Hybrid lattice Boltzmann method on overlapping grids

Abstract

In this work, a hybrid lattice Boltzmann method (HLBM) is proposed, where the standard lattice Boltzmann implementation based on the Bhatnagar-Gross-Krook (LBGK) approximation is combined together with an unstructured finite-volume lattice Boltzmann model. The method is constructed on an overlapping grid system, which allows the coexistence of a uniform lattice nodes spacing and a coordinate-free lattice structure. The natural adaptivity of the hybrid grid system makes the method particularly suitable to handle problems involving complex geometries. Moreover, the provided scheme ensures a high-accuracy solution near walls, given the capability of the unstructured submodel of achieving the desired level of refinement in a very flexible way. For these reasons, the HLBM represents a prospective tool for solving multiscale problems. The proposed method is here applied to the benchmark problem of a two-dimensional flow past a circular cylinder for a wide range of Reynolds numbers and its numerical performances are measured and compared with the standard LBGK ones.

A moving-grid approach for fluid–structure interaction problems with hybrid lattice Boltzmann method

“…A crucial aspect is represented by the direct computation of the forces at the real boundary of the solid body, which is not allowed in the standard LBM. Also, the presence of an unstructured grid allows an high and flexible level of refinement in proximity of the solid body, thus leading to a reduction of the computational cost with respect to the case of uniform grid, as demonstrated in [39,40]. For a further qualitative comparison between MG-HLBM and literature results, we report a complete overview of experimental and numerical findings in aggregated form in Figures 4 and 5 Black circles: present study; gray pentagons: [23]; magenta stars: [33]; red squared: [21]; blue asterisks: [22]; orange triangles: [36]; violet diamonds: [47]; green crosshairs: [24]; brown crosses: [48,49] 0.01 0.1 1 ε Figure 5: Aggregated results for the imaginary part −Im[Θ(β, ε)] of the complex hydrodynamic function (color online).…”

“…The moving grid approach proposed in this work is based on a lattice Boltzmann method applied to hybrid structured and unstructured grids recently proposed by the authors (HLBM) [39]. For clarity of exposition, in this section the key points of such a method are recalled.…”

On the wake interference effects for flow around tandem bodies

“…For the solution of governing model, we choose lattice Boltzmann method (LBM) which has been proven as a promising alternative for computational fluid dynamics simulations [29][30][31][32]. In contrary to other solution approaches that solve the Navier-Stokes equations using some suitable discretization approach, the LBM relies on computing the so-called distribution functions f i that are evolved according to the lattice Boltzmann equation where e i represents velocity directions, is the relaxation time, and f eq i is the equilibrium distribution function.…”

Ligament break-up simulation through pseudo-potential lattice Boltzmann method

“…The major appeals pertain its simplicity and applicability in a wide range of conditions, the easy handling of complex geometries (e.g. porous media), the possibility to combine it with other methods to design hybrid approaches [10,11], and even possible extensions to more complex physics phenomena (e.g. non-Newtonian fluids, [12]).…”