Parallel numeric simulation of peristaltic disorders for memory fluids

Single-integral equations are adequate constitutive models for nonlinear viscoelastic memory fluids. During a numerical simulation it is required then to trace back fluid elements at their path lines starting from the interpolation points within the numerical grid and to compute the deformation history simultaneously by integrating the corresponding system of nonlinear evolution equations. In principle the numerous past time integrations can be allocated to the different processors of a parallel computer. The main features of such a parallel computational method on the basis of a finite-element discretisation are described. The method is used to analyse axisymmetric peristaltic flows, especially in order to highlight the influence of the Deborah number on the pumping characteristics. When looking at the details of a specific flow field, the memory effect becomes apparent by correlating the extra-stress tensor to the strain-rate tensor locally. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.