Simulating two-dimensional viscoelastic fluid flows by means of the “Tensor Diffusion” approach
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Date
2019-12
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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”.