The generalized composite dynamic framework for the lattice Boltzmann method and its applications

Abstract

Composite dynamics in lattice Boltzmann methods have been used in several areas of research -- in modeling physical phenomena, as a staircase correction or homogenization approach. These dynamics are created by combining multiple simpler dynamics. For flow in porous media, free flow and no-slip walls dynamics are combined to model Darcy like flow behavior, and are often called grayscale or partially saturated methods. Furthermore, they are applied in modeling interfaces, e.g. membranes, reactive walls, and contact resistance. However, individual composite dynamics have been developed for a specific purpose in mind, without a unified framework. This limits the co-development and insights gained from one development branch to the next.

In this submission we present a novel framework that generalizes composite dynamics. Our framework captures previous porous media grayscale methods, while providing mathematical reasoning in relation to the inclusion of forces. It allows for cross development branch comparisons, hence accelerating the creation and improvement of composite dynamics, such as flux boundary condition. Finally, a few applications of our new framework are shown, encompassing subgrid nucleation and homogenized reactive flow in porous media.