Theoretical development of the SPH method and application to transient fluid structure interaction problems.

The smoothed particle hydrodynamic method (SPH) is a meshless method that suffers from several shortcomings. These shortcomings are tensile instability and zero energy modes -which are characterised by unphysical particle clumping- lack of consistency and improper enforcement of essential boundary conditions. The capability of the method also lacks; with most applications limited to either fluid or very simple fluid-structure interactions. This thesis addresses most of the issues that plague SPH as well as extending the capability to more complex fluid-structure interactions. Particle clumping has been reduced by the introduction and rigorous mathematical and code development of a mixed formulation procedure that while is prevalent in finite element, has never been applied to the SPH method. Unlike every other attempt in literature to solve the particle clumping problem, this approach addresses the cause as opposed to treat the symptoms, which gives it mathematical rigour and generality. Furthermore, a moving least squares procedure was applied to the code to smooth pressure by using a first order consistent scheme, this gave an unexpected side effect in the form of velocity differences between simulations that used the procedure and those that did not. This was investigated and conclusions drawn into the nature of why this difference occurred. Extension of the capability of the method occurred by the addition of rotational boundary conditions and modification of the contact algorithm to account for a no-slip boundary condition to achieve successful simulation of complex fluid-structure interaction problems. These problems were three benchmark cases involving the interaction of an elastic body and free surface flow. Validation occurred throughout the development of the code and simulations. Code validation was by comparison to theory, while the results of the beam deflection were compared to LS-Dyna. The benchmark cases were compared to both experimental results and to another paper who modelled the problem using a partitioned finite volume solver. All coding and simulations in this work was done within in the inhouse Meshless continuum mechanics (MCM) code.