-adaptive discontinuous Galerkin methods for simplified approximations of frequency-dependent radiative transfer
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- 作者：Stefano Giani stefano.giani@durham.ac.uk" class="auth_mail" title="E-mail the corresponding author ; Mohammed Seaid ; m.seaid@durham.ac.uk" class="auth_mail" title="E-mail the corresponding author
- 关键词：Radiative transfer ; Simplified PN approximations ; Discontinuous Galerkin method ; hphp-adaptivity ; Non-gray media
- 刊名：Computer Methods in Applied Mechanics and Engineering
- 出版年：2016
- 出版时间：1 April 2016
- 年：2016
- 卷：301
- 期：Complete
- 页码：52-79
- 全文大小：4871 K
文摘
We investigate the performance of a class of hp-adaptive discontinuous Galerkin methods for the numerical solution of simplified 
approximations of radiative transfer in non-gray semitransparent media. By introducing an optical scale and using asymptotic expansions in the radiative transfer equation we formulate the simplified approximations. The optical spectrum is decomposed in frequency bands and the simplified equations are solved for each frequency band. As a numerical solver for the simplified equations we consider a high-order discontinuous Galerkin method. The solver belongs to a class of finite element methods whose approximate solutions are discontinuous across inter-element boundaries; this property renders the method ideally suited for the hp-adaptivity. An error estimator is shown to provide reliable and practically useful upper bounds for the numerical errors independent of the optical scales used in the simulations. The proposed method is simple, fast and highly accurate. The performance of the method is analyzed on several applications in frequency-dependent radiative transfer. The aim of such a method compared to the conventional finite element methods is to solve the simplified equations efficiently and with a high level of accuracy on unstructured meshes with different elements. The obtained results demonstrate the ability of the proposed method to capture the main radiative features.
approximations of radiative transfer in non-gray semitransparent media. By introducing an optical scale and using asymptotic expansions in the radiative transfer equation we formulate the simplified approximations. The optical spectrum is decomposed in frequency bands and the simplified equations are solved for each frequency band. As a numerical solver for the simplified equations we consider a high-order discontinuous Galerkin method. The solver belongs to a class of finite element methods whose approximate solutions are discontinuous across inter-element boundaries; this property renders the method ideally suited for the hp-adaptivity. An error estimator is shown to provide reliable and practically useful upper bounds for the numerical errors independent of the optical scales used in the simulations. The proposed method is simple, fast and highly accurate. The performance of the method is analyzed on several applications in frequency-dependent radiative transfer. The aim of such a method compared to the conventional finite element methods is to solve the simplified equations efficiently and with a high level of accuracy on unstructured meshes with different elements. The obtained results demonstrate the ability of the proposed method to capture the main radiative features.