Running the code

This code is used to produce the results of this paper. The code is run by python3 main.py k where k represents an experiment number. For example python3 main.py 0gerenates the first table in tables/2D_Hartmann-P2_P1_P1.txt. More on this later. The experiments are generated in pickle files contained in the pickles/ directory. Creating new pickle files will be discussed in the next section.

Changing parameters with pickler.py

All the parameters of the code can be changed through pickler.py. In particular, the workflow is to change the desired parameter(s) in pickler.py, run the command python3 main.py pickle k where k is the number of the new experiment (currently there are 0-7 already in use), and then python3 main.py k will run your experiment with the updated parameters.

Tables, plotting and XMLs

The code by default writes the LaTeX tables to the tables/ directory. The files therein are organized by first the number of dimensions (currently 2D for all experiments in the article) then experiement name (Hartmann or lid_driven) then the polynomial order for the primal product space e.g. P2_P1_P1 for (u, p, B). The tables are printed out in LaTeX table format so they can be easily copied and pasted. You can toggle plotting by the do_plotting flag in pickler.py. Finally, for the lid driven cavity, the solution automatically gets saved in the XMLs directory. Then, the next time the specific parameters are used, the saved file is read in as an inital guess for the nonlinear solver. This allows for the homotopy argument for the Reynold's number.

Pickle files 4-7 for the lid driven cavity

For these experiments, an initial guess is being loaded from the files in the folder init_guesses which can be extracted tar -xvf init_guesses.tar. This is necessary to run the lid driven cavity tests, since the solver stalls for large Reynold's number.

Running in parallel

Thanks to the magic of FEniCS, one can seamlessly run the code in parallel by using mpiexec -n <np> python3 main.py k.

Collaborators

Ari Rappaport - Inria, Paris
Jehanzeb Chaudhry - University of New Mexico
John Shadid - University of New Mexico/Sandia National Laboratories
J. Chaudhry’s work is supported by the NSF-DMS 1720402