The lattice-Boltzmann Method, Background and Application to Large Scale Fluid Mechanics Problems

Andreas ten Cate

Chemical Engineering, Princeton University

 

The lattice-Boltzmann method is an efficient numerical scheme for the time dependent simulation of fluid flow problems. The method has been introduced in the early nineties and has its basis in cellular automata models for fluid flow. The method is based on the concept that macroscopic fluid motion originates from the individual motion and collisions of the molecules of a fluid. In the lattice-Boltzmann method the fluid is represented by mass that resides on a discrete grid that at discrete time intervals propagates along links that connect the grid nodes. The propagated masses collide upon arrival at a grid node. It can be demonstrated that by applying appropriate collision rules that conserve mass and momentum, the method simulates the incompressible Navier-Stokes and continuity equations.

At the algorithm level, the lattice-Boltzmann method provides an efficient, stable, second order accurate numerical scheme that has excellent parallelization properties. Since the collision rules are applied locally, no neighbor communication is required for the update of a grid node other than mass propagation. As a consequence, the method scales practically linear on parallel computers. Because of this good scalability, the method is highly suitable for simulation of large scale flow problems that require high spatial resolution. Examples that will be discussed in the presentation are the direct simulation of turbulent flow, the simulation of turbulent flows with large eddy type turbulence modeling and the flow in complex geometries such as clusters of particles.

Important issues in the use of the lattice-Boltzmann method, as will be demonstrated by the examples, are the choice of no-slip boundary condition and the possible need for grid refinement. Since the lattice-Boltzmann method is still relatively new, these two issues are topics of ongoing research. In this presentation I will discuss two principally different types of moving boundary conditions and explain how, depending on the type of flow problem studied, these two boundary conditions may require different parallelization strategies. Finally I will also address a method for grid refinement that is currently being developed and present recent results in which grid refinement has been successfully applied.