MRT-LBM simulation of four-lid-driven cavity flow bifurcation

This paper seeks to make a systematic study over the complex four-lid-driven cavity flows using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). The flow is generated by moving the top wall to the right and the bottom wall to the left, while moving the left wall downwards and the right wall upwards, with an identical moving speed. The present MRT-LBM results reveal a lot of important features of bifurcated flow, such as the multiplicity of stable asymmetric and unstable symmetric cavity flow patterns when the Reynolds number exceeds its first critical value (corresponding to the first steady bifurcation), and the second steady bifurcation phenomena on the first unstable solution at the second critical Reynolds number (corresponding to the second steady bifurcation), as well as the flow periodicity after the third critical Reynolds number is reached (referred to as Hopf bifurcation point). The present MRT simulations have predicted that the critical Reynolds numbers are at 359±1 and 721±6 for the second steady bifurcation and the Hopf bifurcation, respectively. For the study of periodic four-lid-driven flows, the stream function and the phase-space trajectory are investigated in detail. Through comparison against the stability analysis and numerical results reported elsewhere, not only does the MRT-LBM approach exhibit its fairly satisfactory accuracy, but also its remarkable capability for investigating the multiplicity of complex flow patterns.