Coupling fully resolved light particles with the lattice Boltzmann method on adaptively refined grids

Abstract

The simulation of geometrically resolved rigid particles in a fluid relies on coupling algorithms to transfer momentum both ways between the particles and the fluid. In this article, the fluid flow is modeled with a parallel lattice Boltzmann method using adaptive grid refinement to improve numerical efficiency. The coupling with the particles is realized with the momentum exchange method.When implemented in plain form, instabilities may arise in the coupling when the particles are lighter than the fluid. The algorithm can be stabilized with a virtual mass correction specifically developed for the lattice Boltzmann method.The method is analyzed for a wide set of physically relevant regimes, varying independently the body-to-fluid density ratio and the relative magnitude of inertial and viscous effects. These studies of a single rising particle exhibit periodic regimes of particle motion as well as chaotic behavior, as previously reported in the literature. The new coupled lattice Boltzmann method is compared with available experimental and numerical results. This serves to validate the presented method and additionally it leads to new physical insight for some of the parameter settings.

Unified directional parabolic-accurate lattice Boltzmann boundary schemes for grid-rotated narrow gaps and curved walls in creeping and inertial fluid flows

“…The violation of the Galilean invariance (VGI) of the LBM velocity solution is attributed either to (1) third-order momentum truncation [100]; (2) incorrect viscous stress [101,102] due to absence of its cubic-velocity correction by the quadratic NSE term E (u) q in Eq. (3b); (3) inaccuracy of the boundary scheme on a static solid surface subject to the tangential motion [103]; and (4) deficient reconstruction on the moving solid-fluid interface due to (i) mass-flux [8,79,83], (ii) "refill" of the new-born nodes [82,83,104], and (iii) momentumexchange algorithm [105], and also a combination of all these effects, where it has been understood [59] that the drag measured on the cylinder surface shows a much better agreement between the static and moving frames when the multireflection-based "refill" combines with the same accuracy-order modified momentum-exchange [59], which improves the standard force computation [2,4,55] for the stress approximation from the middle of the cut link towards the solid surface.…”

“…The lattice Boltzmann method (LBM) [1][2][3] applies for fluid modeling within a wide range of engineering, biological and physical problems with complex static and moving surfaces, such as particle-laden ones [4][5][6][7][8][9], suspensions of soft particles [10], red blood cells [11] and pulsatile [12,13] flows, porous flow in materials [14], synthetic structures [15][16][17][18][19][20], or natural rocks [21][22][23][24]. These problems are essentially described by the Stokes and finite Reynolds number regimes, and characterized by a coarse grid resolution over a narrow fluid path.…”

“…The parametrization means that when combined with the proper collision operator and linear force implementation [71], the steady-state Stokes flow error estimate and adjacent permeability measurements are viscosity-independent, whereas the NSE incompressible steady-state momentum solution is set by the grid Reynolds number Re g = U /ν, [8,22,[72][73][74]. The directional two-relaxation-time TRT collision operator [57,60] plays a crucial role in the parametriza-tion and accuracy, in both bulk and boundary.…”

“…The directional two-relaxation-time TRT collision operator [57,60] plays a crucial role in the parametriza-tion and accuracy, in both bulk and boundary. The TRT solution is parametrized by prescribing any fixed value to its free collision number ; the multiple-relaxation-time MRT collisions [75] achieve such an exact parametrization either within their TRT subclass τ ± i = τ ± , or when scaling their additional symmetric rates (τ + i − 1 2 ) in proportion with ν, [8,17]. When compressible effects are negligible, the MRT boundary effects remain practically controlled by alone [16,17].…”

Lattice-Boltzmann Modelling for Inertial Particle Microfluidics Applications — A Tutorial Review

“…Therefore, it should be possible to have a more refined fluid region around the particles and a coarser mesh elsewhere. Local grid refinement for LB simulations is an active research field, e.g., [329][330][331][332][333][334]. However, dynamic grid refinement around moving particles using the LB method is largely unexplored.…”