A Finite-Volume Solution with a Bidirectional Upwind Difference Scheme for the Three-Dimensional Radiative Transfer Equation
A Finite-Volume Solution with a Bidirectional Upwind Difference Scheme for the Three-Dimensional Radiative Transfer Equation
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DOI：
10.1175/2007jas2312.1
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发表时间：
2007-11
影响因子：
3.1
通讯作者：
H. Ishida;S. Asano
中科院分区：
文献类型：
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作者：
H. Ishida;S. Asano
摘要提出了一种新的非均匀大气三维辐射传输方程（RTE）显式离散解的计算方法。为了分离3D RTE方法中涉及的独立变量，根据辐射方向，使用球调和级数展开来离散这些项，并根据空间坐标，应用有限体积法来离散这些项。为了使方程确定，提出了一种双向迎风差分格式，该格式是球谐变换RTE中偏微分项离散化的专用格式。3D RTE可以被公式化为联立线性方程，其以具有稀疏矩阵的向量矩阵方程的形式表示。采用逐次超松弛法求解该方程。在二维云模式中对太阳辐射的辐射传输计算表明，这是一个很好的方法。
Abstract A new calculation scheme is proposed for the explicitly discretized solution of the three-dimensional (3D) radiation transfer equation (RTE) for inhomogeneous atmospheres. To separate the independent variables involved in the 3D RTE approach, the spherical harmonic series expansion was used to discretize the terms, depending on the direction of the radiance, and the finite-volume method was applied to discretize the terms, depending on the spatial coordinates. A bidirectional upwind difference scheme, which is a specialized scheme for the discretization of the partial differential terms in the spherical harmonic-transformed RTE, was developed to make the equation determinate. The 3D RTE can be formulated as a simultaneous linear equation, which is expressed in the form of a vector–matrix equation with a sparse matrix. The successive overrelaxation method was applied to solve this equation. Radiative transfer calculations of the solar radiation in two-dimensional cloud models have shown that this ...