论文标题
动力扩散渐近造型的蒙特卡洛算法，用于扩散缩放的玻尔茨曼-BGK
Kinetic-diffusion asymptotic-preserving Monte Carlo algorithm for Boltzmann-BGK in the diffusive scaling
论文作者
论文摘要
我们制定了一种新型的蒙特卡洛策略，用于模拟玻尔兹曼-BGK模型，并具有低碰撞和高倾斜度的机制。提出的解决方案以保持低碰撞状态的准确性并消除高碰撞机制中的爆炸模拟成本，使用杂交颗粒，这些杂交颗粒既表现出动力学行为又取决于局部碰撞。在这项工作中，我们开发了一种方法，该方法在固定步骤大小的多个时间步长上保持正确的均值，差异和相关性，以在固定步骤大小的所有碰撞值中，在时间步长的空间同质性的条件下。在低碰撞制度中，该方法恢复为标准速度跳跃过程。在高倾斜状态下，该方法崩溃到标准的随机步行过程中。我们分析了在低碰撞制度中提出的方案的误差，我们在该方案中获得了时间步长的收敛顺序。我们此外，我们在高倾斜度制度中提供了一种分析，该分析证明了渐近保护特性。
We develop a novel Monte Carlo strategy for the simulation of the Boltzmann-BGK model with both low-collisional and high-collisional regimes present. The presented solution to maintain accuracy in low-collisional regimes and remove exploding simulation costs in high-collisional regimes uses hybridized particles that exhibit both kinetic behaviour and diffusive behaviour depending on the local collisionality. In this work, we develop such a method that maintains the correct mean, variance, and correlation of the positional increments over multiple time steps of fixed step size for all values of the collisionality, under the condition of spatial homogeneity during the time step. In the low-collisional regime, the method reverts to the standard velocity-jump process. In the high-collisional regime, the method collapses to a standard random walk process. We analyze the error of the presented scheme in the low-collisional regime for which we obtain the order of convergence in the time step size. We furthermore provide an analysis in the high-collisional regime that demonstrates the asymptotic-preserving property.
