Lattice Boltzmann method computation of the incompressible flow past an impulsively started cylinder

Abstract

Computation of impulsively started flows presents difficulties associated with the presence of a singularity at time equal to zero. When using the lattice Boltzmann method, the standard practice is to start the computation from a potential flow field that is not part of the solution. A different approach to the problem is presented in this article where three new criteria for the selection of computational parameters in highly unsteady flow environments are presented. These criteria, which do not overrule the conventional one that sets limits to the computational Mach number, are based on fluid physics considerations. They represent additional constrains related to (a) the distance traveled by sound waves at early times, (b) the importance of viscous length during the onset of impulsive motion, and (c) the presence of spurious reflected pressure waves at the beginning of computations. The proposed methodology was tested in the case of an impulsively started cylinder, and the results were compared to those of analytical, numerical, and experimental nature published in specialized literature. It is intended that this study facilitates the computation of highly unsteady flows for researchers who use the lattice Boltzmann method.