Particle-Based Mesoscale Hydrodynamic Techniques

– Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale simulation techniques in more detail, we propose new two methods, which are intermediate between DPD and MPC — DPD with a multibody thermostat (DPD-MT), and MPC-Langevin dynamics (MPC-LD). The key features are applying a Langevin thermostat to the relative velocities of pairs of particles or multi-particle collisions, and whether or not to employ collision cells. The viscosity of MPC-LD is derived analytically, in very good agreement with the results of numerical simulations. Soft matter systems such as polymer solutions, colloidal suspensions, vesicles, cells, and microemulsions exhibit many interesting dynamical behaviors, where hydrodynamic flow plays an important role, as do thermal fluctuations. Several mesoscale simulation techniques for the flow of complex fluids accompanied by thermal fluctuations have been developed in the last decades, such as direct simulation Monte Carlo (DSMC) [1, 2], the Lattice Boltzmann method [3], dissipative particle dynamics (DPD) [4–12], and multi-particle collision (MPC) dynamics [13–17]. These methods have many similarities. The most important common feature is the local mass and momentum conservation, which is crucial to obtain hydrodynamic behavior in the continuum limit. Since most of these methods were developed independently, the relations between them are not well explored so far. In this letter, we clarify the relations between the particle-based off-lattice methods, particularly DPD and MPC, and use this insight to propose two new intermediate methods (all summarized in Fig. 1). We start from the relations between the Langevin and the Andersen’s thermostat (AT) [18]. The underdamped Langevin equation of N particles is given by m dvi dt = −∇iU + fLT, (1) fLT = −γvi + σξi(t), (2) where ∇i = ∂/∂ri, m is the mass of a fluid particle, and ri and vi are the position and velocity of the i-th particle, respectively. The force fLT represent the Langevin thermostat. To satisfy (∗) E-mail:[email protected]