Numerous approaches have been proposed for solving partial differential equations; all these
methods have their own advantages and disadvantages depending on the problems being treated. In
recent years there has been much development of particle methods for mechanical problems.
Among these are the Smoothed Particle Hydrodynamics (SPH), Reproducing Kernel Particle
Method (RKPM), Element Free Galerkin (EFG) and Moving Least Squares (MLS) methods. This
development is motivated by the extension of their applications to mechanical and engineering
problems.
Since numerical experiments are one of the basic tools used in computational mechanics, in
physics, in biology etc, a robust spatial discretization would be a significant contribution towards
solutions of a number of problems. Even a well-defined stable and convergent formulation of a
continuous model does not guarantee a perfect numerical solution to the problem under
investigation.
Particle methods especially SPH and RKPM have advantages over meshed methods for problems,
in which large distortions and high discontinuities occur, such as high velocity impact,
fragmentation, hydrodynamic ram. These methods are also convenient for open problems. Recently,
SPH and its family have grown into a successful simulation tools and the extension of these
methods to initial boundary value problems requires further research in numerical fields.
In this thesis, several problem areas of the SPH formulation were examined. Firstly, a new approach based on ‘Hamilton’s variational principle’ is used to derive the equations of motion in the SPH form. Secondly, the application of a complex Von Neumann analysis to SPH method reveals the
existence of a number of physical mechanisms accountable for the stability of the method. Finally, the notion of the amplification matrix is used to detect how numerical errors propagate permits the identification of the mechanisms responsible for the delimitation of the domain of numerical stability.
By doing so, we were able to erect a link between the physics and the numerics that govern the SPH formulation.
| Identifer | oai:union.ndltd.org:CRANFIELD1/oai:dspace.lib.cranfield.ac.uk:1826/133 |
| Date | 09 1900 |
| Creators | Gourma, Mustapha |
| Contributors | Vignjevic, Rade |
| Publisher | Cranfield University, School of Engineering; College of Aeronautics |
| Source Sets | CRANFIELD1 |
| Language | en_UK |
| Detected Language | English |
| Type | Thesis or dissertation, Doctoral, PhD |
| Format | 1883 bytes, 6358627 bytes, text/plain, application/pdf |
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