The biannual International Workshop on Numerical Methods in Non-Newtonian Flows started in 1979 in Rhode Island, USA, and had its nineteenth edition in 2019, in Peso da Régua, Portugal. In the late 1970s, at a time when Newtonian CFD had already started to materialize into competing commercial products, the large scatter of numerical results for the same viscoelastic non-Newtonian flow problems and the corresponding conflicting physical interpretations of data, which were very much associated with the lack of accuracy and convergence difficulties ensuing from the so-called high–Weissenberg number problem (HWNP), led to the establishment of a series of regular workshops that introduced proper benchmarks and focused research efforts in the field. CR refers to flow simulations with fluids that are described by non-Newtonian models, more complex than the generalized Newtonian fluid, since specific techniques to address the inherent numerical difficulties associated with the complex constitutive equations are needed even if the simulations are aimed at a fluid mechanics perspective. Over the last 40 years, computational rheology (CR), the application of computational fluid dynamics (CFD) to fluids with non-Newtonian rheology, has developed into a mature discipline, which simultaneously helps to understand a wide range of physical phenomena while also providing useful tools for engineering design. Many synthetic fluids, as well as some natural fluids, show complex rheological behavior in which viscoelasticity is a relevant fluid property.
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