We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates uses bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to ``relabel'' collided particles as uncollided particles. From a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

翻译：我们提出了一种针对时变粒子输运问题的混合方法，该方法将蒙特卡洛（MC）估计与基于离散纵标的确定性解相结合。在空间离散化方面，MC算法计算分段常数解，而离散纵标法采用双线性间断有限元。通过问题混合化，蒙特卡洛求解的子问题不再包含散射项，从而形成简洁高效的求解流程。在时间步之间，我们采用投影方法将碰撞粒子"重新标记"为未碰撞粒子。基于一系列标准二维笛卡尔坐标系测试问题的数值实验表明，相较于标准离散纵标法解，本文提出的混合方法在计算精度上得到提升，且计算复杂度降低约一个数量级。