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A Frequency-domain Approach for the P1 Approximation of Time-dependent Radiative Transfer

Addam, M.; Bouhamidi, A.; Seaid, M.

A Frequency-domain Approach for the P1 Approximation of Time-dependent Radiative Transfer Thumbnail


Authors

M. Addam

A. Bouhamidi



Abstract

We propose a new frequency-domain method to solve the simplified P1 approximation of time-dependent radiative transfer equations. The method employs the Fourier transform and consists of two stages. In the first stage the equations are transformed into an elliptic problem for the frequency variables. The numerical solutions of this problem are approximated using a Galerkin projection method based on the tensor-product B-spline interpolants. In the second stage a Gauss–Hermite quadrature procedure is proposed for the computation of the inverse Fourier transform to recover the numerical solutions of the original simplified P1 problem. The method avoids the discretization of the time variable in the considered system and it accurately resolves all time scales in radiative transfer regimes. Several test examples are used to verify high accuracy, effectiveness and good resolution properties for smooth and discontinuous solutions.

Citation

Addam, M., Bouhamidi, A., & Seaid, M. (2015). A Frequency-domain Approach for the P1 Approximation of Time-dependent Radiative Transfer. Journal of Scientific Computing, 62(3), 623-651. https://doi.org/10.1007/s10915-014-9870-9

Journal Article Type Article
Acceptance Date May 13, 2014
Online Publication Date May 29, 2014
Publication Date Mar 1, 2015
Deposit Date Nov 30, 2015
Publicly Available Date Dec 4, 2015
Journal Journal of Scientific Computing
Print ISSN 0885-7474
Electronic ISSN 1573-7691
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 62
Issue 3
Pages 623-651
DOI https://doi.org/10.1007/s10915-014-9870-9
Keywords Radiative transfer Simplified P1 approximation, Frequency-domain method, Galerkin projection, Gauss–Hermite quadrature, Tensor-product B-spline interpolation.

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Copyright Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-014-9870-9





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