Parallel Performance of Lattice Boltzmann and Implicit Finite Difference Approaches to the Approximation of the Two-Dimensional Diffusion Equation

The reduction of computation times is an important aspect of interactive computational fluid dynamics simulations. The lattice Boltzmann method has proved to be an important technique for the numerical solution of partial differential equations because it has nearly ideal scalability on parallel computers for many applications. Utilizing the two-dimensional diffusion equation, Tt=μ(Txx+Tyy), this paper examines the parallel performance for the lattice Boltzmann method and the alternating direction implicit (ADI) method. In this study for 50 time steps the non-cache optimized parallel lattice Boltzmann method was on average two times faster than the parallel ADI method. The cache optimized parallel lattice Boltzmann was on average seven times faster than the parallel ADI method.