球对称介质中辐射转移的间断Galerkin有限元法
Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry
摘要：
间断伽辽金有限元法（DG-FEM）被成功地应用于处理各种各样的输运问题的数值。在这项工作中，我们使用DG-FEM的全部能力来解决球对称的辐射转移方程。本文提出了一种直接求解球对称辐射转移方程二维问题的间断Galerkin方法。在球形大气中的输运方程比在平面平行的情况下更复杂，这是由于相对于极角的额外导数的出现。DG-FEM形式主义允许任意复杂的散射相函数的精确积分，独立于角网格分辨率。我们表明，不连续Galerkin方法是能够准确地描述扩展大气中的辐射转移，并捕捉不连续性或复杂的散射行为，可能存在于某些辐射转移任务的解决方案，因此，可能会导致严重的数值问题，其他辐射转移解决方案的方法。
英文摘要：
The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically-symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case due to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.
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