Validation data for a hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) method

An arbitrary Lagrangian Eulerian smoothed particle hydrodynamics (ALE-SPH) method with a boundary volume fraction formulation for fluid-structure interaction

We present a new weakly-compressible smoothed particle hydrodynamics (SPH) method capable of modeling non-slip fixed and moving wall boundary conditions. The formulation combines a boundary volume fraction (BVF) wall approach with the transport-velocity SPH method. The resulting method, named SPH-BVF, offers detection of arbitrarily shaped solid walls on-the-fly, with small computational overhead due to its local formulation. This simple framework is capable of solving problems that are difficult or infeasible for standard SPH, namely flows subject to large shear stresses or at moderate Reynolds numbers, and mass transfer in deformable boundaries. In addition, the method extends the transport-velocity formulation to reaction-diffusion transport of mass in Newtonian fluids and linear elastic solids, which is common in biological structures. Taken together, the SPH-BVF method provides a good balance of simplicity and versatility, while avoiding some of the standard obstacles associated with SPH: particle penetration at the boundaries, tension instabilities and anisotropic particle alignments, that hamper SPH from being applied to complex problems such as fluid-structure interaction in a biological system.

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

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.

Validation data for a hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) method

We present the validation of the hybrid sSSA-SDPD method for advection-diffusion-reaction problems coupled to discrete biochemical systems, as presented in the publication "A hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) for advection-diffusion-reaction problems" (Drawert et al., 2019). We validate 1D diffusion, and 2D diffusion cases against their analytical solutions. We present graphs and tables of data showing the error in the simulation method.