Toulouse 2D numerical radiative transfer codes : MALI and Gauss-Seidel

Authors : F. Paletou and L. Léger (Contact: frederic.paletou/at/univ-tlse3.fr)

  • Purpose:

We propose two numerical codes for 2D multilevel non-LTE radiative transfer, assuming complete frequency redistribution, for static, homogeneous and isolated structures. They were initially developed for solar prominence radiative modeling of various spectral lines of H or He. Two versions are proposed, respectively using the following numerical schemes:

– Multilevel Accelerated Lambda Iteration (MALI),

– A Gauss-Seidel iterative scheme in a 2D cartesian grid.

  • More informations:

– Léger, Chevallier & Paletou, 2007, A&A, 470, 1-9

– Paletou & Léger, 2007, Journal of Quantitative Spectroscopy & Radiative Transfer, 103, 57-66

– Lambert, Paletou, Josselin & Glorian, 2016, Eur. J. Phys., 37

– Auer & Paletou, 1994, A&A, 284, 675-686

– PhD, L. Léger, 2008, “Transfert de rayonnement hors-ETL multidimensionnel. Application au spectre de l’hélium dans les protubérances solaires” (text in French, but many developments worth it for anyone)

More references :

Léger & Paletou, 2009, A&A, 498, 869-875     /     Paletou, 1997, Astron. Astrophys., 317, 244-247

Paletou & Auer, 1995, Astron. Astrophys., 297, 771-778     /     Heinzel, 1995, A&A, 299, 563-573

Trujillo & Fabiani, 1995, the Astrophysical Journal, 455, 646-657     /     Rybicki & Hummer, 1991, Astron. Astrophys., 245, 171-181

Olson, Auer & Buchler, 1986, J. Quant. Spectros. Radiat. Transfer, vol 35, N°6, 431-442

Mihalas, Auer & Mihalas, 1978, the Astrophysical Journal, 220, 1001-1023     /     Avrett, 1968, Resonance lines in Astrophysics, NCAR

Laurence H. Auer (1941-2023)

  • Fortran files and documentations:

doi : 10.48326/idoc.medoc.radtransfer.2d-crd-mali-gs

Codes are provided under the GNU General Public Licence (GPL) version 3 or any later version.

MALI code and Gauss-Seidel code were successfully tested on PCs running linux with gfortran compiler. The source codes are available here : MALI, Gauss-Seidel. For running the code, see the README file. For more details on the codes, see the documentation.

Tutorial about iterative methods including Gauss-Seidel iterations in radiative transfer : http://rttools.irap.omp.eu/

  • Initiation to MALI : 1D MALI code. The source codes are available here and are provided under the GNU General Public Licence (GPL) version 3 or any later version. doi :10.48326/idoc.medoc.radtransfer.1d-crd-mali-semiinf
  • Input files (test case):

MALI code :

  • input : file including the number of reduced frequencies, the number of directions, the grid in Z (max. optical depth, first optical depth step, number of points for a logarithmic-type mesh for isothermal slabs), the grid in Y (max. optical depth, first optical depth step; same as Z), the choice to read the grid from extra file, the maximum number of iterations, the uniform slab temperature (K), the model-atom (H, Ca or Na), the (fixed) background continuum opacity, the number of ‘natural’ iterations before applying acceleration of convergence, the expected relative error (from an iteration to another)
  • several reference data files of populations (H, Ca, Na) from 2D slab models, resulting from ‘fully converged’ (i.e. using a large number of iterations) populations: populationsH.save, populationsCa.save, populationsNa.save
  • several reference data files of populations (H, Ca, Na) from 1D slab models of similar vertical extension as 2D slabs: populationsH1d.res, populationsCa1d.res, populationsNa1d.res

Gauss-Seidel code :

  • input : file including the number of reduced frequencies, the number of directions, the grid in Z (max. optical depth, first optical depth step, number of points for a logarithmic-type mesh for isothermal slabs), the grid in Y (max. optical depth, first optical depth step, same as Z), the maximum number of iterations, the uniform slab temperature (K), the model-atom (H, Ca or Na), the (fixed) background continuum opacity, the option SOR (Successive Over-Relaxation)
  • Output files (test case):

MALI code :

  • population2d.res : density of populations in 2D obtained after convergence
  • population.res : density of populations along mid symmetry axis for 1D comparisons, obtained from 2D computations
  • mali2d.res : file including three sets of maximum relative errors on source function, populations and vs. 1D populations of reference

Gauss-Seidel code :

  • sor2d.res : file including the SOR parameter value, the density of populations in 2D, the maximum relative error on source function, and on populations from an iteration to another

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