A new approach to the deformation fields method for solving complex flows using integral constitutive equations

In this paper, we present a newapproach to the deformation fields method that has recently been introduced to solveintegral type models in complex flows (E.A.J.F. Peters, M.A. Hulsen, B.H.A.A. van den Brule, J. Non-NewtonianFluid Mechanics 89 (2000) 209 -228). The new approach is based on a change of the reference time of the fields froman absolute time to a time relative to the current time. This basically removes most, if not all, stability and accuracyproblems that exist in the original method compared to using differential models. Also the new implementation ismuch more flexible with respect to the time integral discretisation, opening the way to adaptive refinement. The newimplementation has been tested for two problems: the standard 2:1 benchmark of a the flow around a sphere usin! ga UCM model and the flow around a sphere in a different geometry using a PSM model.