A Frequency-Domain Approach for the $$\hbox {P}_1$$ P 1 Approximation of Time-Dependent Radiative Transfer

Abstract

(2015) 'A frequency-domain approach for the P1 approximation of time-dependent radiative transfer.', Journal of scientic computing., 62 (3). pp. 623-651. Further information on publisher's website:http://dx.doi.org/10.1007/s10915-014-9870-9Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s10915-014-9870-9Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe propose a new frequency-domain method to solve the simplified P 1 approximation of timedependent 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 P 1 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.