Lattice Boltzmann Methods for Shallow Water Flows
Lattice Boltzmann Methods for Shallow Water Flows
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DOI：
10.1007/978-3-662-08276-8
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发表时间：
2003-10
期刊：
影响因子：
--
通讯作者：
J. Zhou
中科院分区：
文献类型：
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作者：
J. Zhou
格子玻尔兹曼方法（LBM）是一种现代数值技术，非常有效，灵活地模拟复杂/变化的几何形状中的不同流动。它是从格子气自动机（LGA）发展而来的，目的是克服LGA的困难。LBM中的核心方程是连续波耳兹曼方程的一种特殊离散形式，这使得它在统计物理学中是不言自明的。该方法以极其简化的方式描述了粒子运动的微观图像，并在宏观水平上给出了流体的正确平均描述。格子Boltzmann方法是一种直接求解流体方程的方法，它将离散的微观现象和连续的宏观现象联系起来，从而使粒子的平均速度在时间和空间上表现得与流体中的流动速度一样，这与传统的基于直接求解流动方程的计算流体力学（CFD）方法不同。该方法具有计算简单、过程并行、边界条件易于实现等特点。正是这些特点使得格子Boltzmann方法在不同的领域成为一种非常有前途的计算方法。近年来，它受到广泛关注，成为计算流体力学中一个非常有潜力的研究领域。然而，大多数出版的书籍仅限于Navier-Stokes方程的格子Boltzmann方法。另一方面，浅水流动在许多实际情况中存在，如潮汐流动、波浪、明渠流动和溃坝流动。其基本特点是在近似条件下，垂直方向的影响可以忽略不计。这使得相当大的简化，在数学公式取代的垂直动量方程与静水压力分布。因此，这种流动通常用浅水方程来描述。浅水方程的数值解是研究海洋、环境和水利工程中广泛存在的水流问题的一种非常成功的工具，如河口和海岸的潮流、河流、水库和明渠水流等。在文学中，有很多的作品--
The lattice Boltzmann method (LBM) is a modern numerical technique, very efficient, flexible to simulate different flows within complex/varying geometries. It is evolved from the lattice gas automata (LGA) in order to overcome the difficulties with the LGA. The core equation in the LBM turns out to be a special discrete form of the continuum Boltzmann equation, leading it to be self-explanatory in statistical physics. The method describes the microscopic picture of particles movement in an extremely simplified way, and on the macroscopic level it gives a correct average description of a fluid. The averaged particle velocities behave in time and space just as the flow velocities in a physical fluid, showing a direct link between discrete microscopic and continuum macroscopic phenomena.In contrast to the traditional computational fluid dynamics (CFD) based on a direct solution of flow equations, the lattice Boltzmann method provides an indirect way for solution of the flow equations. The method is characterized by simple calculation, parallel process and easy implementation of boundary conditions. It is these features that make the lattice Boltzmann method a very promising computational method in different areas. In recent years, it receives extensive attentions and becomes a very potential research area in computational fluid dynamics. However, most published books are limited to the lattice Boltzmann methods for the Navier-Stokes equations. On the other hand, shallow water flows exist in many practical situations such as tidal flows, waves, open channel flows and dam-break flows. The basic feature of the flows is that the vertical effect can be neglected compared with the horizontal one with a good approximation. This allows a considerable simplification in the mathematical formulation by replacing the vertical momentum equation with the hydrostatic pressure distribution. As a result, such flows are usually described with the shallow water equations. A numerical solution of the shallow water equations turns out to be a very successful tool in studying a wide range of flow problems occurring in ocean, environmental and hydraulic engineering, for instance, tidal flows in estuary and coastal regions, river, reservoir and open channel flows. In literature, there are many compu-