Iterative space-angle discontinuous Galerkin method for radiative transfer equation

3区物理与天体物理 Q1 Engineering

Waves in Random and Complex Media Pub Date : 2023-11-02 DOI:10.1080/17455030.2022.2116661

Hang Wang, Reza Abedi, Saba Mudaliar

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引用次数: 0

Abstract

AbstractThe radiative transfer equation (RTE) is an integro-differential equation that describes the radiation energy absorbing, emitting, and scattering in both space and angle, which can be up to five-dimensional problems. It is difficult for a RTE solver to satisfy both accuracy and efficiency (less computational resources) for such high dimensional problems. In this paper, an iterative solver for one-dimensional cylindrical radiative transfer problems using the space-angle discontinuous Galerkin (DG) method is developed to achieve both accuracy and efficiency. The iterative solver is based on the angular decomposition (AD) scheme, which slices the spatial-angular domain into slabs and decouples the angular integration between slabs. Both Jacobi and successive over-relaxation (SOR) iterative schemes are investigated by numerical analysis and examples. The comparison of the two iterative schemes suggests that an appropriate relaxation factor for the SOR method may accelerate the convergence. Finally, the iterative scheme is more efficient than the direct solution of the system both in terms of memory usage and computational time, especially for finer meshes.Keywords: Radiate transfer equationdiscontinuous galerkinspace-angleiterative schemejacobi methodsuccessive over-relaxation methodangular decomposition Disclosure statementNo potential conflict of interest was reported by the author(s).

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辐射传递方程的迭代空间角不连续伽辽金法

摘要辐射传递方程(RTE)是描述辐射能量在空间和角度上的吸收、发射和散射的积分-微分方程，可以达到五维问题。对于这样的高维问题，RTE求解器很难同时满足精度和效率(较少的计算资源)。本文利用空间角不连续伽辽金(DG)方法，提出了求解一维圆柱辐射传递问题的迭代求解方法。该迭代求解器基于角分解(AD)方案，将空间-角域分割为若干块，解耦块之间的角积分。通过数值分析和实例研究了Jacobi迭代格式和逐次过松弛(SOR)迭代格式。两种迭代方案的比较表明，适当的松弛因子可以加快SOR方法的收敛速度。最后，在内存使用和计算时间方面，迭代方案比系统的直接求解更有效，特别是对于更细的网格。关键词:辐射传递方程不连续galerkinspace-角迭代方案jacobi方法逐次超松弛法线性分解披露声明作者未报告潜在的利益冲突。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Waves in Random and Complex Media 物理-物理：综合

自引率

0.00%

发文量

677

审稿时长

3.0 months

期刊介绍： Waves in Random and Complex Media (formerly Waves in Random Media ) is a broad, interdisciplinary journal that reports theoretical, applied and experimental research related to any wave phenomena. The field of wave phenomena is all-pervading, fast-moving and exciting; more and more, researchers are looking for a journal which addresses the understanding of wave-matter interactions in increasingly complex natural and engineered media. With its foundations in the scattering and propagation community, Waves in Random and Complex Media is becoming a key forum for research in both established fields such as imaging through turbulence, as well as emerging fields such as metamaterials. The Journal is of interest to scientists and engineers working in the field of wave propagation, scattering and imaging in random or complex media. Papers on theoretical developments, experimental results and analytical/numerical studies are considered for publication, as are deterministic problems when also linked to random or complex media. Papers are expected to report original work, and must be comprehensible and of general interest to the broad community working with wave phenomena.