论文标题
与各向同性散射内核求解缩放的离散辐射转移方程的上风不连续的Galerkin方法的均匀收敛
Uniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scattering kernel
论文作者
论文摘要
我们提出了用于应用于稳态辐射传递方程离散离散化的不连续的Galerkin方法的错误分析。在某些温和的假设下，我们表明DG方法相对于缩放参数$ \ VAREPSILON $均匀收敛，该缩放参数$ \ varepsilon $表征了系统中散射的强度。但是，速率不是最佳的，可以通过边界层的存在来污染。在一维平板几何形状中，当不存在边界层时，我们证明了最佳的收敛性，并分析了平衡内部和边界层误差的简单策略。在此简化设置中还提供了一些数值测试。
We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild assumptions, we show that the DG method converges uniformly with respect to a scaling parameter $\varepsilon$ which characterizes the strength of scattering in the system. However, the rate is not optimal and can be polluted by the presence of boundary layers. In one-dimensional slab geometries, we demonstrate optimal convergence when boundary layers are not present and analyze a simple strategy for balance interior and boundary layer errors. Some numerical tests are also provided in this reduced setting.
