Investigation of LBM curved boundary treatments for unsteady flows

Abstract

The standard Lattice Boltzmann Method is based on an orthogonal, equidistant lattice structure. Therefore, representation of curved boundaries deserves further attention. In comparison to the straightforward possibility of representing a curved boundary by a staircase, there are more sophisticated approaches for an accurate modelling of a curved boundary in the literature. Therefore, in the present paper, three such methods are compared with each other, and with the straightforward staircase approximation, which is chosen to be a symmetrically placed circular bluff body in channel flow at Reynolds number 500. As the reference solution, results obtained by a commercial CFD code are used, which are obtained by an exact representation of the curved boundaries, using non-orthogonal finite volume discretisation. Four different mesh resolutions are used. On coarse meshes, the results were different. On sufficiently fine lattice structures / finite volume meshes, all LBM results were very similar to the CFD results. As the mesh was refined from coarse to fine, the extrapolation method was observed to approach to the fine-mesh solution more slowly than the alternative methods. Thus, it is concluded that under the considered LBM curved boundary treatment procedures the extrapolation method has a comparably inferior performance. The remaining methods show a similar performance to each other.