Keywords: lattice Boltzmann method, parallel performance, multiphase flows.

This chapter presents the main features of the lattice Boltzmann method (LBM). While classical CFD solvers are based on the discretization of the Navier-Stokes (NS) equations, the LBM can be derived using the Boltzmann equation, which is the foundation of kinetic theory. The result is a method which is based on the transport equation of the distribution functions rather than on macroscopic variables.

The first part of the chapter briefly introduces the LBM, particularly emphasizing the simplicity of the standard algorithm (given by a sequence of streaming, boundary condition and collision steps) and how to recover macroscopic quantities such as density, momentum and the stress tensor. This standard implementation can be made dramatically faster by merging the streaming and collision steps. Also the layout of data is important to increase the performance. All these aspects are discussed in the second part of the chapter.

Some parallel applications related to multiphase flows are then presented. Either liquid-gas or particle suspension flows can be effectively treated by the parallel LBM. In respect of this last application it is important to underline that the objects are not treated as point masses but are instead fully resolved on the same grid used for the fluid. Therefore there is no remeshing, giving LBM a great advantage over other numerical techniques. The conclusion is that the coupling of a versatile numerical model like the LBM with an optimized parallelization can be an excellent tool to deal with complex geometries. The last part of the chapter provides some examples including the binary droplet collision, the suspension sedimentation and the simulation of biological fluids such as blood.

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