ and run the program again.\\
+ Note, that you do not have to recompile the program if you make changes to the parameter file.
Change the boundary conditions in the file
@@ -389,8 +389,8 @@ For the visualization of the results using paraview please refer to section \ref
simplex grids, like \texttt{ALUGrid}. If this is not the case please skip this exercise.
Change the types of elements used for discretizing the domain. In line \ref{tutorial-coupled:set-gridcreator} of the problem
file the type of gridcreator is chosen. By choosing a different grid creator you can discretize the domain with different elements.
- Hint: You can find gridcreators in \texttt{dumux/common/}, change for example from \texttt{cubegridcreator.hh} to \texttt{simplexgridcreator.hh}.
- Besides having to change the grid creator it is also necessary to change the ALUGrid type in line \ref{tutorial-coupled:set-grid} from \texttt{Dune::cube}
+ Hint: You can find gridcreators in \texttt{dumux/io/}, change for example from \texttt{cubegridcreator.hh} to \texttt{simplexgridcreator.hh}.
+ Besides having to change the grid creator it is also necessary to change the ALUGrid type in line \ref{tutorial-coupled:set-grid-ALU} from \texttt{Dune::cube}
to \texttt{Dune::simplex}.
The shape of the employed elements can be visualized in paraview by choosing \texttt{Surface with Edges}.
@@ -423,11 +423,11 @@ However, this is a rather complicated fluid system which
considers mixtures of components and also uses tabulated components that need to be initialized -- i.e. the tables need to be filled with values.
The initialization of the fluid system is normally done in the constructor of the problem by calling \texttt{GET\_PROP\_TYPE(TypeTag, FluidSystem)::init();}.
Remember that the constructor function always has the same name as the respective class, i.e. \texttt{TutorialProblemCoupled(..)}.\\
-As water flow replacing a gas is much faster, test your simulation only until $2000$ seconds and start with a time step of $1$ second.\\
+As water flow replacing a gas is much faster, test your simulation only until $2000$ seconds and start with a time-step of $1$ second.\\
Please reverse the changes made in this part of the exercise, as we will continue to use immiscible phases from here on and hence do not need a complex fluid system.
\item \textbf{Changing Constitutive Relations} \\
- Use an unregularized linear law with an entry pressure of $p_e = 0.0\;\text{Pa}$ and maximal capillary pressure of e.g. $p_{c_{max}} = 2000.0\;\text{Pa}$ instead of using a
+ Use an unregularized linear law with an entry pressure of $p_e = \unit[0.0]{Pa}$ and maximal capillary pressure of e.g. $p_{c_{max}} = \unit[2000.0]{Pa}$ instead of using a
regularized Brooks-Corey law for the
relative permeability and for the capillary pressure saturation relationship. To do that you have
to change the material law property (line \ref{tutorial-coupled:eff2abs}) in \texttt{tutorialspatialparams\_coupled.hh}. Leave the type definition of \texttt{Scalar} and remove
@@ -444,7 +444,7 @@ Call the \texttt{set}-functions from the constructor of the \texttt{tutorialspat
Set up a model domain with the soil properties given in Figure
\ref{tutorial-coupled:exercise1_d}. Adjust the boundary conditions
so that water is again flowing from the left to the right of the
-\begin{figure}[bt]
+\begin{figure}[ht]
\centering
\begin{tikzpicture}[>=latex]
% basic sketch
@@ -464,7 +464,7 @@ Call the \texttt{set}-functions from the constructor of the \texttt{tutorialspat
\end{tikzpicture}
\caption{Exercise 1g: Set-up of a model domain with a heterogeneity. Grid spacing: $\Delta x = \unit[20]{m}$ $\Delta y = \unit[20]{m}$.}\label{tutorial-coupled:exercise1_d}
\end{figure}
-domain. You can use the fluids of exercise 1b).\\
+domain. You can use the fluids of exercise 1b.\\
\textbf{Hint:} The current position of the control volume can be obtained using \texttt{element\allowbreak.geometry()\allowbreak.corner(scvIdx)}, which
returns a vector of the global coordinates of the current position.\\
When does the front cross the material border? In paraview, the
@@ -483,7 +483,7 @@ The new files should contain the definition of new classes with names
that relate to the file name, such as
\texttt{Ex2TutorialProblemCoupled}. Make sure that you also adjust the
guardian macros in lines \ref{tutorial-coupled:guardian1} and
-\ref{tutorial-coupled:guardian1}
+\ref{tutorial-coupled:guardian2}
in the header files (e.g. change
\mbox{\texttt{DUMUX\_TUTORIALPROBLEM\_COUPLED\_HH}} to\\
\mbox{\texttt{DUMUX\_EX2\_TUTORIALPROBLEM\_COUPLED\_HH}}). Include the new problem file in \texttt{tutorial\_coupled.cc}.
@@ -502,11 +502,11 @@ After this, change the run-time parameters so that they match the
domain described by figure \ref{tutorial-coupled:ex2_Domain}. Adapt
the problem class so that the boundary conditions are consistent with
figure \ref{tutorial-coupled:ex2_BC}. Initially, the domain is fully
-saturated with water and the pressure is $p_w = 5 \times
-10^5\;\text{Pa}$. Oil infiltrates from the left side. Create a grid
+saturated with water and the pressure is $p_w = \unit[5 \times
+10^5]{Pa}$. Oil infiltrates from the left side. Create a grid
with $20$ cells in $x$-direction and $10$ cells in $y$-direction. The
-simulation time should be set to $10^6\;\text{s}$ with an
-initial time step size of $100\;\text{s}$. Then, you can compile the program.
+simulation time should be set to $\unit[10^6]{s}$ with an
+initial time-step size of $\unit[100]{s}$. Then, you can compile the program.
\begin{figure}[ht]
@@ -567,7 +567,7 @@ initial time step size of $100\;\text{s}$. Then, you can compile the program.
\end{figure}
\begin{itemize}
- \item Increase the simulation time to e.g. $4\times 10^7 \;\text{s}$. Investigate the saturation: Is the value range reasonable?
+ \item Increase the simulation time to e.g. $\unit[4\times 10^7]{s}$. Investigate the saturation: Is the value range reasonable?
\item What happens if you increase the resolution of the grid?
\end{itemize}
@@ -596,8 +596,88 @@ Create a new file for the benzene component called \texttt{benzene.hh}
and implement a new component. (You may get a hint by looking at
existing components in the directory \verb+/dumux/material/components+). \\
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 a viscosity of $0.00112 \, \text{Pa} \; \text{s}$.
+and benzene. Benzene has a density of $889.51\,\text{kg} /
+\text{m}^3$ and a viscosity of $0.00112\,\text{Pa} \, \text{s}$.
+
+
+\subsubsection{Exercise 5: Time Dependent Boundary Conditions}
+
+In this exercise we want to investigate the influence of time dependent boundary conditions. For this, redo the steps of exercise 2 and create a new problem and spatial parameters file.
+
+After this, change the run-time parameters so that they match the
+domain described by figure \ref{tutorial-coupled:ex5_Domain}. Adapt
+the problem class so that the boundary conditions are consistent with
+figure \ref{tutorial-coupled:ex5_BC}. Here you can see the time dependence of the nonwetting saturation, where water infiltrates only during $\unit[10^5]{s}$ and $\unit[4 \cdot 10^5]{s}$. To implement these time dependencies you need the actual time $t_{n+1}=t_n + \Delta t$ and the endtime of the simulation. For this you can use the methods \texttt{this->timeManager().time()}, \texttt{this->timeManager().timeStepSize()} and \texttt{this->timeManager().endtime()}.
+
+Initially, the domain is fully saturated with oil and the pressure is $p_w = 2 \times
+10^5\,\text{Pa}$. Water infiltrates from the left side. Create a grid
+with $100$ cells in $x$-direction and $10$ cells in $y$-direction. The
+simulation time should be set to $5 \cdot 10^5\,\text{s}$ with an
+initial time-step size of $10\,\text{s}$. To avoid too big time-step sizes you should set the parameter \texttt{MaxTimeStepSize} for the group \texttt{TimeManager} (in your input file) to $\unit[1000]{s}$. Then, you can compile the program.
+
+\begin{figure}[ht]
+\centering
+\begin{tikzpicture}[scale=0.7,>=latex]
+ % basic sketch
+ \fill [pattern=north west lines] (0,0) rectangle ++(10,-0.25);
+ \fill [pattern=north west lines] (0,5) rectangle ++(10,0.25);
+ \draw (0,0) rectangle ++(10,5);
+ \foreach \y in {0.5,1.5,...,4.5}
+ \draw [->](10.2,\y) -- ++(0.8,0);
+ % arrows
+ \draw[|<->|] (-0.2,0) -- ++(0,5);
+ \node [anchor=east] at (-0.2,1.5){$\unit[50]{m}$};
+ \draw[|<->|] (0,5.35) -- ++(10,0);
+ \node [anchor=south] at (2.5,5.2){$\unit[100]{m}$};
+ % labels
+ \node [anchor=south] at (5,5.25){no flow};
+ \node [anchor=north] at (5,-0.25){no flow};
+ \node [anchor=west] at(11,2){$q_n = \unitfrac[1 \cdot 10^{-3}]{kg}{m^2 s}$};
+ \node [anchor=west] at(11,3){$q_w = 0$};
+ \node [anchor=west] at(-4,2){$S_n(t)$};
+ \node [anchor=west] at(-4,3){$p_w = \unit[2 \cdot 10^5]{Pa}$};
+ \node [anchor=south west] at (2.5,3.4){$\mathbf{K} = \unit[10^{-7}]{m^2}$};
+ \node [anchor=south west] at (2.5,2.6){$\phi = 0.2$};
+ \node [anchor=south west] at (2.5,1.8){\textsc{Brooks-Corey Law}};
+ \node [anchor=south west] at (2.5,1.0){$\lambda = 2, \; p_e = \unit[500]{Pa}$};
+\end{tikzpicture}
+\caption{Set-up of the model domain and the soil parameters}\label{tutorial-coupled:ex5_Domain}
+\end{figure}
+
+\begin{figure}[ht]
+\centering
+\begin{tikzpicture}[scale=0.9,>=latex]
+ % Draw axes
+ \draw [<->,thick] (0,6) node (yaxis) [above] {$S_n$}
+ |- (11,0) node (xaxis) [right] {time\,[s]};
+ \draw plot[smooth,samples=100,domain=0:1] (6*\x + 2 ,{5*sin((\x+1)*pi r)+5});
+ \draw [-] (0,5) -- (2,5);
+ \draw [-] (8,5) -- (10,5);
+ \draw [dashed] (2,5) -- (2,0);
+ \draw [dashed] (8,5) -- (8,0);
+ \draw [dashed] (10,5) -- (10,0);
+
+ % axes labeling
+ \draw [-] (-0.1,5) -- (0.1,5);
+ \node [anchor=west] at(-0.5,5){$1$};
+ \draw [-] (-0.1,0) -- (0.1,0);
+ \node [anchor=west] at(-0.5,0){$0$};
+ \draw [-] (2,0.1) -- (2,-0.1);
+ \node [anchor=west] at(1.5,-0.4){$1\cdot10^{5}$};
+ \draw [-] (8,0.1) -- (8,-0.1);
+ \node [anchor=west] at(7.5,-0.4){$4\cdot10^{5}$};
+ \draw [-] (10,0.1) -- (10,-0.1);
+ \node [anchor=west] at(9.5,-0.4){$5\cdot10^{5}$};
+
+ \node [anchor=base] at (5,3){$1-\sin(\pi\frac{\text{time}-10^5}{3\cdot 10^5 })$};
+\end{tikzpicture}
+\caption{Time Dependent Boundary Conditions}\label{tutorial-coupled:ex5_BC}
+\end{figure}
+
+\begin{itemize}
+ \item Open paraview and plot the values of $S_n$ at time $\unit[5 \cdot 10^5]{s}$ over the $x$-axis.\\ (\texttt{Filter->Data Analysis->Plot Over Line})
+ \item What happens without any time-step restriction?
+\end{itemize}
\clearpage \newpage
%%% Local Variables:
diff --git a/doc/handbook/tutorial-decoupled.tex b/doc/handbook/tutorial-decoupled.tex
index 4d9d529be4e8175b21d06de50d99455a54be935c..9753d70fdc4ecb969df25806ab56843ef832084e 100644
--- a/doc/handbook/tutorial-decoupled.tex
+++ b/doc/handbook/tutorial-decoupled.tex
@@ -141,7 +141,7 @@ for the problem of interest are specified in line
Now we arrive at some model parameters of the applied two-phase decoupled
model. First, in line \ref{tutorial-decoupled:cflflux} a flux function for the evaluation of the cfl-criterion is defined. This is optional as there exists also a default flux function. The choice depends on the problem which has to be solved. For cases which are not advection dominated the one chosen here is more reasonable.
Line \ref{tutorial-decoupled:cflfactor} assigns the CFL-factor to be used in the
-simulation run, which scales the time step size (kind of security factor). The last property in line \ref{tutorial-decoupled:gravity}
+simulation run, which scales the time-step size (kind of security factor). The last property in line \ref{tutorial-decoupled:gravity}
is optional and tells the model not to use gravity.
After all necessary information is written into the property system and
@@ -153,12 +153,12 @@ As its property, the problem class itself is also derived from a parent,
which is not needed in this tutorial.
Beside the definition of the boundary and initial conditions (discussed in
-subsection \ref{tutorial-coupled:problem} from 4$^th$ paragraph on page \pageref{tutorial-coupled:boundaryStart}), the problem class also contains
+subsection \ref{tutorial-coupled:problem} from 4$^{th}$ paragraph on page \pageref{tutorial-coupled:boundaryStart}), the problem class also contains
general information about the current simulation. First, the name used by
the \texttt{VTK-writer} to generate output is defined in the method of line
\ref{tutorial-decoupled:name}, and line \ref{tutorial-decoupled:restart} indicates
whether restart files are written. As decoupled schemes usually feature small
-timesteps, it can be usefull to set an output interval larger than 1. The respective function is called in line \ref{tutorial-decoupled:outputinterval}, which gets the output interval as argument.
+time-steps, it can be usefull to set an output interval larger than 1. The respective function is called in line \ref{tutorial-decoupled:outputinterval}, which gets the output interval as argument.
The following methods all have in common that they may be dependent on space.
Hence, they all have either an \texttt{element} or an \texttt{intersection} as their
@@ -181,7 +181,7 @@ Listing \ref{tutorial-decoupled:spatialparamsfile} shows the file
\end{lst}
As this file only slightly differs from the coupled version, consult
chapter \ref{tutorial-coupled:description-spatialParameters} for explanations.
-However, as a standard Finite-Volume--scheme is used, in contrast to the box-method
+However, as a standard Finite Volume scheme is used, in contrast to the box-method
in the coupled case, the argument list here is the same as for the problem
functions: Either an \texttt{element}, or only the global position if the function is called \texttt{...AtPos(...)}.
@@ -198,7 +198,7 @@ For Exercise 1 you only have to make some small changes in the tutorial files.
\item \textbf{Altering output}
To get an impression what the results should look like you can first run the original version of the decoupled tutorial model by typing \texttt{./tutorial\_decoupled}. The runtime parameters which are set can be found in the input file (listing~\ref{tutorial-decoupled:parameter-file}). If the input file has the same name than the main file (e.g. \texttt{tutorial\_decoupled.cc} and \texttt{tutorial\_decoupled.input}), it is automatically chosen. If the name differs the program has to be started typing \texttt{./tutorial\_decoupled -parameterFile <filename>.input}. For more options you can also type \texttt{./tutorial\_decoupled -h}. For the visualisation with paraview please refer to \ref{quick-start-guide}.\\
-As you can see, the simulation creates many output files. To reduce these in order to perform longer simulations, change the method responsible for output (line \ref{tutorial-decoupled:outputinterval} in the file \texttt{tutorialproblem\_decoupled}) as to write an output only every 20 timesteps. Compile the main file by typing \texttt{make tutorial\_decoupled} and run the model. Now, run the simulation for 5e5 seconds.
+As you can see, the simulation creates many output files. To reduce these in order to perform longer simulations, change the method responsible for output (line \ref{tutorial-decoupled:outputinterval} in the file \texttt{tutorialproblem\_decoupled}) as to write an output only every 20 time-steps. Compile the main file by typing \texttt{make tutorial\_decoupled} and run the model. Now, run the simulation for 5e5 seconds.
\item \textbf{Changing the Model Domain and the Boundary Conditions} \\
Change the size of the model domain so that you get a rectangle
@@ -209,17 +209,17 @@ Change the boundary conditions in the file \texttt{tutorialproblem\_decoupled.hh
Now you can change the fluids. Use DNAPL instead of Oil and Brine instead of Water. To do that you have to select different components via the property system in the problem file:
\begin{enumerate}
\item Brine: The class \texttt{Dumux::Brine} acts as an adapter to the fluid system that alters a pure water class by adding some salt. Hence, the class \texttt{Dumux::Brine} uses a pure water class, such as \texttt{Dumux::H2O}, as a second template argument after the data type \texttt{<Scalar>} as a template argument (be sure to use the complete water class with its own template parameter).
- \item DNAPL: A standard set of chemical substances, such as Water and Brine, is already included (via a list of \texttt{\#include ..} commandos) and hence easily accessible by default. This is not the case for the class \texttt{Dumux::SimpleDNAPL}, however, which is located in the folder \texttt{dumux/material/components/}. Try to include the file as well as select the component via the property system.
+ \item DNAPL: A standard set of chemical substances, such as Water and Brine, is already included (via a list of \texttt{\#include ..} commandos) and hence easily accessible by default. This is not the case for the class \texttt{Dumux::DNAPL}, however, which is located in the folder \texttt{dumux/material/components/}. Try to include the file as well as select the component via the property system.
\end{enumerate}
If you want to take a closer look at how the fluid classes are defined and which substances are already available please browse through the files in the directory
\texttt{/dumux/material/components}.
\item \textbf{Use the \Dumux fluid system}\label{dec-ex1-fluidsystem} \\
-\Dumux usually organizes fluid mixtures via a \texttt{fluidsystem}, see also chapter \ref{sec:fluidframework}. 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}, see also chapter \ref{sec:fluidframework}. In order to include a fluidsystem you first have to comment the lines \ref{tutorial-decoupled:2p-system-start} to \ref{tutorial-decoupled: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/h2oairsystem.hh} in the material folder, and set a property \texttt{FluidSystem} with the appropriate type, \texttt{Dumux::H2OAirFluidSystem<TypeTag>}. However, this rather complicated fluidsystem uses tabularized fluid data, which need to be initialized (i.e. the tables need to be filled with values) in the constructor body of the current problem by adding \texttt{GET\_PROP\_TYPE(TypeTag, FluidSystem)::init();}. Remember that the constructor function always has the same name as the respective class, i.e. \texttt{TutorialProblemDecoupled(..)}.\\
To avoid the initialization, use the simpler version of water \texttt{Dumux::SimpleH2O} or a non-tabulated version \texttt{Dumux::H2O}. This can be done by setting the property \texttt{Components} type \texttt{H2O},
as is done in all the test problems of the decoupled 2p2c model.\\
-The density of the gas is magnitudes smaller than that of oil, so please decrease the injection rate to $q_n = -3 \times 10^{-4}$ $\left[\frac{\textnormal{kg}}{\textnormal{m}^2 \textnormal{s}}\right]$. Also reduce the simulation duration to 2e4 seconds.\\
+The density of the gas is magnitudes smaller than that of oil, so please decrease the outfow rate to $q_n = 3 \times 10^{-4}$ $\left[\frac{\textnormal{kg}}{\textnormal{m}^2 \textnormal{s}}\right]$. Also reduce the simulation duration to 2e4 seconds.\\
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{Heterogeneities} \\
@@ -245,7 +245,7 @@ Set up a model domain with the soil properties given in figure \ref{tutorial-deo
\caption{Exercise 1d: Set-up of a model domain a heterogeneity. $\Delta x = \Delta y = \unit[20]{m}$.}
\label{tutorial-deoucpled:exercise1_d}
\end{figure}
-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}
\subsubsection{Exercise 2}
@@ -271,10 +271,10 @@ After this, change the domain size (parameter input file) to match the domain de
by figure \ref{tutorial-decoupled:ex2_Domain}. Adapt the problem class
so that the boundary conditions are consistent with figure
\ref{tutorial-decoupled:ex2_BC}. Initially, the domain is fully saturated
-with water and the pressure is $p_w = 2 \times 10^5 \text{Pa}$ . Oil
+with water and the pressure is $p_w = 2 \times 10^5 \, \text{Pa}$ . Oil
infiltrates from the left side. Create a grid with $20$ cells in
$x$-direction and $10$ cells in $y$-direction. The simulation time
-should be set to $2e4 \text{s}$.
+should be set to $\unit[1e6]{s}$.
Now include your new problem file in the main file and replace the
\texttt{TutorialProblemDecoupled} type tag by the one you've created and
@@ -305,13 +305,13 @@ compile the program.
\node [anchor=south west] at (11,5.4){$\mathbf{K} = \unit[10^{-7}]{m^2}$};
\node [anchor=south west] at (11,4.6){$\phi = 0.2$};
\node [anchor=south west] at (11,3.8){\textsc{Brooks-Corey Law}};
- \node [anchor=south west] at (11,3.0){$\lambda = 1.8, p_b = \unit[1000]{Pa}$};
+ \node [anchor=south west] at (11,3.0){$\lambda = 1.8, p_e = \unit[1000]{Pa}$};
\draw [->] (11,4) -- (9.5,2.5);
\draw [dashed] (11,-1) rectangle ++(7,3.5);
\node [anchor=south west] at (11,1.4){$\mathbf{K} = \unit[10^{-9}]{m^2}$};
\node [anchor=south west] at (11,0.6){$\phi = 0.15$};
\node [anchor=south west] at (11,-0.2){\textsc{Brooks-Corey Law}};
- \node [anchor=south west] at (11,-1.0){$\lambda = 2, p_b = \unit[500]{Pa}$};
+ \node [anchor=south west] at (11,-1.0){$\lambda = 2, p_e = \unit[1500]{Pa}$};
\draw [->] (11,1.5) -- (7,2.5);
\end{tikzpicture}
\caption{Set-up of the model domain and the soil parameters}\label{tutorial-decoupled:ex2_Domain}
@@ -331,7 +331,7 @@ compile the program.
\node [anchor=south] at (5,5.25){no flow};
\node [anchor=north] at (5,-0.25){no flow};
\node [anchor=west] at(11,2){$q_n = 0$};
- \node [anchor=west] at(11,3){$q_w = \unitfrac[3 \cdot 10^{-4}]{kg}{m^2 s}$};
+ \node [anchor=west] at(11,3){$q_w = \unitfrac[2 \cdot 10^{-4}]{kg}{m^2 s}$};
\node [anchor=west] at(-4,2){$S_w = 0$};
\node [anchor=west] at(-4,3){$p_w = \unit[2 \cdot 10^5]{Pa}$};
\end{tikzpicture}
@@ -339,7 +339,7 @@ compile the program.
\end{figure}
\begin{itemize}
- \item What happens if you increase the resolution of the grid? Hint: Paraview can visualize the timesteps via the ``Animation View'' (to be enabled unter the button \textit{View}).
+ \item What happens if you increase the resolution of the grid? Hint: Paraview can visualize the time-steps via the ``Animation View'' (to be enabled unter the button \textit{View}).
\item Set the CFL-factor to 1 and investigate the saturation: Is the value range reasonable?
\item Further increase the CFL-factor to 2 and investigate the saturation.
\end{itemize}
@@ -356,10 +356,85 @@ systems in the directory \verb+/dumux/material/fluidsystems+.)
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 a viscosity of $0.00112 \, \text{Pa} \; \text{s}$.
+and a viscosity of $0.00112 \, \text{Pa} \, \text{s}$.
+\subsubsection{Exercise 5: Time Dependent Boundary Conditions}
-\subsubsection{Exercise 5}
+In this exercise we want to investigate the influence of time dependent boundary conditions. For this, redo the steps of exercise 2 and create a new problem and spatial parameters file.
+
+After this, change the run-time parameters so that they match the
+domain described by figure \ref{tutorial-decoupled:ex5_Domain}. Adapt
+the problem class so that the boundary conditions are consistent with
+figure \ref{tutorial-decoupled:ex5_BC}. Here you can see the time dependence of the wetting saturation, where water infiltrates only during $10^5\,\text{s}$ and $4 \cdot 10^5\,\text{s}$. To implement these time dependencies you need the actual time $t_{n+1}=t_n + \Delta t$ and the endtime of the simulation. For this you can use the methods \texttt{this->timeManager().time()}, \texttt{this->timeManager().timeStepSize()} and \texttt{this->timeManager().endtime()}.
+
+Initially, the domain is fully saturated with oil and the pressure is $p_w = 2 \times
+10^5\,\text{Pa}$. Water infiltrates from the left side. Create a grid
+with $100$ cells in $x$-direction and $10$ cells in $y$-direction. The
+simulation time should be set to $5 \cdot 10^5\,\text{s}$ with an
+initial time-step size of $10\,\text{s}$. To avoid too big time-step sizes you should set the parameter \texttt{MaxTimeStepSize} for the group \texttt{TimeManager} (in your input file) to $\unit[100]{s}$. You should only create output files every $100^{th}$ time-step (see exercise 1a). Then, you can compile the program.
+
+\begin{figure}[ht]
+\centering
+\begin{tikzpicture}[scale=0.7,>=latex]
+ % basic sketch
+ \fill [pattern=north west lines] (0,0) rectangle ++(10,-0.25);
+ \fill [pattern=north west lines] (0,5) rectangle ++(10,0.25);
+ \draw (0,0) rectangle ++(10,5);
+ \foreach \y in {0.5,1.5,...,4.5}
+ \draw [->](10.2,\y) -- ++(0.8,0);
+ % arrows
+ \draw[|<->|] (-0.2,0) -- ++(0,5);
+ \node [anchor=east] at (-0.2,1.5){$\unit[50]{m}$};
+ \draw[|<->|] (0,5.35) -- ++(10,0);
+ \node [anchor=south] at (2.5,5.2){$\unit[100]{m}$};
+ % labels
+ \node [anchor=south] at (5,5.25){no flow};
+ \node [anchor=north] at (5,-0.25){no flow};
+ \node [anchor=west] at(11,2){$q_n = \unitfrac[1 \cdot 10^{-3}]{kg}{m^2 s}$};
+ \node [anchor=west] at(11,3){$q_w = 0$};
+ \node [anchor=west] at(-4,2){$S_w(t)$};
+ \node [anchor=west] at(-4,3){$p_w = \unit[2 \cdot 10^5]{Pa}$};
+ \node [anchor=south west] at (2.5,3.4){$\mathbf{K} = \unit[10^{-7}]{m^2}$};
+ \node [anchor=south west] at (2.5,2.6){$\phi = 0.2$};
+ \node [anchor=south west] at (2.5,1.8){\textsc{Brooks-Corey Law}};
+ \node [anchor=south west] at (2.5,1.0){$\lambda = 2, \; p_e = \unit[500]{Pa}$};
+\end{tikzpicture}
+\caption{Set-up of the model domain and the soil parameters}\label{tutorial-decoupled:ex5_Domain}
+\end{figure}
+
+% \draw (0,0) sin (5,5) cos (10,0);
+\begin{figure}[ht]
+\centering
+\begin{tikzpicture}[scale=0.9,>=latex]
+ % Draw axes
+ \draw [<->,thick] (0,6) node (yaxis) [above] {$S_w$}
+ |- (11,0) node (xaxis) [right] {time\,[s]};
+ \draw plot[smooth,samples=100,domain=0:1] (6*\x + 2 ,{5*sin((\x)*pi r)});
+ \draw [dashed] (0,5) -- (5,5);
+
+ % axes labeling
+ \draw [-] (-0.1,5) -- (0.1,5);
+ \node [anchor=west] at(-0.5,5){$1$};
+ \draw [-] (-0.1,0) -- (0.1,0);
+ \node [anchor=west] at(-0.5,0){$0$};
+ \draw [-] (2,0.1) -- (2,-0.1);
+ \node [anchor=west] at(1.5,-0.4){$1\cdot10^{5}$};
+ \draw [-] (8,0.1) -- (8,-0.1);
+ \node [anchor=west] at(7.5,-0.4){$4\cdot10^{5}$};
+ \draw [-] (10,0.1) -- (10,-0.1);
+ \node [anchor=west] at(9.5,-0.4){$5\cdot10^{5}$};
+
+ \node [anchor=base] at (5,2){$\sin(\pi\frac{\text{time}-10^5}{3\cdot 10^5 })$};
+\end{tikzpicture}
+\caption{Time Dependent Boundary Conditions}\label{tutorial-decoupled:ex5_BC}
+\end{figure}
+
+\begin{itemize}
+ \item Open paraview and plot the values of $S_w$ at time $\unit[5 \cdot 10^5]{s}$ over the $x-$axis.\\ (\texttt{Filter->Data Analysis->Plot Over Line})
+ \item What happens without any time-step restriction?
+\end{itemize}
+
+\subsubsection{Exercise 6}
If both the coupled and the decoupled tutorial are completed, one should have noticed that the function arguments in the problem function differ slighty, as the numerical models differ. However, both are functions that depend on space, so both models can also work with functions based ond \mbox{\texttt{...AtPos(GlobalPosition \& globalPos)}}, no matter if we model coupled or decoupled. Try to formulate a spatial parameters file that works with both problems, the coupled and the decoupled. Therein, only use functions at the position.
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