基于Chebyshev谱方法的多孔介质二维方腔内自然流动模拟

采用Chebyshev配置点谱方法对局部热平衡状态下多孔介质方腔内的自然流动进行了模拟,使用Chebyshev-Gauss-Lobatto配置点对无量纲化的控制方程进行了空间上的离散,离散方程组采用高效矩阵对角化方法进行了求解.将所得结果与已有文献进行了对比,计算结果吻合良好.为验证该数值方法的精度,构造了一个精确解对该方法的求解误差进行了测试,结果表明,Chebyshev配置点谱方法具有很高的计算精度.最后,在验证程序正确性的基础上,研究了Ra对流场、温度场及努塞尔数的影响.

Simulation of Natural Convection in Square Porous Cavity Based on Chebyshev Spectral Method

The Chebyshev spectral collocation method (CSCM) was used to simulate natural convection in the square porous cavity under a local thermal equilibrium condition. Using the Chebyshev-Gauss-Lobatto collocation points， the dimensionless govering equations can be spatially discredited. The matrix diagonalization method was used to solve these discredited equations. The simulation results were in well agreement with the existing data. Meanwhile， the exact solutions were further constructed to valid the method and the CSCM effectiveness was proved. Finally， the effects of Rayleigh number on the streamlines， the isotherms and the Nusselt number were studied based on the CSCM simulations.