Comparison/Validation Study of Lattice Boltzmann and Navier Stokes for Various Benchmark Applications: Report 1 in Discrete Nano-Scale Mechanics and Simulations Series

Abstract : For purposes relating to the U.S. Army s need for materials modeling and force protection, this work provides justification for assigning effective equivalence between two commonly used fluid simulation methods namely the Navier-Stokes (NS) and Lattice Boltzmann methods. The Lattice Boltzmann Method (LBM) has become increasingly popular as an alternative approach to traditional NS-based techniques for modeling various incompressible fluid flow applications. The LBM has recently increased its range of applicability to include numerous fields of interest including those involving multiphase and thermo-fluid structure interactions. This report documents a comparison/validation effort accompanying the development of a standard Lattice Boltzmann solver with immersible moving boundaries. The primary goal is to validate the model by comparing it with various laminar, incompressible flow cases simulated using a finite volume-based NS solver. Simulations involving four standard benchmark studies were analyzed: (1) the flow through a rectangular channel, (2) the flow through a lid-driven cavity, (3) the flow over a back-step, and (4) the flow over a stationary circular cylinder. For the specific applications and Reynolds numbers simulated, the results showed excellent agreement between the two cases. Disparities were observed only when the theoretical constraints of the LBM were exceeded.