Transport phenomena in collective dynamics: from micro to social hydrodynamics

The fittest survive: Adaptive lattice Boltzmann models for fluid dynamics

Ilya Karlin

ETH Zurich

Minimal kinetic models and particularly the lattice Boltzmann methods (LBM) attract attention as an alternative to complex flow simulations. In this talk, I will review the adaptive LBM based on the notion of entropy. These include the entropic lattice Boltzmann method (ELBM9 and recent entropic multirelaxation KBC models. Adaptive LBM differ from all the others by locally adjusting fluxes to the requirements imposed by the discrete-time analog of Boltzmann’s H-theorem (entropy increase as per the second law of thermodynamics). The two models differ in that all fluxes (including the viscous stress and non-equilibrium energy flux) are locally adapted in the ELBM while only the higher-order kinetic fluxes are adapted in the KBC. The adaptation brings the unmatched stability and accuracy to LBM. Applications to turbulent flows in complex geometries, shock-vortex interaction and novel droplet rebound mechanisms on macro-textured super-hydrophobic surfaces will be presented.