Stabilizing Lattice Boltzmann Simulation of Flows Past Bluff Bodies by Introduction of Ehrenfests' Limiters
thesisposted on 16.03.2011, 16:45 by Tahir Saeed Khan
The lattice Boltzmann method (LBM) have emerged as an alternative computational approach to the conventional computational fluid dynamics (CFD). Despite being computationally efficient and popular numerical method for simulation of complex fluid flow, the LBM exhibits severe instabilities in near-grid scale hydrodynamics where sharp gradients are present. Further, since the LBM often uses uniform cartesian lattices in space, the curved boundaries are usually approximated by a series of stairs that also causes computational inaccuracy in the method. An interpolation-based treatment is introduced for the curved boundaries by Mei et al. One of the recipe to stabilize the LBM is the introduction of Ehrenfests' step. The objective of this work is to investigate the efficiency of the LBM with Ehrenfests' steps for the flows around curved bluff bodies. For this purpose, we have combined the curved boundary treatment of Mei et al. and the LBM with Ehrenfests' steps and developed an efficient numerical scheme. To test the validity of our numerical scheme we have simulated the two-dimensional flow around a circular cylinder and an airfoil for a wide range of low to high Reynolds numbers (Re ≤ 30, 000). We will show that the LBM with Ehrenfests' steps can quantitatively capture the Strouhal-Reynolds number relationship and the drag coefficient without any need for explicit sub-grid scale modeling. Comparisons with the experimental and numerical results show that this model is a good candidate for the turbulence modeling of fluids around bluff bodies.