二维柱坐标系辐射输运方程保球对称的离散纵标格式

 离散纵标格式是计算辐射输运方程的常用格式之一. 但是, 传统的离散纵标格式求解二维柱坐标系辐射输运方程模拟一维球对称问题时, 会出现明显的非对称现象, 球对称性被破坏. 针对该问题, 本文分析了传统离散纵标格式不能够保持球对称性的原因, 提出了空间基于柱坐标系、方向基于球坐标系的辐射输运方程, 并对该方程设计了新的离散纵标格式, 从理论上证明了当空间网格取球对称剖分时该离散格式能够保持一维球对称性的充分必要条件. 通过对真空球区域辐射输运、与物质耦合辐射输运等球对称算例的数值模拟, 验证了该格式的保球对称性, 球对称误差能够达到机器精度. 非对称辐射驱动模型以及非对称网格剖分条件下的数值模拟等算例也取得了较好的结果.

Construction of geometric partial differential equations in computational geometry spherical-symmetry-preserving discrete ordinates method for the radiation transport equation in two-dimension cylindrical coordinates

Using the traditional discrete ordinates method to solve the radiative transport equation in the 2-D cylindrical coordinates to simulate the 1-D spherical symmetric problem, the spherical symmetry will break. In this paper, the reason for the destruction of the spherical symmetry is analyzed. The radiative transport equation based on the 2-D cylindrical coordinates for the space discretization and the spherical coordinates for the ordinate discretization is introduced, and a new spherical-symmetry-preserving discrete ordinates algorithm is derived. The spherical-symmetry-preserving property of the new algorithm is verified numerically.