In many equilibrium or nonequilibrium statistical physics problems, fluctuations play a crucial role. Often those problems are too complex to be solved analytically. Accordingly, numerical algorithms keeping track of the fluctuations are needed. Cellular automata (CA) and Lattice Boltzmann (LB) models are two possible approaches to simulate complex systems. CA models keep track of many-body correlations and provide a description of the fluctuations. However, they lead to a noisy dynamics and impose a restriction on the possible values of the viscosity. On the other hand, LB models are numerically more efficient and offer much more flexibility to adjust the physical parameters, but they neglect the fluctuations. We have developed a new multiparticle lattice model which reconciles both approaches. The main characteristics of this approach are explained, and our model is used to study the kinetics of two-dimensional ballistic annihilation.