An accurate and fast moving mesh Discontinuous Galerkin package for solving the 1D isotropic transport equation for the purpose of coupling to rad-transfer problems
Download the file moving_mesh_radiative_transfer and open the file. Invoke python via python3.
before invoking python, run pytest in the top level folder.
To solve the transport equation for a specific source,
import moving_mesh_transport.solver
Running
solver.run_plane_IC(uncollided = True, Moving = True)
Will read in parameters from moving_mesh_transport/congfig.yaml and run an infininte plane pulse source with a moving mesh and using the uncollided solution. Setting uncollided = False does not use the uncollided solution and moving = False solves the equations with a static mesh. (note: the plane pulse takes much longer to run compared to the other sources due to the higher number of discrete angles required to converge).
The commands,
solver.run_square_IC(uncollided = True, Moving = True)
solver.run_square_s(uncollided = True, Moving = True)
solver.run_gaussian_IC(uncollided = True, Moving = True)
solver.run_gaussian_s(uncollided = True, Moving = True)
solver.run_MMS(uncollided = False, Moving = True)
run a square pulse, a square source, a Gaussian pulse, a Gaussian source, and a MMS (Method of Manufactured Solutions) problem. (note: there is only one case for the MMS source)
The command
solver.run_all()
runs all cases for every source.
The terminal will print a RMSE vallue (root mean square error) compared with the benchmark solution. The order of convergence is displayed as Order. The run data (RMSE, computation time, number of spaces, number of angles) will be saved to run_data_RMS.h5, overwriting previous runs that had the same parameters. A plot will be created of the benchmark solution and the solutions returned by the solver.
To interact with the plots produced by the solver,
import matplotlib.pyplot as plt
run
plt.close()
to close the current plot.
To visualize the accuracy of the results
from moving_mesh_transport.plots import make_plots
run
make_plots.plot_all_rms_cells(tfinal, M)
To plot the results from running solver.run_all() where tfinal is the evaluation time and M is the number of basis functions. For the example case, choose tfinal = 1 and M = 6.
To plot a benchmark solutions,
make_plots.plot_bench(tfinal, source_name, fign)
Where source_name can be plane_IC, square_IC, square_source, gaussian_IC, gaussian_source, or MMS.
If you are interested in re-running the benchmark module (which takes quite a while)
from moving_mesh_transport.benchmarks import make_benchmarks
make_benchmarks.make_all()
will integrate the Greens function solution for the plane pulse and produce benchmark results for all of the sources run by the solver except for the MMS source at times 1, 5, and 10. For this reason, running the solver at other final times will return results but the benchmark solution will be 0 for all x.
In config.yaml certain parameters may be easily changed, such as the final evaluation time, number of basis functions, number of cells in the mesh, and number of discrete angles.