间断有限元法求解一维散射性介质内矢量辐射传输
首发时间:2016-09-09
摘要:本文采用间断有限元法(Discontinuous finite element method, DFEM)求解一维散射性介质内矢量辐射传输问题。推导了散射性介质内矢量辐射传输方程的间断有限元离散格式,空间离散采用间断有限元离散将求解域划分为相互独立的单元,角度离散在传统的PCA(Piecewise Constant Approximation)角度离散基础上进行局部加密以得到关键方向上的数值解。采用两个稳态矢量辐射传输算例对间断有限元法求解矢量辐射传输方程的正确性和计算效率进行了验证。在此基础上拓展间断有限元法应用于求解散射性介质内瞬态矢量辐射传输方程,将随着时间推移过程中的瞬态辐射信息和最终的稳态结果相比较验证了本文方法的正确性。
关键词: 工程热物理 间断有限元 矢量辐射传输 瞬态辐射传输 离散格式
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Discontinuous finite element method for vector radiative transfer in one-dimensional scattering media
Abstract:In this paper, a discontinuous finite element method (DFEM) is applied to solve one-dimensional vector radiative transfer in a one dimensional scattering medium. The derivation on discrete form of the vector radiation governing equations is presented, in which the spatial area is discretized into finite non-overlapped discontinuous elements and the angular space is discretized by the conventional Piecewise Constant Approximation (PCA) approach with a local redefined modification to obtain detailed information in interested direction. Two cases of steady vector radiative transfer are tested to verify the correctness and accuracy of the developed DFEM. The DFEM is then applied to solve transient vector radiative transfer in a scattering medium, the time-resolved radiative information is compared with the steady one and results demonstrate the correctness of the DFEM for solving transient vector radiative transfer.
Keywords: Thermo-physics engineering Discontinuous finite element method Vector radiative transfer Transient radiative transfer Discretization scheme
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