Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

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Dissipative particle dynamics (DPD) is a mesoscale particle method that bridges the gap between microscopic and macroscopic simulations. It can be regarded as a coarse-grained molecular dynamics method suitable for larger time and length scales. It has been successfully applied to different areas of interests, especially in modeling the hydrodynamic behavior of complex fluids in mesoscale. This paper presents an overview on DPD including the methodology, formulation, implementation procedure and some related numerical aspects. The paper also reviews the major applications of the DPD method, especially in modeling (1) micro drop dynamics, (2) multiphase flows in microchannels and fracture networks, (3) movement and suspension of macromolecules in micro channels and (4) movement and deformation of single cells. The paper ends with some concluding remarks summarizing the major features and future possible development of this unique mesoscale modeling technique.