The King compressible convection benchmark

The King compressible convection benchmark#

This folder contains input files for the benchmark from King et al. [2010]

King, Scott D., et al. (2010): “A community benchmark for 2-D Cartesian compressible convection in the Earth’s mantle.” Geophysical Journal International 180(1), 73-87.

This includes versions for the ALA and TALA approximations for different values of the Dissipation number Di and the Rayleigh number Ra. The complete input file can be found in ala.prm. All other input files are generated by the script. All models can be started by running


To run a model with a specific set of setting you can modify the loops inside of this script to only generate models you are interested in.

The python script ‘’ can extract the relevant statistics (Nusselt number, root mean square velocity, average temperature, total shear heating and total adiabatic heating in the last time step) of several model runs and copy the results to the screen and a separate file statistics.txt. It also prints a figure of the Nusselt number (heat flux) and convergence rate of the heat flux postprocessors. You can modify which models are plotted inside the script.


Fig. 165 Example convergence of the King benchmark cases with Ra=1e5 and the ALA approximation. Left panel: Nusselt number over cell size h. Right panel: Relative error over cell size. Gray lines indicate the reference values from King et al. [2010] (left panel) and theoretical convergence predicted for different convergence orders (right panel). Dashed lines show a simple heat flux computed as the gradient of temperature, solid lines show the heat flux computed using a consistent boundary flux method.#