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333185 A New Boundary Treatment for Complex Geometries in Smoothed Particle Hydrodynamics

Smoothed
Particle Hydrodynamics (SPH) is a Lagrangian particle method, which was
originally developed in astrophysics to simulate flows in boundary-less
domains. Nowadays, the method is mostly used to solve the governing equations
of fluid flow, including free surface flows^{1}.

However,
the treatment of wall boundaries in SPH is not unique and different approaches
exists, mostly based on particles^{2,3}.
However, engineering applications often require complex shaped geometries,
usually generated by CAD programs, e.g. in the STL format, where an appropriate
use of boundary particles or ghost particles would be highly complicated or
even lead to wrong results (e.g. at corners). Today it is not obvious how to handle
such STL geometries properly in SPH.

In our work, we developed a new approach to model the interaction between SPH particles and wall triangles (i.e., the STL geometry), which can easily be implemented in a SPH code and lead to a proper behavior of fluid particles near walls.

We use the
open-source particle simulator LIGGGHTS (www.liggghts.com),
originally developed for the simulation of granular flow via the Discrete
Element Method (DEM), also providing an SPH module. Our boundary treatment
together with the viscosity model of Morris et al.^{2}
leads to a close agreement of the velocity profiles with the analytical
solution for a channel flow between two plates, specifically an accurately
fulfilled no-slip condition (see Figure 1).

The main focus of our research is the application of SPH to the simulation of mixing in hot melt extrusion processes (HME), which attracted increasing attention in pharmaceutical manufacturing in recent years. The typically used co-rotating twin-screw design consists of a complex shaped, rotating geometry, highly challenging for mesh-based methods due to the deformation of the free volume caused by the screw rotation. Our new method for boundary handling was used to simulate the mixing process within the geometry of a co-rotating twin-screw extruder (snapshots of the distribution of two different particle types in the cross section of a twin-screw are shown in Figure 2).

The presented approach provides a robust basis for efficient simulations of fluid flow in complex, moving geometries in the STL format.

Figure 1: Velocity profiles in a pressure-driven channel flow: analytical solution, dots: SPH solution using the developed boundary conditions.

Figure 2: Snapshots of mixing in a cross-section of a co-rotating twin-screw extruder. Top: initial state, center after 0.05 revolutions, bottom after 1.05 revolutions.

1. Monaghan JJ. Smoothed particle hydrodynamics. *Reports on Progress in Physics*. 2005;68(8):1703-1759.

2. Morris JP, Fox PJ, Zhu Y. Modeling Low Reynolds
Number Incompressible Flows Using SPH. *Journal of Computational Physics*. 1997;136(1);214-226.

3. Colagrossi A, Landrini M.
Numerical simulation of interfacial flows by smoothed particle hydrodynamics. *Journal of Computational Physics*.
2003;191(2):448-475

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