Parallel Efficiency of the Lattice Boltzmann Method for Compressible Flows

Abstract

This chapter evaluates a newly developed lattice-Boltzmann (LB) model for high Mach number compressible flows for parallel computing efficiencies. An adaptive LBmodel for high-speed compressible flows has been implemented on parallel computers. In contrast to standard LB models, this model can handle flows over a wide range of Mach numbers and capture strong shock waves. The present results agree well with those of other computational methods. This compressible flow LB model is of same efficiency as standard LB models but consumes less computer memory. The total computation time is proportional to the total number of nodes. For the cases tested, high parallel efficiency is achieved. The model appears to be a promising scheme for large-scale parallel computational fluid dynamics. The results show that up to 32 computer nodes, the new compressible LB model still show ideal or superlinear speedup. In the present model, due to the adaptive nature of the particle velocities, particles may be sent to nodes far away when the mean velocity is high. Information on only the block boundaries is not sufficient, and one must consider the interactions between interior points of the blocks. Therefore, information from interior points needs to be passed to the adjoining blocks.