Monday, April 13 2020
11:00am - 12:00pm
Computational Mathematics Colloquium
Central Moment Lattice Boltzmann Methods: Modeling and Applications for Complex Flow Simulations

Lattice Boltzmann methods (LBM) are stream-and-collide based algorithms involving the evolution of the particle distribution functions inspired from kinetic theory for computational fluid dynamics. They are efficient, naturally parallelizable and deliver second order accuracy with high fidelity involving relatively low dissipative truncation errors. The collision step in LBM, generally represented as a relaxation process, plays a prominent role in modeling the relevant physics and in tuning the desired numerical properties, such as the numerical stability of the scheme. Among different possible techniques, the central moment LBM, a promising formulation, is generally based on the relaxation of various central moments of the distribution functions to their equilibria at different rates under collision. The latter is usually constructed either directly from the continuous Maxwell distribution function or by exploiting its factorization property. In this presentation, we will first provide an introductory survey of the LBM, and then discuss our contributions based on such classical formulation of the central moment LBM related to enhancing its efficiency and enabling new modeling capabilities for a variety of complex flow applications, such as thermal convection, non-Newtonian flows, and multiphase flows with surface tension effects, including its modulation by the presence of surfactants. In addition, we have recently developed a new formulation for the collision operator of the central moment LBM from a different perspective involving the continuous space-time Fokker-Planck (FP) kinetic equation, which was originally proposed for representing stochastic diffusive processes such as Brownian dynamics, by adapting it as a collision model for the Boltzmann equation for flow simulations. The resulting discrete formulation can be interpreted in terms of the relaxation of the various central moments to “equilibria” that depend only on the adjacent, lower order post-collision moments. We designate such newly constructed chain of equilibria as the Markovian central moment attractors and the relaxation rates are based on scaling the drift coefficient of the FP model by the order of the participating moment. We will conclude by presenting this more recent modified FP-guided central moment LBM and demonstrate its accuracy and robustness by its comparison against other collision models for some benchmark flows.
 Speaker: Kannan Premnath Affiliation: CU Denver Department of Mechanical Engineering Location: See Zoom link from email