Project file on GitHub
## Overview

## Problem description

### Model setups

#### Diffusion only / Diffusion and Storage

#### Diffusion, Storage, and Advection

*Diffusion, Storage, and Advection* project file
#### Diffusion, Storage, Advection, and Dispersion

#### Diffusion, Storage, Gravity, and Dispersion

*Diffusion, Storage, Gravity, and Dispersion* project file
#### Diffusion, Storage, Advection, and Decay

*Diffusion, Storage, Advection, and Decay* project file
#### Changes With Inclusion of Non Boussinesq-Effects

This benchmark compiles a number of simple, synthetic setups to test different processes of saturated component transport of a solute.

The development of the equation system is given in this PDF. In the following, we present the different setups.

We use quadratic mesh with \(0 < x < 1\) and \(0 < y < 1\) and a resolution of 32 x 32 quad elements with edge length \(0.03125 m\). The domain material is homogeneous and anisotropic. Porosity is \(0.2\), storativity is \(10^{-5}\), intrinic permeability is \(1.239 \cdot 10^{-7} m^2\), dynamic viscosity is \(10^{-3} Pa \cdot s\), fluid density is \(1 kg\cdot m^{-3}\), molecular diffusion is \(10^{-5} m^2\cdot s^{-1}\). If not stated otherwise, retardation coefficient is set to \(R=1\), relation between concentration and density is \(\beta_c = 0\), decay rate is \(\theta = 0\), and dispersivity is \(\alpha = 0\).

Boundary conditions vary on the left side individually for each setup; right side is set as constant Dirichlet concentration \(c=0\); top and bottom are no-flow for flow and component transport. Initial conditions are steady state for flow (for the equivalent boundary conditions respectively) and \(c=0\).

Left side boundary conditions for these two setups are pressure \(p=0\) and concentration \(c=1\). The *Diffusion only* setup results in the final state of the *Diffusion and Storage* setup. For the former, retardation is set to \(R=0\), while for the latter, \(R=1\).

The *Diffusion only* project file

The *Diffusion and Storage* project file

Left side boundary conditions for this setup are pressure \(p=1\) and concentration \(c=1\).

TheLeft side boundary conditions for these setups are pressure \(p=1\) and concentration \(c=1\). The latter is once given over the full left side, and in a second setup over half of the left side. Longitudinal and transverse dispersivity is \(\alpha_l = 1 m\) and \(\alpha_t = 0.1 m\).

The *Diffusion, Storage, Advection, and Dispersion* project file

The *Diffusion, Storage, Advection, and Dispersion Half* project file

Boundary condition for this setup is pressure \(p=0\) for the top left corner and concentration \(c=1\) for half of the left side. Relation between concentration and gravity is \(\beta_c = 1\).

TheLeft side boundary conditions for this setup are pressure \(p=1\) and concentration \(c=1\). Decay rate is \(\theta = 0.001 s^{-1}\).

TheThe changes to the original setup are described in this PDF.

This article was written by Marc Walther. If you are missing something or you find an error please let us know.
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