SUMMARYCentral moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify the collision process and forcing, and thereby naturally maintaining Galilean invariance, an important characteristic of fluid flows. When the different central moments are relaxed at different rates like in a standard multiple relaxation time (MRT) formulation based on raw moments, it is endowed with a number of desirable physical and numerical features. Because the collision operator exhibits a cascaded structure, this approach is also known as the cascaded LBM. While the cascaded LBM has been developed sometime ago, a systematic study of its numerical properties, such as the accuracy, grid convergence, and stability for well-defined canonical problems is lacking, and the present work is intended to fulfill this need. We perform a quantitative study of the performance of the cascaded LBM for a set of benchmark problems of differing complexity, viz., Poiseuille flow, decaying Taylor-Green vortex flow, and lid-driven cavity flow. We first establish its grid convergence and demonstrate second-order accuracy under diffusive scaling for both the velocity field and its derivatives, that is, the components of the strain rate tensor, as well. The method is shown to quantitatively reproduce steady/unsteady analytical solutions or other numerical results with excellent accuracy. The cascaded MRT LBM based on the central moments is found to be of similar accuracy when compared with the standard MRT LBM based on the raw moments, when a detailed comparison of the flow fields are made, with both reproducing even the small scale vortical features well. Numerical experiments further demonstrate that the central moment MRT LBM results in significant stability improvements when compared with certain existing collision models at moderate additional computational cost.

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The crater formation on granular particle beds is important for engineering applications, chemical and process industries as well as for an explanation of related natural phenomena. In this article, experimental studies on the formation of a crater and the subsequent movement of granular particles are carried out. Granular beds consisting of mono-dispersed or poly-dispersed spherical glass-beads are subjected to an air-jet impingement. The impinging air-jet causes creation of craters of various sizes and shapes (such as saucer shape, parabolic shape, parabolic shape with an intermediate region, U shape, and craters with conical slants with a curved bottom surface). The experimental observations reveal two predominant regimes, categorized based on the crater stability, namely, a stable regime or an unstable regime. The mechanisms for the crater formation such as viscous erosion, diffused gas eruption, bearing capacity failure, and diffusion driven flow or combination of them are identified. It is observed that the steady-state depth of a crater increases linearly with an increase in the air-jet flow-rate. The temporal growth of crater depth shows logarithmic variation for a given flow rate. A regime map of the observed crater shapes is presented.