Symmetrized operator split schemes for force and source modeling in cascaded lattice Boltzmann methods for flow and scalar transport

Abstract

Operator split forcing schemes exploiting a symmetrization principle, i.e., Strang splitting, for cascaded lattice Boltzmann (LB) methods in two- and three-dimensions for fluid flows with impressed local forces are presented. Analogous scheme for the passive scalar transport represented by a convection-diffusion equation with a source term in a novel cascaded LB formulation is also derived. They are based on symmetric applications of the split solutions of the changes on the scalar field or fluid momentum due to the sources or forces over half time steps before and after the collision step. The latter step is effectively represented in terms of the post-collision change of moments at zeroth and first orders, respectively, to represent the effect of the sources on the scalar transport and forces on the fluid flow. Such symmetrized operator split cascaded LB schemes are consistent with the second-order Strang splitting and naturally avoid any discrete effects due to forces or sources by appropriately projecting their effects for higher-order moments. All the force or source implementation steps are performed only in the moment space and they do not require formulations as extra terms and their additional transformations to the velocity space. These result in particularly simpler and efficient schemes to incorporate forces or sources in the cascaded LB methods unlike those considered previously. Numerical study for various benchmark problems in 2D and 3D for fluid flow problems with body forces and scalar transport with sources demonstrate the validity and accuracy, as well as the second-order convergence rate of the symmetrized operator split forcing or source schemes for the cascaded LB methods.

Cascaded lattice Boltzmann method based on central moments for axisymmetric thermal flows including swirling effects

“…We will now present cascaded LB methods based on central moments and MRT for the computation of thermal convective flows in the cylindrical coordinates with axial symmetry, by also taking into account azimuthal rotational/swirling effects. A triple distribution functions based LB approach is considered, where the geometric source terms arising in the pseudo-2D macroscopic equations are represented using symmetric operator splitting around the cascaded collision steps [45]. The solution of the resulting cascaded LB models then yields the local fluid flow variables such as the radial axial and azimuthal velocity fields, pressure (or density) field, and the temperature field in the meridian plane.…”

“…where g p α is the post-collision distribution function and q = ( q o , q 1 , · · · q 4 ) represents the changes of different moments under a cascaded collision prescribed as a relaxation process in terms of central moments, which reads as [45]…”

“…The use of symmetric operation split formulations based on pre-collision and post-collision source steps for incorporating the geometric source terms for axisymmetric thermal flows including swirl effects leads to a particulary simplified formulation, which is consistent with the classical Strang splitting. The application of central moments based cascaded LB schemes using MRT can enhanced numerical stability of the LB simulations, and the use of symmetric operator splitting yields a scheme that is second order in time, as demonstrated numerically [45]. Such an axisymmetric cascaded LB approach for the simulation of thermally stratified and/or rotating flows in cylindrical geometries can lead to reduced computational and memory costs when compared This paper is organized as follows.…”

Hybrid recursive regularized thermal lattice Boltzmann model for high subsonic compressible flows

“…In order to overcome the insufficient stability observed in the BGK model, several improved collision models with enhanced stability have been proposed, e.g. multi-relaxationtime models [6,7], entropic LB models [8,9], regularized BGK models [10,11], or cumulant/cascaded LB models [12,13].…”

Local vorticity computation approach in double distribution functions based lattice Boltzmann methods for flow and scalar transport

“…We prescribe the central moment equilibria based on those of the local Maxwellian, by replacing the density with the scalar field φ (see e.g., [54,55,56]). Usually, the third order central moment equilibria then becomeη eq xxy =η eq xyy = 0 and the corresponding raw moment equilibria areη eq xxy = c 2 sφ φu y + φu 2 x u y and η eq xyy = c 2 sφ φu x + φu x u 2 y [54,55,56]. On the other hand, to enable local computation of the vorticity field, our derivation in Secs.…”