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arXiv 1809.09052math.NAcs.NA
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一种用于辐射传输方程的自适应移动网格间断Galerkin方法

An adaptive moving mesh discontinuous Galerkin method for the radiative transfer equation

Xiamen University(厦门大学);Institute of Applied Physics and Computational Mathematics(应用物理与计算数学研究所);University of Kansas(堪萨斯大学)

Min Zhang, Juan Cheng, Weizhang Huang, Jianxian Qiu

AI总结:

本文提出了一种自适应移动网格间断Galerkin方法来求解辐射传输方程,结合离散 ordinates 方法进行角向离散化,通过动态网格适应策略提高计算精度和效率,并在一维和二维数值例子中验证了方法的适应性、精度和效率。

摘要:

辐射传输方程描述了辐射与散射和吸收介质的相互作用,并在科学和工程的各个领域有重要应用。它是一个包含时间、空间和角变量的积分微分方程,其在角方向包含一个积分项,而在空间方向是双曲的。其数值求解的挑战包括处理其高维性、积分项的存在以及解在空间方向上发展出的不连续性和尖锐层。本文采用自适应移动网格间断Galerkin方法进行空间离散化,结合离散 ordinates 方法进行角向离散化。前者采用基于移动网格偏微分方程的动态网格适应策略以提高计算精度和效率。其网格适应能力、精度和效率在若干一维和二维数值例子中得到了验证。

英文摘要:

The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time, space and angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needs to handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions. Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinate method for angular discretization. The former employs a dynamic mesh adaptation strategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency are demonstrated in a selection of one- and two-dimensional numerical examples.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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