A Comparative Review of Smoothed Particle Hydrodynamics, Dissipative Particle Dynamics and Smoothed Dissipative Particle Dynamics

Smoothed particle hydrodynamics (SPH), dissipative particle dynamics (DPD) and smoothed dissipative particle dynamics (SDPD) are three typical and related particle-based methods. They have been increasingly attractive for solving fluid flow problems, especially for the biofluid flow, because of their advantages of ease and flexibility in modeling complex structure fluids. This work aims to review what the exact similarities and differences are among them, by studying four simple fluid flows: (i) self-diffusion of quiescent flow, (ii) time-dependent Coutte flow, (iii) time-dependent Poiseuille flow, and (iv) lid-driven cavity flow. The simulations show that SPH, DPD and SDPD can give the similar results. SPH generates quite smooth results and has zero system temperature due to the absence of thermal fluctuations, suitable for macroscale problems. However, DPD and SDPD have fluctuating results around the reference results and nonzero system temperature with considerable thermal fluctuations, suitable for mesoscale problems. SDPD is more convenient than DPD to some extent, because it is not required to pre-define the force coefficients. SDPD can adopt more diverse equation of state (EOS) than DPD, because its EOS is user-defined unlike the EOS of DPD, inbuilt in the formulations.