## 4 Dpd
Finally, SDPD, which is derived from SPH and is similar to MD in terms of moving particles interactions simulation, introduced Lagrangian discretization of NS equations and an exact discretized fluctuation theorem and adopted a thermostat similar to the one in DPD, improving most of the original method's drawbacks [90]. This method has all the advantages of the other three methods and none of their disadvantages, which made it the most common DPD method. SDPD has several advantages over the conventional DPD method, such as allowing direct input of fluid transport coefficients and selecting desired arbitrary equation of state; resulting in full control over fluid compressibility [91]. This method, however, has all the drawbacks of the SPH method because of the closely related particle-based nature of it compared to SPH [90]. Thus, one would still need to input high accuracy real physical values, such as viscosity, to the method to reduce the inaccuracies. Moreover, the pressure field of the problem needs to be calculated separately by using the equation of state via solving the Poisson equation of pressure, given its inherent continuum-originated build-in models [93]. Another drawback relates to the lack of a direct relationship or link between the viscosity of the fluid and the velocity profile, which was alleviated in SDPD [94]. These methods have been extensively used for simulation of particle sorting systems, for instance, in deterministic lateral displacement devices, modeling blood flow problems including RBCs related simulations, blood-related diseases, and disorders, particles like plasma and proteins, bacteriology and parasitology over the recent years [89; 91; 92; 93; 94]. SDPD method has proven to be especially suitable for simulation of blood flow and by being coupled with the immersed boundary method. The fluid-RBCs interactions, which are an essential area of focus in cell sorting and cell separation problems, can also be accurately modeled instead of being modeled as physically connected particles, which makes it an accurate and computationally efficient method for blood flow problems [93]. This method can also be applied to understand the behavior of healthy and unhealthy RBCs in real physics as well. For years, lacking appropriate boundary conditions and high-performance computing hindered implementing particle-based methods in simulation of blood flow in microvascular networks and similar complex problems. Likewise, the SDPD method suffered the same hindrances and could not be used for many of the investigations, despite all other improvements since the time the original DPD method was introduced [95]. Some issues to be tackled in terms of the computational speed of this method are; for instance, irregular patterns of computation resulting in hindering its parallel computing capability and the maximum speed limit and having an order of magnitude higher interaction instructions than in MD for each time step. Building a neighborhood list in each time step for each of the particles and finally, implementation of an extra thermostat for some of the forces and interactions [95]. New computers and algorithms for higher performance computing were presented recently and are shown to solve these two problems in the future. Recent advances in numerical computing capabilities and new parallel algorithms for these particle-based methods made the implementation of numerical simulations easier and capable of reaching higher time scales, which is a crucial factor for simulation to replace the expensive experimental tests on devices. Aside from advances in computational technologies, efforts have been devoted to increasing the method's efficiency and speed and thus, reaching higher computation times and computational domains with a higher number of entities. For instance, one can mention the development of new open flow boundary conditions, which are clustered in the periodic boundary condition category.