Unstructured grid finite-element methods for fluid mechanics

Abstract

. The development of unstructured grid based finite element methods for the simulation of fluid flows is reviewed. The review concentrates on solution techniques for the compressible Euler and Navier Stokes equations, employing methods which are based upon a Galerkin discretisation in space together with an appropriate finite difference representation in time. It is assumed that unstructured assemblies of triangles are used to achieve the spatial discretisation in two dimensions, with unstructured assemblies of tetrahedra employed in the three dimensional case. Adaptive grid procedures are discussed and methods for accelerating the iterative solution convergence are considered. The areas of incompressible flow modelling and optimisation are also included. 1. Introduction Over the past thirty years, there has been an intense research activity in the area of computational fluid dynamics. A large proportion of this activity has been driven by the aerospace industry, with its requirements...