Crystallographic Lattice Boltzmann Method

Abstract

Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows.

Under-resolved and large eddy simulations of a decaying Taylor–Green vortex with the cumulant lattice Boltzmann method

“…This includes the standard BGK method [35], classical MRT models [16], regularized lattice Boltzmann models [22], recursively regularized lattice Boltzmann models [23], the classical entropic lattice Boltzmann model [25], the KBC model [24] and classical central moment models [17,18]. The problem of velocitydependent viscosity is not present in models with increased isotropy such as those using a body-centred cubic lattice [8]. Using the standard D3Q27 lattice, the problem can be removed by a modification of the relaxation rate [47] or the equilibrium moments [21].…”

“…Advanced discretization of momentum space usually involves the utilization of many discrete speeds [4][5][6][7], or a lattice structure other than the Cartesian simple cubic lattice (e.g. body-centred cubic lattices [8,9]). From a finite difference perspective it is most natural to try to improve a method by enlarging or rearranging its stencil.…”

Deciphering pore-level precipitation mechanisms

“…For the description of simultaneous transport, dissolution and precipitation processes along with the resulting changes of the microscopic pore geometry we applied the lattice Boltzmann method (LB) 12 , 24 – 27 . The LB method is a computational technique based on a special discretization of the kinetic Boltzmann equation and provides the necessary fluid dynamic framework (See Methods section).…”

Entropic multirelaxation-time lattice Boltzmann method for moving and deforming geometries in three dimensions

“…However, spurious shocks for turbulence simulation at the boundary limit their usage to resolved and moderate Reynolds number flows. An interesting realization of the bounce-back can be found for a recent, so-called crystallographic LBM, in [40]. Another common approach for complex moving objects is the immersed boundary method (IBM), which was originally proposed by Peskin [42] for the simulation of blood flow.…”