Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics, in short SPH, is a discretization method in space that is applied to continuum mechanics in particular.

Project Description

Being a meshfree method based on particles that move along the velocity field of the represented matter, SPH often offers big advantages over meshbased methods such as Finite Elements when it comes to free surface flows or high deformations of elastic materials. To discretize a partial differential equation using the SPH method, the considered volume is subdivided. These subdivisions are then reduced to one point, the so-called particle, which gets all the important values such as velocity, density but also tension and thermal energy as a mean value taken over the whole subdivision. Therefore, particles are partial volumes with an undefined volume expansion, that move along the velocity field of the represented matter. The spatial functions in the differential equation can now be approximated by smoothing and summing up the discrete values at the particle positions using a kernel function, often similar to a Gaussian function. The approximation's spatial derivatives can be calculated straight away due to the differentiable kernel function. This leaves an ordinary differential equation in time that can be solved with one of the many time stepping schemes. 

This image shows Peter Eberhard

Peter Eberhard

Prof. Dr.-Ing. Prof. E.h.
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