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.
Key words: Lattice-Boltzmann; Finite Element; Finite Volume; CFD; benchmark;