﻿ 一种定常可压缩流动的格子Boltzmann模型 A Lattice Boltzmann Model for the Steady State Compressible Flows

International Journal of Fluid Dynamics
Vol.05 No.01(2017), Article ID:19880,12 pages
10.12677/IJFD.2017.51002

A Lattice Boltzmann Model for the Steady State Compressible Flows

Bo Yan1, Jianchao Wang1, Guangwu Yan2

1College of Civil Engineering, Jilin Jianzhu University, Changchun Jilin

2College of Mathematics, Jilin University, Changchun Jilin

Received: Feb. 20th, 2017; accepted: Mar. 6th, 2017; published: Mar. 9th, 2017

ABSTRACT

In this paper, a multi-energy-level lattice Boltzmann model for the steady state compressible flows is proposed. Firstly, the Chapman-Enskog expansion and the multi-spatial scale expansion are used to describe the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different spatial scales. Secondly, the modified partial differential equation of the Euler equation with the higher-order truncation error is obtained. Thirdly, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical one.

Keywords:Lattice Boltzmann Model, Compressible Flows, Steady State Lattice Boltzmann Equation

1吉林建筑大学土木工程学院，吉林 长春

2吉林大学数学学院，吉林 长春

1. 引言

2. 格子Boltzmann模型

2.1. 格子Boltzmann方程

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Figure 1. Schematic of lattice. (a) type A, (b) type B

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2.2. 平衡态分布中的系数

Navier-Stokes方程的恢复与矩的对称性有关

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2.3. 宏观方程

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3. 数值例子

3.1. 4Mach数圆柱绕流 [46]

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Figure 2. Numerical result of 4 Mach number incoming flow around a circular cylinder. (a) is the density contours, (b) is the pressure contours

Table 1. The L1 norm errors of the flows around a circular cylinder with 4 Mach number incoming at line x = 0.25

(a) (b)

Figure 3. Numerical result of 3 Mach number incoming flow around a rectangle. (a) is the density contours, (b) is the pressure contours

3.2. 3Mach数前台阶流

，即入流Mach数为。边界条件与图2相同。图3给出了入流Mach数为3时，绕前台阶流动的数值模拟结果。其中图3(a)为密度等值线图，图3(b)为压力等值线图。其它参数为，网格数为，Mach数为3，等值线条数为30。数值结果表明，LBM模型所得到的结果与经典结果吻合的较好。

4. 结论

A Lattice Boltzmann Model for the Steady State Compressible Flows[J]. 流体动力学, 2017, 05(01): 10-21. http://dx.doi.org/10.12677/IJFD.2017.51002

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