The "Tensor Diffusion" approach for simulating viscoelastic fluids

Abstract

In this work, the novel "Tensor Diffusion" approach for simulating viscoelastic fluids is proposed, which is based on the idea, that the extra-stress tensor in the momentum equation of the flow model is replaced by a product of the strain-rate tensor and a tensor-valued viscosity. At least for simple flows, this approach offers the possibility to reduce the full nonlinear viscoelastic model to a generalized "Tensor Stokes" problem, avoiding the need of considering a separate stress tensor in the solution process. Besides fully developed channel flows, the “Tensor Diffusion” approach is evaluated as well in the context of general two-dimensional flow configurations, which are simulated by a suitable four-field formulation of the viscoelastic model respecting the "Tensor Diffusion". However, substituting the extra-stress tensor by the "Tensor Diffusion" in the complete flow model is desired for general two-dimensional flows as well, again to be able to reduce the full nonlinear viscoelastic model to a Stokes-like problem.