A frequency-domain approach for the \(\text P_1\) approximation of time-dependent radiative transfer. (English) Zbl 1319.65126
Summary: We propose a new frequency-domain method to solve the simplified \(\text P_1\) 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 \(\text P_1\) 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.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45K05 | Integro-partial differential equations |
| 78A40 | Waves and radiation in optics and electromagnetic theory |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 65D32 | Numerical quadrature and cubature formulas |
| 65D05 | Numerical interpolation |
Keywords:
radiative transfer; simplified \(\text P_1\) approximation; frequency-domain method; Galerkin projection; Gauss-Hermite quadrature; tensor-product B-spline interpolation; numerical examples; Fourier transform; inverse Fourier transformReferences:
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