Simulations of flow instability in three dimensional deep cavities with multi relaxation time lattice Boltzmann method on graphic processing units

The D3Q19 multi relaxation time (MRT) lattice Boltzmann model is adopted to simulate the instability phenomenon within a three-dimensional cavity at various depth-width aspect ratios ranging from 1 to 3. The computations are conducted on a single node multi graphic processing unit (GPU) system, consisting of three nVIDIA M2070 devices using OpenMP. Results show that transition takes place between 1750 < Recr < 1950, for cubic cavity and 1100 < Recr < 1450, for deep cavity flows with aspect ratio 2 and 3. This indicates that an increase of the depth-width aspect ratio would induce the transition at lower Reynolds number and is consistent with the previous results for two-dimensional cavities, though the critical Reynolds number is approximately 75% lower for three dimensional cavity.