## 5 Other Particle-Based Methods
Most of these methods are mesh-free, which makes them merely implementable for complex fluid-structure problems as mentioned before, and are similar, in nature, to one of the particle-based techniques discussed previously. BEM is another mesh-free method, in which computational discretized points are only defined on the physical and inlet-/outlet boundaries of the problem, and the analytical solutions for velocity fields in the problem results from integration formulations on the boundary and the quantities inside the boundaries can be calculated using somewhat complex integration formulations [115] depending on the geometry and condition of problem being investigated. An advantage of this method is that it can be easily used for problems with complex geometries since there is only a computational grid required for the boundaries. By using advanced integration formula, it is proven to be the most useful and accurate for infinite length problems compared to other similar methods. However, this method is determined to be the most reliable for stokes flow regimes, and it is not applicable for some cellular flow problems with a length-scale exceeding 100 micrometers and other methods are needed to be chosen instead [116]. MPS is very similar to SPH method in its nature, where the governing equations are derived from NS equations and the physical properties are calculated using a similar function as the kernel function in SPH method [117] and using weighted averaging functions based on the distance between two particles. The mathematical implementation of MPS is somewhat difficult if trying to reach a higher accuracy, which can be considered a drawback by some researchers, while the accuracy is not noticeably different. DP is another type of these methods, which is a Meso-scale method similar to original DPD or SDPD, where different forces of different nature are defined and act separately on the particles, i.e., conservative, dissipative and random forces. The difference between this method and SDPD, however, is the existence of new function to control and take into account the rotation of each particle throughout the simulation. Some of these methods have had minimal applications in the literature, and thus, an in-detail explanation of them is out of the scope of this work. A short review on some of these methods, however, can be found in [64; 114; 118]. A few examples of the results obtained from related simulations using these particle methods are presented in Figure 10. Note that, the application of simulations conducted based on the original forms of these methods is not common in RBC-related investigation, however, the hybrid versions of these methods with DPD or LBM methods can be seen in the literature as it was mentioned earlier in this work. As this method improved over recent years, some commercial software packages have been developed based on these methods to simplify the process and increase the efficiency of using these methods in investigating desired particle flow related problems. Table 2 summarizes some of the most common tools developed based on these models. These software tools are mainly developed using C++ and FORTRAN languages and have easy interfaces to be used by a typical user. However, one would need basic knowledge of the algorithm they are created based upon as well as a basic understanding of available libraries in Windows and Linux operating systems.