Smoothed Particle Hydrodynamics

Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the dynamics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan (1977) and Lucy (1977) initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a mesh-free Lagrangian method (where the coordinates move with the fluid), and the resolution of the method can easily be adjusted with respect to variables such as the density.

The smoothed-particle hydrodynamics (SPH) method works by dividing the fluid into a set of discrete elements, referred to as particles. These particles have a spatial distance (known as the "smoothing length", typically represented in equations by ${\displaystyle h}$), over which their properties are "smoothed" by a kernel function. This means that the physical quantity of any particle can be obtained by summing the relevant properties of all the particles which lie within the range of the kernel. For example, using Monaghan's popular cubic spline kernel the temperature at position ${\displaystyle \mathbf {r} }$ depends on the temperatures of all the particles within a radial distance ${\displaystyle 2h}$ of ${\displaystyle \mathbf {r} }$.

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