基于GPU的二维梯形空腔流的格子Boltzmann模拟与分析  

GPU based lattice Boltzmann simulation and analysis of two-dimensional trapezoidal cavity flow

作　　者：陈百慧 施保昌[1,2,3] 汪垒 柴振华[1,2,3] Chen Bai-Hui;Shi Bao-Chang;Wang Lei;Chai Zhen-Hua(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China;Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China;Institute of Interdisciplinary Research for Mathematics and Applied Science,Huazhong University of Science and Technology,Wuhan 430074,China;School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China;Center for Mathematical Science,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]华中科技大学数学与统计学院,武汉430074 [2]华中科技大学,工程建模与科学计算湖北重点实验室,武汉430074 [3]华中科技大学数学与应用学科交叉创新研究院,武汉430074 [4]中国地质大学(武汉)数学与物理学院,武汉430074 [5]中国地质大学(武汉)数学科学中心,武汉430074

出　　处：《物理学报》2023年第15期137-158,共22页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12072127,51836003)资助的课题.

摘　　要：采用格子Boltzmann方法模拟上下壁面驱动的二维梯形空腔流,并使用GPU-CUDA程序进行加速计算.主要采用本征正交分解方法,分析了4种壁面驱动条件的流场模态,并探究了雷诺数和驱动速度方向对流场形态的影响.结果表明:1)当上壁面单驱动(T1a)时,若雷诺数为1000—8000,流场处于稳态流动;雷诺数为8500时,流场处于周期性非稳态流动;雷诺数大于10000时,流场处于非周期非稳态流动.2)当下壁面单驱动(T1b)时,若雷诺数在1000—8000之间,流场处于稳态流动;雷诺数增大至11500时,流场处于周期性非稳态流动;雷诺数大于12500时,流场进入非周期非稳态流动.3)当上下壁面同方向同速度双驱动(T2a)时,若雷诺数在1000—10000区间,流场均为稳态流动;雷诺数为12500—15000时,流场处于周期性非稳态流动;当雷诺数大于20000时,流场为非周期非稳态流动.4)当上下壁面反方向同速度双驱动(T2b)时,若雷诺数在1000—5000之间,流场处于稳态流动;雷诺数为6000时,流场处于周期性非稳态流动;雷诺数大于8000时,流场为非周期非稳态流动.In this study,we utilize the lattice Boltzmann method to investigate the flow behavior in a twodimensional trapezoidal cavity,which is driven by both sides on the upper wall and lower wall.Our calculations are accelerated through GPU-CUDA software.We conduct an analysis of the flow field mode by using proper orthogonal decomposition.The effects of various parameters,such as Reynolds number(Re)and driving direction,on the flow characteristics are examined through numerical simulations.The results are shown below.1)For the upper wall drive(T1a),the flow field remains stable,when the Re value varies from 1000 to 8000.However,when Re=8500,the flow field becomes periodic but unstable.The velocity phase diagram at the monitoring point is a smooth circle,and the energy values of the first two modes dominate the energy of the whole field.Once Re exceeds 10000,the velocity phase diagram turns irregular and the flow field becomes aperiodic and unsteady.2)For the lower wall drive(T1b),the flow is stable when Re value is in a range of 1000-8000,and it becomes periodic and unsteady when Re=11500.The energy values of the first three modes appear relatively large.When Re is greater than 12500,the flow field becomes aperiodic and unsteady.At this time,the phase diagram exhibits a smooth circle,with the energy values of the first two modes almost entirely dominating the entire energy.3)For the case of upper wall and lower wall moving in the same direction at the same speed(T2a),the flow field remains stable when Re changes from 1000 to 10000.When Re varies from 12500 to 15000,the flow becomes periodic and unstable.The velocity phase diagram is still a smooth circle,with the first two modes still occupying a large portion of the energy.Once Re exceeds 20000,the energy proportions of the first three modes significantly decrease,and the flow becomes aperiodic and unsteady.4)For the case in which the upper wall and lower wall are driven in opposite directions at the same velocity(T2b),the flow field remains stable when Re changes fro

关 键 词：格子BOLTZMANN 方法 梯形空腔 双壁面驱动 GPU-CUDA 计算 

分 类 号：O35[理学—流体力学]