Smooth lattice general relativity, and SPH simulations of swimming linked bodies

In this thesis, two quite different bodies of work are presented. The first is the study of the smooth lattice approach to numerical relativity which has been developed by Brewin (1998a,b, 2002). The aim of the research was to further test the viability of the method. Previously, it had been used to model a Kasner cosmology and a Schwarzschild black hole. Both were shown to produce excellent results. In this thesis, the details and results for a long-term, stable integration of a (one-dimensional) symmetric gravitational collapse are given. In the second body of work, smoothed particle hydrodynamics (SPH) was used to model swimming linked bodies. These simulations are an attempt to model the motion of real swimming animals, such as fish or eels. The calculations were for three linked, rigid bodies in two-dimensions. However, the set of equations provided are easily generalised for more bodies, and for three dimensions. The results are shown for a range of body and fluid parameters. The common link between the two areas of research is that they are computational in nature. Both involve the study and development of specific numerical algorithms, and their application to particular problems. Whilst a significant amount of time was spent on developing the mathematical formulae, the vast majority was spent on the numerical implementation, i.e. writing and testing code, using both C and Fortran programming languages. The calculations were all done on a standard Apple eMac desktop computer. The thesis has been split into two parts to reflect that the two bodies of work are separate. In each part, the relevant mathematical and numerical details are described, and the associated results are presented.