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Central 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 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. Since 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 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, i.e. 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. 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.
Cascaded lattice-Boltzmann method (Cascaded-LBM) employs a new class of collision operators aiming to improve numerical stability. It achieves this and distinguishes from other collision operators, such as in the standard single or multiple relaxatio
Fluid motion driven by thermal effects, such as that due to buoyancy in differentially heated three-dimensional (3D) enclosures, arise in several natural settings and engineering applications. It is represented by the solutions of the Navier-Stokes e
We present a new 3D lattice Boltzmann (LB) algorithm based on central moments for the D3Q27 lattice using a cuboid grid, which is parameterized by two grid aspect ratios that are related to the ratios of the particle speeds with respect to that along
Simulating inhomogeneous flows with different characteristic scales in different coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBM) can be accomplished efficiently using rectangular lattice grids. We develop and
An Onsager-like relation is proposed as a new criterion for constructing and analysing the lattice Boltzmann (LB) method. For LB models obeying the relation, we analyse their linearized stability, establish their diffusive limit, and find new constra