长腔体内混合流体行进波对流的高精度数值模拟

High accuracy numerical simulation of traveling wave convection in binary fluid mixture in large aspect ratio rectangular cell

该文构造了含源项的对流-扩散方程的高精度紧致格式,并应用于求解描述混合流体行进波对流系统的控制方程。其中,对流项采用四阶精度的紧致格式离散,扩散项用四阶对称格式离散。首先对长高比为46腔体内的混合流体行进波对流系统进行验证性计算,得到了瞬态的对传波(counterpropagating wave)以及两种类型的调制行进波(modulated traveling wave)。验证结果与其他前人的数值模拟结果非常吻合。该文计算得到了延伸行进波(extend traveling wave),在此基础上通过减小瑞利数,分析了局部行进波的稳定性对Rayleigh数r的关系,并确定了局部行进波的稳定范围为r=1.12～1.22。

A high order compact upwind scheme was developed for solving convection diffusion equation with source term.The schemewas applied to solve the governing equations that describe binary fluid mixtures convection systems.The convection terms were discretized with fourth order compact upwind finite difference schemes and the viscous terms were discretized with fourth order accurate symmetrical compact finite difference schemes.Numerical simulations of the traveling wave convection patterns in fluid mixtures inside a large rectangular chamber with an aspect ratio Γ=46were performed. Counter-propagating waves and two types of modulated traveling wave were obtained.The results are in good agreement with those obtained by other scholars,which proves the validity of the present method.Besides,extend traveling waves were obtained by further computation.Based on above,the dependence of the localized traveling wave on Rayleigh number and the stability of localized traveling wave exists with the range of r=1.12-1.22were discussed.