The time-dependent, gray, linear 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.

使用具有再生核的无网格局部 Petrov-Galerkin 方法对瞬态、灰色、线性辐射传输方程进行离散化。积分是使用 Voronoi 细分来执行的，它创建了一个统一的分区，该分区仅取决于内核的位置和范围。积分分辨率自动跟随粒子，无需手动调整。离散化包括流线逆风 Petrov-Galerkin 稳定，以防止振荡和改善数值条件。角正交可选择性地细化以增加选定方向上的角分辨率。时间离散是使用后向欧拉完成的。每个方向的传输求解和散射源的求解均使用 Krylov 迭代方法完成。