SPHinXsys (pronunciation: s'finksis) is an acronym from Smoothed Particle Hydrodynamics for industrial compleX systems. It provides C++ APIs for physical accurate simulation and aims to model coupled industrial dynamic systems including fluid, solid, multi-body dynamics and beyond with SPH (smoothed particle hydrodynamics), a meshless computational method using particle discretization.

Included physics
Fluid dynamics, solid dynamics, fluid-structure interactions (FSI), and their coupling to multi-body dynamics (with SIMBody library)

SPH method and algorithms
SPH is a fully Lagrangian particle method, in which the continuum media is discretized into Lagrangian particles and the mechanics is approximated as the interaction between them with the help of a kernel, usually a Gaussian-like function. SPH is a mesh free method, which does not require a mesh to define the neighboring configuration of particles, but construct of update it according to the distance between particles. A remarkable feature of this method is that its computational algorithm involves a large number of common abstractions which link to many physical systems inherently. Due to such unique feature, SPH have been used here for unified modeling of both fluid and solid mechanics.

The SPH algorithms are based on the published work of the authors. The algorithms for the discretization of the fluid dynamics equations are based on a weakly compressible fluid formulation, which is suitable for the problems with incompressible flows, and compressible flows with low Mach number (less than 0.3). The solid dynamics equations are discretized by a total Lagrangian formulation, which is suitable to study the problems involving linear and non-linear elastic materials. The FSI coupling algorithm is implemented in a kinematic-force fashion, in which the solid structure surface describes the phase-interface and, at the same time, experiences the surface forces imposed by the fluid pressure and friction.

Geometric models
2D models can be built using basic shapes (polygon and circle) and full version of binary operations. 3D models can be generated by simple shapes (brick and sphere), imported from external STL files and processed by applying simple binary operations, e.g. add and substract.
Material models
Newtonian fluids with isothermal linear equation of state. Non-newtonian fluids with Oldroyd-B model. Linear elastic solid, non-linear elastic solid with Neo-Hookian model and anisotropic muscle model.

Multi-resolution modeling
Uniform resolution is used within each fluid or solid bodies. However, it is allowed to use different resolutions for different bodies. For example, one is able to using higher resolution for a solid body which is interacting with a fluid body with lower resolution.

Parallel Computing
Intel Threading Building Blocks (TBB) is used for the multi-core parallelism.

Authors
Xiangyu Hu, Luhui Han, Chi Zhang, Shuoguo Zhang, Massoud Rezavand, Yongchuan Yu

Project Principle Investigator
Xiangyu Hu (xiangyu.hu@tum.de), Department of Mechanical Engineering, Technical University of Munich

Acknowledgements
German Research Foundation (Deutsche Forschungsgemeinschaft) DFG HU1527/6-1, HU1527/10-1 and HU1527/12-1.