To use the lattice Boltzmann method to solve the following problems: (1) flows with high Reynolds number; and (2) inhomogeneous multi-phase and multi-component fluids with interfaces.
We propose to apply the method of the lattice Boltzmann equation (LBE) for the aforementioned problems. The LBE method has the following advantages: (1) intrinsic parallelism; (2) fast computational speed and high accuracy; (3) capability to handle complex moving geometries for flow-structure interactions; and (4) ease to incorporate model interactions such that thermodynamics is consistently included in the interfacial dynamics (liquid-vapor or liquid-liquid interfaces). The lattice Boltzmann equation is a simplified finite-difference form of the continuous Boltzmann equation. The lattice Boltzmann method conserves the hydrodynamic moments (mass, momentum, and energy) exactly while reduces the momentum space to a few discrete point such that it becomes set of equations involving only localized calculations.
Results have clearly shown that the LBE method can be a very competitive method for computational fluid dynamics (CFD) in terms of computational efficiency and accuracy. The LBE method is especially effective in dealing with stiff problems due disparate separation of time scales. In the flow-structure interaction problems, the time scales are that of mean flow (slow) and solid structure (fast). Recently, we have successfully obtained a grant for application of the LBE method for flow-structure interactions. Our work on curved boundary treatment has been published in J. Comput. Phys. Regarding multi-phase fluids, we have recently worked out a theory to study liquid-vapor phase transition based upon kinetic theory, and this work has been accepted by Physical Review Letters.
Problems with disparate time scales and moving boundaries are ubiquitous in reality, and yet they remain as challenges to conventional CFD methods. The lattice Boltzmann method offers an alternative which is particularly suitable in dealing these phenomena. For flow-structure interaction problems, the time step in the lattice Boltzmann equation is small enough and computations involved in each time step are very simple such that the LBE algorithms can be very effective. As for the phase transition problems, the lattice Boltzmann method treats the interfaces as an emerging phenomenon (or a thermodynamical result) due to the inter-particle interactions. Such an approach avoids the explicit tracking of interfaces and provides a consistent thermodynamics, and can be applied to difficult problems such as boiling, cavitation, and spinodal decomposition in mixtures.
We have developed 2D and 3D LBE codes with Fortran and MPI, on Beuwolf-style clusters and MPPs. Our tests show that the LBE codes scale linearly with the number of processors. Our effort in the near future will concentrate on development of codes which can handle complicated boundaries in 3D. The LBE codes to simulate boiling are also under development. We have used the 3D LBE method to simulate the vortex breakup in a tank with rotating bottom, and with various obstacles.
Figure 1: LBE simulation of a tank with rotating bottom. System 95x95x135, max velocity U=0.12, radius R=47, viscosity = 0.0018, Re = 3000. Contours of velcity magnitude. From left to right, and top to bottom, t = 0, 4000, 8000, and 12000 in lattice units. The vortex breakdown at the center is well captured in the simulations.
Figure 2: LBE simulation of a tank with stirring mechanism. Parameters are the same as in Figure 1. Top Right: rotating bottom and a plate. Bottom: rotating bottom and a side comb, with different vorticity values. The required changes in geometry are easily accomplished in the LBE simulations.
Li-Shi Luo
ICASE, NASA Langley Research Center
email: luo@icase.edu
