Recently, asymptotic-preserving Monte Carlo simulation methods have been developed to simulate the Boltzmann-BGK equation with advective–diffusive limiting behaviour over a broad range of regimes. These simulation methods hybridize a particle tracing Monte Carlo scheme for the kinetic equation and a random walk (RW) Monte Carlo simulation for the advection–diffusion limit, combining the precision of the former with the efficiency of the latter. In the RW part of the simulation, details of the travelled path are absent. This complicates the extraction of integral quantities of interest such as mass, momentum, and energy sources. Here, we present a new estimation strategy that couples the RW parts of the particle trajectories with a deterministic simulation of the corresponding fluid model. The contributions of the RW parts to quantities of interest are then computed from a single time step of this fluid model in a post-processing step. We illustrate this new estimation strategy for a fusion-relevant test-case and focus on the bias and variance present when using this estimator.

中文翻译：

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估计作为玻尔兹曼-BGK 模型随机游走近似的后处理步骤

最近，已经开发了渐近保持蒙特卡罗模拟方法来模拟具有平流 - 扩散限制行为的 Boltzmann-BGK 方程在广泛的范围内。这些模拟方法混合了动力学方程的粒子追踪蒙特卡罗方案和平流扩散极限的随机游走 (RW) 蒙特卡罗模拟，将前者的精度与后者的效率相结合。在模拟的 RW 部分，缺少行进路径的细节。这使得提取感兴趣的积分量（例如质量、动量和能量源）变得复杂。在这里，我们提出了一种新的估计策略，它将粒子轨迹的 RW 部分与相应流体模型的确定性模拟相结合。然后在后处理步骤中从该流体模型的单个时间步长计算 RW 部分对感兴趣数量的贡献。我们为融合相关的测试用例说明了这种新的估计策略，并关注使用该估计器时存在的偏差和方差。