StaRMAP

StaRMAP (Staggered grid Radiation Moment Approximation) is a simple method to solve spherical harmonics moment systems, such as the the time-dependent PN and SPN equations, of radiative transfer. The approach works for arbitrary moment order N, making use of the specific coupling between the moments in the PN equations. The method allows for an efficient implementation in Matlab. The StaRMAP project is reproducible research: all program and example files can be downloaded below.

Program Code

Current version (03/13/2015): 1.9
StaRMAP_ver1p9.zip Zip file of all project files (given below)
 ChangeLog.txt List of changes from previous version
 README.txt A brief documentation
 starmap_closure_pn.m Creates PN moment matrices
 starmap_closure_spn.m Creates SPN moment matrices
 starmap_create_beam.m Creates example file starmap_ex_beam_auto.m, beam in void and medium
 starmap_create_hemisphere_filter_convergence.m  Creates example file starmap_ex_hemisphere_filter_convergence_auto.m, FPN convergence for hemisphere test
 starmap_create_mms.m Creates example file starmap_ex_mms_auto.m, manufactured solution
 starmap_ex_boxes.m Example file: boxes test case
 starmap_ex_controlrod.m Example file: control rod test
 starmap_ex_gauss_filter_convergence.m Example file: FPN convergence for Gauss test
 starmap_ex_homogeneous.m Example file: comparison of various closures for spreading initial hump
 starmap_ex_lattice.m Example file: lattice/checkerboard test
 starmap_ex_lattice_diffusion.m Example file: lattice/checkerboard test with various diffusive closures
 starmap_ex_lattice_filter.m Example file: lattice/checkerboard test with filtering
 starmap_ex_lattice_filter_convergence.m Example file: FPN convergence for lattice/checkerboard test
 starmap_ex_linesource.m Example file: line source test
 starmap_ex_linesource_filter.m Example file: line source test with filtering
 starmap_ex_linesource_filter_reconstruction.m Example file: line source test with angular reconstruction in a point
 starmap_ex_l2norm.m Example file: evolution of L2 norm of numerical solution
 starmap_solver.m The computational code
Old Version (10/10/2014): 1.5
StaRMAP_ver1p5.zip Zip file of all project files
 
StaRMAP_ver1p5_create_figures.zip Zip file of files used to create the figures and tables for the paper
[Frank, Hauck, Kuepper, Convergence of filtered spherical harmonic equations for radiation transport (2014)]
Old Version (07/14/2013): 1.1
StaRMAP_ver1p1.zip Zip file of all project files
Old Version (11/11/2012): 1.0
StaRMAP_ver1p0.zip Zip file of all project files

Authors and Contributors

Authors: Benjamin Seibold, Martin Frank
Contributors: Edgar Olbrant (v1.0), Kerstin Küpper (v1.5)

Gallery of Examples

Numerical convergence analysis using a manufactured solution.

Convergence plots

Temporal evolution of discrete L2 norm of numerical solution.

Evolution of L2 norm

Checkerboard test case with various moment orders (P3, P5, P15, and P39).

Checkerboard with P3 Checkerboard with P5 Checkerboard with P15 Checkerboard with P39

Line source test case, computed with P19 and P39.

Line source with P19 Line source with P39

Beam that starts in void and hits forward scattering medium, computed with P9 and P39.

Beam with P9 at t=0.3 Beam with P9 at t=0.6
 
Beam with P39 at t=0.3 Beam with P39 at t=0.6

Control rod test case, computed with SP3.

Control rod with SP3 at t=0.9

Boxes test, demonstrating the equivalence of PN and SPN under the given assumptions.

Boxes test with P9 Boxes test with P9 Difference between P9 and SP9

Videos of Presentations Related to StaRMAP

October 2014: Talk by Benjamin Seibold at the Workshop on Moment Methods in Kinetic Theory II, Fields Institute, Toronto, StaRMAP - A staggered grid moment approach and its asymptotic preserving properties (video of talk: interactive and static)
October 2014: Talk by Martin Frank at the Workshop on Moment Methods in Kinetic Theory II, Fields Institute, Toronto, Convergence of filtered spherical Harmonic equations for radiation transport (video of talk: interactive and static)

Related Publications

B. Seibold, M. Frank, StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer, ACM Trans. Math. Software, Vol. 41, No. 1, 2014.
E. Olbrant, E. W. Larsen, M. Frank, B. Seibold, Asymptotic derivation and numerical investigation of time-dependent simplified PN equations, J. Comput. Phys., Vol. 238, 2013, pp. 315-336.