Finite Element Distributed Computation for Viscoelastic Rotating Flows

This paper is concerned with the parallel computation of incompressible viscoelastic rotating flows. Such flows arise in many industrial settings being particularly important in the food industries, for materials such as dough. Here, the material is driven by one or two stirrers, rotating about the centre of a cylindrical vessel, fixed to a lid. The stirrers may be positioned in eccentric arrangement with respect to the axis of the vessel. The motivation for this work is to advance fundamental technology modelling the kneading of dough with the ultimate aim to predict the optimal design of dough mixers themselves, hence, leading to efficient dough processing. The numerical method employed is a time-marching semi-implicit Parallel-Taylor-Galerkin scheme, posed in a cylindrical polar coordinate system. This scheme is second-order in time and based on a fractional-staged pressure-correction formulation. Parallel computations are performed, via domain decomposition, on homogeneous and heterogeneous distributed networks using the Parallel Virtual Machine message passing protocol. Parallel timings are compared against those for sequential computation. Ideal linear speed-up is observed with increasing numbers of processors. This is achieved through a sophisticated implementation that effectively masks communication within pure computation costs.