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

Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015)] as well as for three-dimensional one-way coupled simulations of engine-type geometries in $\mathrm{B}$. Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016)] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of $\mathrm{Re}=40000$ and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.

Figure 1

Temporal velocity evolution of a sedimenting sphere.

Figure 2

Schematic of a plunging airfoil.

Figure 3

Volume rendering of vorticity for various phases of the plunging airfoil. (a) $\phi =0$. (b) $\phi =0.25$. (c) $\phi =0.5$. (d) $\phi =0.75$.

Figure 4

Phase-averaged velocity profiles at $x/c=1.5$.

Figure 5

Phase-averaged velocity profiles at $x/c=2$.

Figure 6

Evolution of lift and drag coefficient over three exemplary cycles of a plunging airfoil.

Figure 7

Volume rendering of vorticity of the swimmers wake, showing the typical double row vortex street (see also the movie in the Supplemental Material [50]).

Figure 8

Temporal evolution of the forward velocity $U_{\parallel }$ and lateral velocity $U_{\perp }$.