The development of adaptive finite element solvers

Adaptive procedures for viscoelastic flows have been implemented using a semi-implicit finite element Taylor-Galerkin/pressure correction scheme, for both an Oldroyd-B and a Phan-Thien-Tanner model (ROPA/EPSRC and other funding).

The adaptive meshing technique has followed h-refinement by grid remeshing, based on a Delaunay procedure. This work has resulted in a number of high quality publications, see for example, Mutlu et al., and Rameshwaran et al.. Error estimates based on velocity gradients have predicted the corresponding element sizes to generate meshes with more accurate solutions. Examples of flow past a rigid sphere in a cylindrical tube and tube-tooling wire-coating flow illustrate the considerable optimisation attainable with adaptivity. In Matallah et al. [j18], a similar temporal adaptive philosophy has been successfully devised to accelerate convergence rate to steady state for viscoelastic flows.