Benchmark computations based on Lattice-Boltzmann, Finite Element and Finite Volume Methods for laminar Flows

The goal of this article is to contribute to a more precise discussion of the question whether Lattice-Boltzmann (LB) methods can be regarded as efficient CFD solvers. After a short review of the basic model and recommendable extensions, we compare the accuracy and computational efficiency of two research simulation codes based on the LB and the Finite-Element method (FEM) for incompressible laminar two-dimensional flow problems in complex geometries. As LB methods are weakly compressible by nature, we also study the influence of the Mach number on the solution by comparing compressible and incompressible results obtained by the LB code and the commercial code CFX. Our results indicate, that for the quantities studied (lift, drag, pressure drop) our LB prototype is at least competitive for incompressible transient problems, but asymptotically slower for steady-state Stokes flow as the asymptotic algorithmic complexity of the classical LB-method is not optimal compared to the multigrid solvers incorporated in the FEM and CFX code. For the weakly compressible case, the LB approach has a significant wall clock time advantage as compared to CFX. In addition, we demonstrate that the influence of the finite Mach number in LB simulations of incompressible flow is easily underestimated.