基于耗散结构的贝纳德对流研究  

Bernard convection prediction based on dissipative structure

作　　者：李睿航 方爱平[1] 陈子龙 齐颢然 张笑儒 程涵宇 冯乐 罗禧祯 田蓬勃[1] 刘萍[1] 王小力[1] LI Rui-hang;FANG Ai-ping;CHEN Zi-long;QI Hao-ran;ZHANG Xiao-ru;CHENG Han-yu;FENG Le;LUO Xi-zhen;TIAN Peng-bo;LIU Ping;WANG Xiao-li(School of Science,Xi an Jiaotong University,Xi an,Shaanxi 710049,China)

机构地区：[1]西安交通大学理学院,陕西西安710049

出　　处：《大学物理》2020年第12期75-80,85,共7页College Physics

基　　金：教育部高等学校教学研究项目(DJZW201911xb,DWJZW201705xb);西安交通大学本科教学改革研究基础课专项(1802Z-04);西安交通大学本科教学改革研究项目(17ZX05,1803Z)资助。

摘　　要：贝纳德对流作为一种常见的流体自组织现象,常常具有难以预测的特点,本文从耗散结构入手,以流体力学的手段研究并模拟了特定边界条件下的贝纳德对流.首先,根据不可压缩流体满足的连续性方程,能量守恒方程和纳维-斯托克斯方程,引入Boussinesq近似和流函数方法化简贝纳德对流的控制方程,结合理想流体的边界条件,对得到的方程进行变量分离,并引入洛伦茨系统以及瑞利数无量纲数以描述流体的控制方程.其次,利用有限差分法求解贝纳德对流的控制方程,分析不同参数时对应的相空间轨迹,并给出一定条件下的贝纳德对流的转变温度.最后,使用计算机模拟计算,基于格子玻尔兹曼方法处理流体微元间的相互作用,将体积为0.008l m 3的三维立体容器按正立方体等体积划分为106个小立方体进行模拟,分析模拟得到的贝纳德对流,验证了这种方法的可行性.A common phenomenon of fluid self-organization named Bernard convection is often difficult to predict,the paper starts from the dissipative structure,then studies and simulates the Bernard convection under specific boundary conditions by means of hydrodynamics.First of all,according to the continuity equation,energy conservation equation and Navier-Stokes equation of incompressible fluid,Boussinesq approximation and flow function method are introduced to simplify the control equation of Bernard convection.Because of the nonlinearity of the equation,combined with the boundary conditions of ideal fluid,variable separation is carried out for the obtained equation,and Lorentz system and Rayleigh number are introduced to describe the governing equation of the fluid.Secondly,the finite difference method is used to solve the control equation of Bernard convection,analyze the phase space trajectories corresponding to different parameters,and give the transition temperature of Bernard convection under certain conditions.Finally,based on the lattice Boltzmann method to deal with the interaction between the micro elements of the fluid,combining with appropriate boundary conditions,the volume of 0.008l cubic meter three-dimensional container is divided into 106 small cubes according to the normal cube to verify the feasibility of this method by analyzing simulation of Bernard convection.

关 键 词：贝纳德对流 纳维斯托克斯方程 有限差分法 格子玻尔兹曼方法 

分 类 号：O552[理学—热学与物质分子运动论]