Smoothed-particle hydrodynamics
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a meshfree Lagrangian method (where the co-ordinates move with the fluid), and the resolution of the method can easily be adjusted with respect to variables such as density. By construction, SPH is a meshfree method, which makes it ideally suited to simulate problems dominated by complex boundary dynamics, like free surface flows, or large boundary displacement. The lack of a mesh significantly simplifies the model implementation and its parallelization, even for many-core architectures. SPH can be easily extended to a wide variety of fields, and hybridized with some other models, as discussed in Modelling Physics. As discussed in section on weakly compressible SPH, the method has great conservation features. The computational cost of SPH simulations per number of particles is significantly less than the cost of grid-based simulations per number of cells when the metric of interest is related to fluid density (e.g., the probability density function of density fluctuations). This is the case because in SPH the resolution is put where the matter is. Setting boundary conditions in SPH such as inlets and outlets and walls is more difficult than with grid-based methods. In fact, it has been stated that "the treatment of boundary conditions is certainly one of the most difficult technical points of the SPH method". This challenge is partly because in SPH the particles near the boundary change with time. Nonetheless, wall boundary conditions for SPH are available The computational cost of SPH simulations per number of particles is significantly larger than the cost of grid-based simulations per number of cells when the metric of interest is not (directly) related to density (e.
