Finite element methods (FEM) applied to computational fluid dynamics open up the possibility of numerical simulation of highly complex fluid flows occurring in industrial situations. The state-of-the-art limitation on the use of FEM is computer resources: the method requires the solution of a very large system of algebraic equations, currently effected by inverting the Jacobian matrix, a process involving very high costs in computer time, IO and peripheral storage. This research project aims to investigate and implement a new matrix-free solution technique that obviate the costly matrix inversion; this technique is based on a variant of the conjugate gradient method. Recent research and testing on simple problems has indicated the prospect of a dramatic saving in costs. Successful implementation in a FEM, fluid dynamics context will vastly expand the range of flows (turbulent, non- Newtonian, three-dimensional) that can be simulated with currently available hardware.
