*4.4.1. Complete numerical simulations (CNSs) for multiphase flow*

Complete numerical simulation (CNS) methods are numerical techniques where the Navier-Stokes equations are applied to finite-size particles instead of introducing point-mass and point-force assumptions. Particle motion is governed by the Newton's second law, based on the hydrodynamic forces calculated from the fluid equations. For CNS-based multiphase flow, all surface and collision forces due to fluid-particle and particle-particle interactions should be accurately calculated to obtain the velocity, pressure, and stress fields surrounding each particle [35]. Specifically, mesh scales for CNS methods are much lower than particle sizes; hence, surface forces such as drag force and lift force, as well as interaction force between particles can be directly integrated from the shear stress and pressure distribution along the particle surfaces. This avoids empirical correlations, such as drag and lift coefficients.

Compared with CFPD models which are based on Euler-Euler or Euler-Lagrange methods, CNS is a mesoscale model that can accurately describe motions of particles with arbitrary shapes. As such, CNS of multiphase flows can promote fundamental understanding of the underlying physics, e.g., the nonlinear and geometrically complicated phenomena of particleparticle and particle-wall interactions.

With the enhancement of the computational power in the future, CFPD models will be replaced by DNS and CNS methods to simulate unconventional lung aerosol dynamics. However, the computational cost of DNS and CNS methods is still too high for engineering application. Applying these methods to a large number of particles is not realistic according to the current computational resources [79].

#### *4.4.2. Discrete element method (DEM)*

Discrete element method (DEM) can provide transient forces and torques acting on individual particles. DEM was first proposed by Cundall and Strack [81] based on molecular dynamics. The most attractive feature of DEM method is its relatively efficient algorithms for the contact detection and contact force calculation between arbitrary shaped particles [82]. Soft-sphere models are the most common type of models used in DEM, which simplify particle-particle interaction force with spring-dashpot-slider systems [27]. Determinations of the stiffness coefficients and damping coefficients are essential in DEM interaction models. Contact forces are calculated in two steps in DEM methods [83]:


Additionally, for nonspherical particles, representation of the particle shape is also essential in DEM simulations. Two major treatments of the particle shape representation are widely used for the contact detection and contact force calculation between nonspherical particles [84]: superquadric method and multisphere method. The algorithm to integrate DEM with Euler-Euler and Euler-Lagrange models (see **Figure 12** for a standard flow chart) for dense particulate flow is straightforward [38]. However, there are two key challenges:


Computational Fluid-Particle Dynamics Modeling for Unconventional Inhaled Aerosols in Human Respiratory Systems http://dx.doi.org/10.5772/65361 77

particles and flow domains is too large. Therefore, efficient algorithms need to be developed.

**Figure 12.** The algorithm of coupling DEM with conventional multiphase flow models.
