Numerical Study of Lid-Driven Square Cavity Flow with Embedded Circular Obstacles Using Spectral/hp Element Methods

Abstract

We show a successful numerical study of lid-driven square cavity flow with embedded circular obstacles based on the spectral/hp element methods. Various diameters of embedded two-dimensional circular obstacles inside the cavity and Reynolds numbers Re (from 100 to 5000) are considered. In order to verify the effectiveness and accuracy of the current methods, numerical results are investigated by comparing with those available in the literature obtained by the moving immersed boundary method (MIBM) and the lattice Boltzmann method (LBM). The present spectral/hp element methods have been not only successfully applied to study and visualize the primary and induced vortices but also capture new vortices on the lower right, upper left and upper right positions of the circular obstacle when Reynolds number Re = 100 and Re = 5000, which is not observed in the lattice Boltzmann method. The current data and figures are in good agreement with the published results. The results of the present study show that the spectral/hp element methods are effective and accurate in simulation of lid-driven cavity flow with embedded circular obstacles, and the present methods have the following advantages: less preprocesses required and high-resolution characteristics.