A novel finite element technique for the solution of engineering flow problems

A new technique known as the bubble function method is developed for the modelling of fluid flow problems. The main motivation for this work has been the desire to resolve difficulties that traditional methods show in dealing with multi-scale behaviour in flow regimes. All of the traditionally used methods require excessive mesh refinement in the simulations of systems that combine different scale of behaviour in one domain. The present bubble function method avoids such crude remedies and instead of using an elegant mathematical technique for the conjunctive approximation of fine and coarse scale phenomena. Using numerical experiments it is shown that the implementation of the bubble function method generates accurate and stable solutions for a wide range of problems. This range includes convection and reaction dominated transport phenomena, and various types of porous flow systems, it can also be extended to transient flow simulations. To demonstrate the applicability of the present technique it has been used to solve a realistic problem, namely solute dispersion in an estuary. The results of this simulation show good agreement with field survey data.