论文标题
动力学方程矩模型的分层微麦克罗加速度
Hierarchical Micro-Macro Acceleration for Moment Models of Kinetic Equations
论文作者
论文摘要
流体动力学模拟通常是使用诸如Euler方程之类的廉价宏观模型进行的。但是，对于近平衡条件下的稀有气体，宏观模型不够精确，使用更准确的微观模型的模拟通常很昂贵。在本文中，我们基于矩模型引入了分层微麦克罗加速度，该矩模型结合了宏观模型的速度和微观模型的准确性。层次微麦克罗加速度基于一个灵活的四步骤过程，包括微型步骤，限制步骤，宏步骤和匹配步骤。我们从中得出了几种新的微麦克罗方法，并将其与现有方法进行比较。在一维测试案例中，新方法实现了很高的精度和较大的加速。
Fluid dynamical simulations are often performed using cheap macroscopic models like the Euler equations. For rarefied gases under near-equilibrium conditions, however, macroscopic models are not sufficiently accurate and a simulation using more accurate microscopic models is often expensive. In this paper, we introduce a hierarchical micro-macro acceleration based on moment models that combines the speed of macroscopic models and the accuracy of microscopic models. The hierarchical micro-macro acceleration is based on a flexible four step procedure including a micro step, restriction step, macro step, and matching step. We derive several new micro-macro methods from that and compare to existing methods. In 1D and 2D test cases, the new methods achieve high accuracy and a large speedup.
