Application of the Lattice Boltzmann Method to Steady Incompressible Laminar High Re Flows

An incompressible steady-state formulation of the Lattice Boltzmann Method is applied to laminar flows for a varying range of Reynolds numbers, extending form 50 to 2000. As test cases, the channel and the lid driven cavity flow problems are considered. The effect of the model Mach number on the accuracy is also analyzed by performing computations for different Mach numbers varying within the range 0.1 0.4, comparing the results with each other and with the results obtained by a finite-volume discretization of the incompressible Navier-Stokes equations. For both test cases, it is observed that the implied Mach number by the method does not effect the results within the abovementioned ranges. An important purpose of the study has been to explore the stability limits of the method. Within this context, it is observed that the largest allowable collision frequency decreases with increasing Reynolds and Mach numbers. It is additionally observed that these dependencies are stronger, and the limiting collision frequencies are lower for the channel flow, compared to the lid driven cavity flow. Key-Words: Lattice Boltzmann Method, Computational Fluid Dynamics, Laminar Flow, High Reynolds Number Nomenclature cs lattice sound speed α e r discrete lattice velocity set α f discrete particle distribution function H channel height, cavity edge length Ma Mach number ( s c v u Ma / 2 2 + = ) x position vector x.y 2D Cartesian coordinates p modified static pressure Re Reynolds number (Re = u0 H / ν) t time u, v flow velocity components Greek symbols δ lattice unit (distance between two neighboring lattice nodes) δt time step ν kinematic viscosity ρ density ω collision frequency Suband Superscripts 0 boundary value eq equilibrium value ~ post-collision state Proceedings of the 7th IASME/WSEAS International Conference on FLUID MECHANICS and AERODYNAMICS ISSN: 1790-5095 220 ISBN: 978-960-474-106-9