基于Chebyshev配置点谱方法的多孔介质平板通道内的流体流动数值模拟

Numerical simulation of fluid flow in a porous media parallel plate channel based on Chebyshev collocation spectral method

本文基于Chebyshev配置点谱方法,利用数值模拟研究了多孔介质平板通道内的流体流动问题。针对动量方程的离散,空间上采用Chebyshev配置点谱方法,时间上采用准隐式格式离散,结合改进的投影算法(IPS)将速度和压力的计算解耦为一系列椭圆方程(泊松方程或亥姆霍兹方程),转换椭圆方程为矩阵方程形式后利用二步求解法求解矩阵方程。通过MATLAB编程实现对多孔介质平板通道内的流体流动问题的数值模拟并验证了程序的准确性。在此基础上,讨论了达西数(Da),雷诺数(Re)以及孔隙率(ε)对多孔介质平板通道内流体的速度分布、边界层厚度及入口长度的影响。

Based on Chebyshev collocation spectral method,the fluid flow in a porous media parallel plate channel was studied by numerical simulation.For the discretization of momentum equation,the Chebyshev collocation spectral method was adopted in space and quasi-implicit scheme was adopted in time.The velocity and pressure calculations were decoupled into a series of elliptic equations(Poisson equation or Helmholtz equation)by using the improved projection scheme(IPS).The elliptic equations were transformed into matrix equations,which were solved by the two-step method.The numerical simulation of fluid flow in the porous media parallel plate channel was realized by MATLAB programming and the accuracy of the program was verified.On this basis,the influences of Darcy number(Da),Reynolds number(Re)and porosity factor(ε)on velocity distribution,boundary layer thickness and inlet length of the fluid in the porous media parallel plate channel were discussed.