Investigation into LBM Analysis of Incompressible Laminar Flows at High Reynolds Numbers

The Lattice Boltzmann Method is applied to incompressible, steady, laminar flows at high Reynolds numbers varying in a range form 50 to 2000. The developing channel flow and the lid driven cavity flow are analyzed. The effect of the model Mach number on accuracy is investigated by performing computations at different Mach numbers in the range 0.1 0.4 and comparing the results with finite-volume predictions of the incompressible NavierStokes equations. It is observed that the Mach number does not effect the results within this range, and the results agree perfectly well with the finite-volume solution of the incompressible Navier-Stokes equations. An important purpose of the study has been to explore the stability limits of the method. It is observed that the maximum allowed collision frequency decreases with increasing Reynolds and Mach numbers, and this dependency is more predominant, 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, Incompressible Flow, 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 α w weighting factors 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 m mean value ~ post-collision state WSEAS TRANSACTIONS on FLUID MECHANICS A. C. Benim, E. Aslan, I. Taymaz ISSN: 1790-5087 107 Issue 4, Volume 4, October 2009