Smoothed particle hydrodynamics is a computational method used for simulating fluid flows. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography.

Smoothed particles hydrodynamics (SPH) was invented to simulate non axis- symmetric phenomena in astrophysics (Lucy 1977; Gingold & Monaghan 1977). SPH is a particle method; it does not need a grid to calculate spatial derivatives. Instead, they are found by analytical differentiation of interpolation formulae.

SPH is an interpolation method which allows any function to be expressed in terms of its values at a set if disorder points – the particles.

SPH is a Lagrangian method. The Lagrangian description is a material description, which employs the total time derivative as the combination of local derivative and convective derivative.

The state of a system is represented by an ensamble of particles. The particles have individual material properties and move according to the governing conservation equations.

Picture_799 - SPH Kernel

These particles have a spatial distance (known as the "smoothing length"), 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.

Picture_800 - SPH Spheric Case8