Constant viscosity

• Parabolic/HT/ConstViscosity/square_5500x5500.prj

Hydro-thermal process

For more details on the hydro-thermal process and its implementation in OpenGeoSys, please see hydro-thermal process page in Processes .

Problem description

This is a 2d benchmark of large-scale thermal convection that tests the temperature and pressure dependent fluid density in the hydro-thermal process monolithic approach implementation. It is defined on the domain $\Omega = [0,5500]^2.$ The fluid density is a Linear model with a temperature slope of $-4.3\cdot 10^{-4}\ \mathrm{K}^{-1}$ and a pressure slope of $0.5\cdot 10^{-9}\ \mathrm{Pa}^{-1}$ about a reference density of $1000\ \mathrm{kg}/\mathrm{m}^3$.

• The initial conditions for the pressure is a gradient starting from zero at the top surface to a pressure of circa 54 mega pascal at the bottom given in the data array initial_pressure in the VTU file. The initial temperature is also almost a gradient from top (293 K) to bottom (443 K) of the domain, except there is a small perturbation given by adding $\sin \left( \pi \frac{y}{5500}\right) \cdot \cos \left( \pi \frac{x}{5500}\right).$ See the following images.

TODO 3 images

• For the pressure we set at the top left point of $\Omega$ a Dirichlet-type boundary condition with a value of zero. On the top of $\Omega$ the temperature is fixed to 293 K (20 degree C), at the bottom of $\Omega$ the temperature is set to 443 K (170 degree C) via Dirichlet-type boundary conditions.
• The further parameter specification can be found in the project file linked at the top of this page.
• The steady state temperature is shown in the following on the right figure. The left figure shows the resulting temperature minus the initial gradient. With the temperature-only density model these temperatures were in good accordance with the FEFLOW results and with results from the OGS version < 6; see the note below the figure for the effect of the pressure dependence.

Comparison with FEFLOW solution

The figure was produced with a temperature-only fluid density model. The pressure dependence added afterwards changes the results, so the figure has not been regenerated and is shown for qualitative comparison only.