Unstructured grid finite-element methods for fluid mechanics

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 discretization 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 discretization 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 optimization are also included.