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

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

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.
• Public URL: https://durham-repository.worktribe.com/output/1397377