﻿ 基于多块对接网格的隐式气体运动论统一算法应用研究
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 力学学报  2016, Vol. 48 Issue (1): 95-101  DOI: 10.6052/0459-1879-14-279 0

### 引用本文 [复制中英文]

[复制中文]
Peng Aoping, Li Zhihui, Wu Junlin, Jiang Xinyu. AN APPLICATION OF IMPLICIT GAS-KINETIC UNIFIED ALGORITHM BASED ON MULTIBLOCK PATCHED GRID[J]. Chinese Journal of Ship Research, 2016, 48(1): 95-101. DOI: 10.6052/0459-1879-14-279.
[复制英文]

### 文章历史

2014-09-15 收稿
2015-10-28 录用
2015-10-30 网络版发表

1. 中国空气动力研究与发展中心超高速所, 四川 绵阳 621000;
2. 国家计算流体力学实验室, 北京 100191

1 控制方程与数值方法 1.1 控制方程

 $\dfrac{\partial f}{\partial t} + {\pmb V} \cdot \dfrac{\partial f}{\partial {\pmb r} } = \nu (f^N - f)$ (1)
 $f^N = f_M \left[{1 + \dfrac{4}{5}(1 - Pr )\dfrac{{\pmb c} \cdot {\pmb q} }{nT^2}\Big (\dfrac{c^2}{T} - \dfrac{5}{2} \Big )} \right]$ (2)
 $f_M = \dfrac{n}{\left( {\pi T} \right)^{3 / 2}}\exp \left( { - \dfrac{c^2}{T}} \right) ,\ \ {\pmb c} = {\pmb V}-{\pmb u}$ (3)
 $\nu = \dfrac{8nT^{1 - \chi }}{5\sqrt \pi Kn} ,\quad Kn = \dfrac{\lambda _\infty }{L_{\rm ref} }$ (4)

 $\left( {n,nu,\frac{3}{2}nT + n{u^2},q} \right) = \int {\left( {1,V,{V^2},c{c^2}} \right)f} dV$ (5)

1.2 格心型隐式有限体积方法

 $\begin{array}{l} \frac{{\partial {f_{\sigma ,\delta }}}}{{\partial t}} + \frac{{\partial ({V_{x\sigma }}{f_{\sigma ,\delta }})}}{{\partial x}} + \frac{{\partial ({V_{y\delta }}{f_{\sigma ,\delta }})}}{{\partial y}} = {S_\nu }\\ {S_\nu } = \nu \left( {f_{\sigma ,\delta }^N - {f_{\sigma ,\delta }}} \right) \end{array}$

 $\dfrac{\partial \bar {f}_{IJ} }{\partial t} = - \dfrac{1}{\varOmega _{IJ} } \oint_{\partial \varOmega } {\pmb F} \cdot {\pmb n}ds + \bar {S}_{vIJ}$ (6)

 $\begin{array}{l} \Delta f_{IJ}^ * = \left( {{\Omega _{IJ}}RHS_{IJ}^n + A_{nI - 1/2,J}^ + \Delta {f_{I - 1,J}}\Delta {s_{I - 1/2,J}} + } \right.\\ \;\;\;\;\;\;\;\;\;\left. {A_{nI,J - 1/2}^ + \Delta {f_{I,J - 1}}\Delta {s_{I,J - 1/2}}} \right)/\alpha \\ \alpha = \frac{{{\Omega _{IJ}}}}{{\Delta t}} + A_{nI + 1/2,J}^ + \Delta {s_{I + 1/2,J}} - A_{nI - 1/2,J}^ - \Delta {s_{I - 1/2,J}} + \\ \;\;\;\;\;\;A_{nI,J + 1/2}^ + \Delta {s_{I,J + 1/2}} - A_{nI,J - 1/2}^ - \Delta {s_{I,J - 1/2}} - {\Omega _{IJ}}{A_v} \end{array}$

 $\begin{array}{l} \Delta {f_{IJ}} = \Delta f_{IJ}^ * - (A_{nI + 1/2,J}^ - \Delta f_{IJ}^ * \Delta {s_{I + 1/2,J}} + \\ \;\;\;\;\;\;\;\;\;A_{nI,J + 1/2}^ - \Delta f_{IJ}^ * \Delta {s_{I,J + 1/2}})/\alpha \end{array}$

1.3 物理空间网格处理方法

2 近连续过渡流区并排圆柱绕流计算分析

 图 1 并排圆柱下半部分绕流场多块对接网格布局 Fig.1 Multiblock patched grid for the flow field

 图 2 不同间隔并排圆柱流场马赫数等值线云图 Fig.2 Contours of Mach number past two side-by-side cylinders

 图 3 沿圆柱物面温度跳跃和速度滑移 Fig.3 Temperature jump and velocity slip along the surfaces

3 结 论

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AN APPLICATION OF IMPLICIT GAS-KINETIC UNIFIED ALGORITHM BASED ON MULTIBLOCK PATCHED GRID
Peng Aoping, Li Zhihui, Wu Junlin, Jiang Xinyu
1. Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China;
2. National Laboratory for Computational Fluid Dynamics, Beijing 100191, China
Abstract: Gas Kinetic Unified Algorithm (GKUA) based on Boltzmann model equations is proposed for simulating aerodynamics problems covering various flow regimes. In this algorithm, molecular motions are decoupled from collisions by traditional Computational Fluid Dynamics methods, so that the calculation e ciency would be quite low at the limitation of stabilization conditions of explicit schemes when simulating supersonic flows especially which are near-continuum and continuum flows. In order to improve the e ciency and expand engineering practicability, an implicit method for Boltzmann model equations is constructed by using LU-SGS (Lower-Upper Symmetric Gauss-Seidel) method and cellcentered finite volume method, and multi-block patched grid technique is used in physical space. The present computed results of two side-by-side cylinders in transitional flow regime are found in good agreement with those from Direct simulation Monte-Carlo method simulation. The dependability and feasibility for simulating problems covering various flow regimes by the present method are validated.
Key words: gas-kinetic unified algorithm    implicit scheme    multi-block patched grid    finite volume method    aerodynamics covering various flow regimes