Finite element analysis of compressible flows.

Abstract

In this research a finite element analysis program was developed for the modelling of general compressible Euler flows. An explicit Taylor-Galerkin algorithm was used as the flow solver and was used in conjunction with a flux-corrected transport algorithm in order to obtain high shock resolution without numerical oscillations and overshoots. The solver was applied to two and three dimensional geometries. An axisymmetric extension of the Taylor Galerkin algorithm was also developed. For the two dimensional code, a fully automatic mesh generator was implemented which was able to generate meshes for completely arbitrary geometries, as well as an adaptive refinement algorithm which performs an error analysis on the solution and refines and coarsens the mesh appropriately in order to maintain an optimal mesh resolution. The automatic mesh generator dramatically reduced problem setup time and the adaptive refinement algorithm reduced compllter time by up to 90%" A number of test cases were performed covering a wide range of compressible flows including steady and unsteady flows in air, using the ideal gas model, and shocks in liquids, using the Tait model. Within the limitations of the inviscid and real gas assumptions made, accurate results were obtained,