On the Parallelization of the Lattice-Boltzmann Method

Salvatore Filippone¹ - Nicola Rossi - Gino Bella² - Stefano Ubertini
Università di Roma ``Tor Vergata''
Roma, Italy

The Lattice-Boltzmann (LB) method has witnessed in recent years many theoretical and practical enhancements, greatly increasing its viability as an alternative for fluid dynamics computations to the classic Navier-Stokes equations.

In particular, the great increase in the size of the simulation domains of interest has made it necessary:

• The application of parallel computing techniques in order to keep computing time under control;
• The introduction of unstructured meshes.

The basic differential form of theLB equation is as follows:

$$\frac{\partial f_{k}(\overrightarrow{x},t)}{\partial t}=\ov... ...}_{k}(\overrightarrow{x},t))\, ;\, \forall k\in \{1\ldots n\}$$ (1)

This can be formulated in a finite-volume framework, as shown in [1]; the finite-volume formulation can in turn be implemented with a series of sparse matrix-vector operations. Thus, it is possible to reuse the PSBLAS software [2] to implement the basic operations. In the full paper we report on the specific details of the parallelization techniques and on the results obtained on a set of test cases relevant to fluid dynamics computations in mechanical engineering.