@@ -3,20 +3,20 @@ This tutorial was copied from dumux/test/porousmediumflow/tracer/1ptracer.

# One-phase flow with random permeability distribution and a tracer model

## Problem set-up

This example contains a contaminant transported by a base groundwater flow in a randomly distributed permeability field. The figure below shows the simulation set-up. The permeability values range between 6.12e-15 and 1.5 e-7 $`m^2`$. A pressure gradient between the top an the bottom boundary leads to a groundwater flux from the bottom to the top. Neumann no-flow boundaries are assigned to the left and right boundary. Initially, there is a contaminant concentration at the domain bottom.

This example contains a contaminant transported by a base groundwater flow in a randomly distributed permeability field. The figure below shows the simulation set-up. The permeability values range between 6.12e-15 and 1.5 e-7 $`m^2`$. A pressure gradient between the top an the bottom boundary leads to a groundwater flux from the bottom to the top. Neumann no-flow boundaries are assigned to the left and right boundary. Initially, there is a contaminant concentration at the bottom of the domain.

<imgsrc="img/setup.png"width="500">

## Model description

Two different models are applied to simulate the system: In a first step, the groundwater velocity is evaluated under stationary conditions. Therefore the single phase model is applied.

In a second step, the contaminant gets transported based on the on the groundwater velocity field. It is assumed, that the dissolved contaminant does not affect density and viscosity of the groundwater and thus, it is handled as a tracer by the tracer model. The tracer model is then solved instationarily.

In a second step, the contaminant gets transported based on the groundwater velocity field. It is assumed, that the dissolved contaminant does not affect density and viscosity of the groundwater and thus, it is handled as a tracer by the tracer model. The tracer model is then solved instationarily.

### 1p Model

The single phase model uses Darcy's law as the equation for the momentum conservation:

$` \textbf v = - \frac{\textbf K}{\mu} \left(\textbf{grad}\, p - \varrho {\textbf g} \right) `$

With the darcy velocity $` \textbf v `$, the permeability $` \textbf K`$, the viscosity $` \mu`$, the pressure $`p`$, the density $`\rho`$ and the gravity $`\textbf g`$.

With the darcy velocity $` \textbf v `$, the permeability $` \textbf K`$, the dynamic viscosity $` \mu`$, the pressure $`p`$, the density $`\rho`$ and the gravity $`\textbf g`$.

Darcy's law is inserted into the continuity equation:

...

...

@@ -210,7 +210,7 @@ of the finite volume

```cpp

constautoglobalPos=scvf.ipGlobal();

```

we define a small epslon value

we define a small epsilon value

```cpp

Scalareps=1.0e-6;

```

...

...

@@ -473,7 +473,7 @@ We don't use a solution dependent molecular diffusion coefficient:

@@ -3,20 +3,20 @@ This tutorial was copied from dumux/test/porousmediumflow/tracer/1ptracer.

# One-phase flow with random permeability distribution and a tracer model

## Problem set-up

This example contains a contaminant transported by a base groundwater flow in a randomly distributed permeability field. The figure below shows the simulation set-up. The permeability values range between 6.12e-15 and 1.5 e-7 $`m^2`$. A pressure gradient between the top an the bottom boundary leads to a groundwater flux from the bottom to the top. Neumann no-flow boundaries are assigned to the left and right boundary. Initially, there is a contaminant concentration at the domain bottom.

This example contains a contaminant transported by a base groundwater flow in a randomly distributed permeability field. The figure below shows the simulation set-up. The permeability values range between 6.12e-15 and 1.5 e-7 $`m^2`$. A pressure gradient between the top an the bottom boundary leads to a groundwater flux from the bottom to the top. Neumann no-flow boundaries are assigned to the left and right boundary. Initially, there is a contaminant concentration at the bottom of the domain.

<imgsrc="img/setup.png"width="500">

## Model description

Two different models are applied to simulate the system: In a first step, the groundwater velocity is evaluated under stationary conditions. Therefore the single phase model is applied.

In a second step, the contaminant gets transported based on the on the groundwater velocity field. It is assumed, that the dissolved contaminant does not affect density and viscosity of the groundwater and thus, it is handled as a tracer by the tracer model. The tracer model is then solved instationarily.

In a second step, the contaminant gets transported based on the groundwater velocity field. It is assumed, that the dissolved contaminant does not affect density and viscosity of the groundwater and thus, it is handled as a tracer by the tracer model. The tracer model is then solved instationarily.

### 1p Model

The single phase model uses Darcy's law as the equation for the momentum conservation:

$` \textbf v = - \frac{\textbf K}{\mu} \left(\textbf{grad}\, p - \varrho {\textbf g} \right) `$

With the darcy velocity $` \textbf v `$, the permeability $` \textbf K`$, the viscosity $` \mu`$, the pressure $`p`$, the density $`\rho`$ and the gravity $`\textbf g`$.

With the darcy velocity $` \textbf v `$, the permeability $` \textbf K`$, the dynamic viscosity $` \mu`$, the pressure $`p`$, the density $`\rho`$ and the gravity $`\textbf g`$.

Darcy's law is inserted into the continuity equation:

// We create and initialize the solution vector. As the tracer problem is transient, the initial solution defined in the problem is applied to the solution vector.

...

...

@@ -230,7 +230,7 @@ int main(int argc, char** argv) try