The Navier–Stokes equations are the basis for describing the flow of a viscus material and are used to model fluid motion from weather to air flow over a wing. These equations, however, tend to be notoriously difficult to solve, whether analytically or computationally, even for small systems due to their highly nonlinear nature. Thus, less complicated methods that are more computationally tractable are desirable in domains as varied as hydroelectric power to race car construction. At a fundamental level, fluids are composed of interacting molecules. Lattice Gas Cellular Automata (LGCA) represents an efficient way to simulate these interacting fluid particles on a lattice. LGCA captures the microscopic behavior of the fluid by applying simple collision and propagation rules at each lattice site. This leads to realistic macroscopic behavior that can be used to build insight about real fluid flow. Here, we show the Hardy, Pomeau, and de Pazzis model for simulating a lattice gas. The computational framework presented in this case study can also be expanded to more complicated LGCA.

中文翻译：

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格子气体元胞自动机流体动力学案例研究

Navier-Stokes 方程是描述粘性材料流动的基础，用于模拟从天气到机翼上气流的流体运动。然而，众所周知，这些方程往往难以求解，无论是解析式还是计算式，即使对于小型系统，由于其高度非线性的性质也是如此。因此，在从水力发电到赛车制造等多种多样的领域中，需要在计算上更易于处理的不太复杂的方法。在基本层面上，流体由相互作用的分子组成。晶格气体元胞自动机 (LGCA) 代表了一种在晶格上模拟这些相互作用的流体粒子的有效方法。LGCA 通过在每个晶格位置应用简单的碰撞和传播规则来捕捉流体的微观行为。这导致了现实的宏观行为，可用于建立对真实流体流动的洞察力。在这里，我们展示了用于模拟晶格气体的 Hardy、Pomeau 和 de Pazzis 模型。本案例研究中提出的计算框架也可以扩展到更复杂的 LGCA。