论文标题
基于Voronoi细胞的集成，离散端口方程的无网状离散化运输方程
Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells
论文作者
论文摘要
使用带有再现核的无网局彼得 - 盖尔金方法将时间依赖性的辐射传输方程离散。该集成是使用Voronoi Tessellation进行的，该分区创建了仅取决于内核的位置和程度的统一分区。集成的分辨率自动遵循粒子，不需要手动调整。离散化包括流线上的彼得罗夫 - 盖尔金稳定化，以防止振荡和改善数值调节。角正交可有选择地改进，以增加所选方向上的角分辨率。使用向后的Euler完成时间离散化。使用Krylov迭代方法完成了每个方向的运输求解和散射源的求解。结果表明，线性再现核的时间上的一阶收敛和二阶收敛。
The time-dependent radiation transport equation is discretized using the meshless-local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends on the position and extent of the kernels. The resolution of the integration automatically follows the particles and requires no manual adjustment. The discretization includes streamline-upwind Petrov-Galerkin stabilization to prevent oscillations and improve numerical conditioning. The angular quadrature is selectively refineable to increase angular resolution in chosen directions. The time discretization is done using backward Euler. The transport solve for each direction and the solve for the scattering source are both done using Krylov iterative methods. Results indicate first-order convergence in time and second-order convergence in space for linear reproducing kernels.
