movingmeshradiative_transfer

An accurate and fast moving mesh Discontinuous Galerkin package for solving the 1D isotropic transport equation with or without material energy coupling

Quick start guide

Installation

Download the file moving_mesh_radiative_transfer. Navigate to file location.

Invoke python via python3 -i imports.py.

The program will automatically load the input script transport.yaml. More on input scripts in the next section.

loader is initiated with: load_sol(self, problem_name = 'transport', source_name = 'square_s', rad_or_transfer = 'rad', c = 1.0, s2 = False, cv0 = 0.0)

To simply load precomputed transport results, loader.call_sol(tfinal, M, x0_or_sigma, N_space, mat_or_rad, uncollided, moving)

tfinal: Evaluation time

M: Number of basis functions -1

x0_or_sigma: Relevant for the square and Gaussian sources

N_space: Number of cells

'matorrad': Either 'mat' for material energy density or 'rad' for radiation energy density

uncollided: True or False

moving: True or False

Now, loader.xs returns the spatial points, loader.phi gives the scalar flux, and loader.e gives the material energy density. It is also possible to load the coefficients of the polynomial expansion and the quadrature weights for calculating phi, loader.coeff_mat and loader.ws.

To load results from other radiative transfer problems, loader = load(problem_name, source_name, rad_or_transfer, c, s2, cv0) where

problem_name: is one of ['transport','su_olson', 'su_olson_s2', 'su_olson_s2_thick', 'rad_transfer_const_cv', 'rad_transfer_const_cv_thick', 'rad_transfer_const_cv_s2', 'rad_transfer_const_cv_thick_s2']

source_name: is one of ['plane_IC', 'square_IC', 'gaussian_IC', 'square_source', 'gaussian_source']

rad_or_transfer: is 'rad' for all transport problems and 'transfer' for radiative transfer problems.

c: is the scattering ratio

s2: True or False

cv0: only applies to constant cv cases.

Solver

The solver is automatically imported as run after running imports.py. transport is the default problem, but it can be changed by

run.load(problem_name)

where problem name is one of `['transport','suolson', 'suolsons2', 'suolsons2thick', 'radtransferconstcv', 'radtransferconstcvthick', 'radtransferconstcvs2', 'radtransferconstcvthicks2']'

To actually solve the problem with the parameters given in the chosen input script, run one of:

solver.run_square_IC(uncollided = True, Moving = True)

solver.run_square_source(uncollided = True, Moving = True)

solver.run_gaussian_IC(uncollided = True, Moving = True)

solver.run_gaussian_source(uncollided = True, Moving = True)

`` solver.run_MMS(uncollided = False, Moving = True)

solver.run_plane_IC(uncollided = True, Moving = True)

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).

(note: there is only one case for the MMS source: `uncollided=False, moving=True' and only for transport porlbems)

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 rundataRMS.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 close the plots produced by the solver,

plt.close()

Input scripts

The YAML input scripts, found in the folder, moving_mesh_transport/input_scripts, allow the user to easily modify the problem parameters without quitting python (Or re-compiling all of the functions that numba compiles on the first run.) Simply change the parameters and run.load('problem_name') to load them.

mesh_parameters.yaml contains parameters that apply to all problems. Most of the parameters have to do with the optically thick source mesh.

RMS Plotter

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.

Final notes

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. Please ensure that the lengths of the N_spaces, Ms, and N_angles lists are all the same, or the program will complain.

Testing

before invoking python, run pytest in the top level folder.