A hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) for advection–diffusion–reaction problems

Highlights: • A hybrid spatial SSA and SDPD method is proposed. • It allows the simulation of stochastic advection–reaction–diffusion problems in a Lagrangian description. • Successful validation of the new method in several benchmark problems. • Method is tested on a problem where commercial CAE software and typical deterministic methods cannot capture all dynamics. -- Abstract: We have developed a new algorithm which merges discrete stochastic simulation, using the spatial stochastic simulation algorithm (sSSA), with the particle based fluid dynamics simulation framework of smoothed dissipative particle dynamics (SDPD). This hybrid algorithm enables discrete stochastic simulation of spatially resolved chemically reacting systems on a mesh-free dynamic domain with a Lagrangian frame of reference. SDPD combines two popular mesoscopic techniques: smoothed particle hydrodynamics and dissipative particle dynamics (DPD), linking the macroscopic and mesoscopic hydrodynamics effects of these two methods. We have implemented discrete stochastic simulation using the reaction–diffusion master equations (RDME) formalism, and deterministic reaction–diffusion equations based on the SDPD method. We validate the new method by comparing our results to four canonical models, and demonstrate the versatility of our method by simulating a flow containing a chemical gradient past a yeast cell in a microfluidics chamber.