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In this review, we describe and analyze a mesoscale simulation method forfluid flow, which was introduced by Malevanets and Kapral in 1999, and is nowcalled multi-particle collision dynamics (MPC) or stochastic rotation dynamics(SRD). The method consists of alternating streaming and collision steps in anensemble of point particles. The multi-particle collisions are performed bygrouping particles in collision cells, and mass, momentum, and energy arelocally conserved. This simulation technique captures both full hydrodynamicinteractions and thermal fluctuations. The first part of the review begins witha description of several widely used MPC algorithms and then discussesimportant features of the original SRD algorithm and frequently usedvariations. Two complementary approaches for deriving the hydrodynamicequations and evaluating the transport coefficients are reviewed. It is thenshown how MPC algorithms can be generalized to model non-ideal fluids, andbinary mixtures with a consolute point. The importance of angular-momentumconservation for systems like phase-separated liquids with differentviscosities is discussed. The second part of the review describes a number ofrecent applications of MPC algorithms to study colloid and polymer dynamics,the behavior of vesicles and cells in hydrodynamic flows, and the dynamics ofviscoelastic fluids.

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids