2008-05-21
10:15 at HCI J 574

Free Lattice-Boltzmann!

Andre Bardow

TU Delft, The Netherlands

The Lattice Boltzmann (LB) method is a highly promising approach to the simulation of complex flows. However, the intrinsic coupling of momentum and space discretization restricts the applicability of the traditional Lattice Boltzmann method to uniform, regular lattices which is often disadvantageous in practice. In particular, the choice of a specific velocity model determines simultaneously the velocity, space and time discretization of the Boltzmann equation. In off-lattice Boltzmann methods, these discretizations are independent. Off-lattice Boltzmann methods therefore could offer the opportunity to independently discretize velocity, space and time for problem-adapted simulations. Much research has been done on off-lattice Boltzmann methods to enhance the geometrical flexibility of the LB method. In contrast, the additional freedom gained in velocity space seems to not have been systematically exploited. Both aspects are discussed in this presentation. The general characteristic-based algorithm for off-lattice Boltzmann simulations proposed by the authors [1] preserves all appealing properties of the standard Lattice Boltzmann method while extending the method to unstructured grids. With respect to velocity discretization, we realize the recently proposed multispeed Lattice Boltzmann models [2] by exploiting the flexibility offered by off-lattice Boltzmann methods. We show that the use of multi-speed models indeed gives rise to major improvements in accuracy and that the Hermite model hierarchy provides the sound systematic framework [3]. References: [1] A. Bardow, I. V. Karlin, A. A. Gusev, General characteristic-based algorithm for off-lattice Boltzmann simulations, Europhys. Lett., 75:434-440, 2006; [2] S. S. Chikatamarla, S. Ansumali, I. V. Karlin, Entropic lattice Boltzmann models for hydrodynamics in three dimensions, Phys. Rev. Lett., 97: 010201, 2006. [3] A. Bardow, I. V. Karlin, A. A. Gusev, Multispeed models in off-lattice Boltzmann simulations, Phys. Rev. E 77(2): 025701(R), 2008.