Stabilised finite elements for compressible fluid flow. - Daniel Memory (2014)
A finite element formulation for the Euler equations of fluid dynamics is developed and analysed in this work. An overview of fluid dynamics is presented along with an introduction to the finite element method. The Galerkin method is then applied to model problems to demonstrate its performance. Stabilisation in the form of the Galerkin Least-Squares method is added and different variations of stabilisation parameter are analysed for different governing equations. For temporal discretisation the generalised-Q method is applied and studied. The Euler equations of fluid dynamics are transformed into primitive variable form and are stabilised so that the method can be tested for compressible flow problems. It is shown that certain stabilisation parameters can be successfully adapted for use with the Euler equations in primitive variables in order to simulate inviscid fluids.