The LS-STAG Immersed Boundary Method Modification for Non-Newtonian Viscous Fluids Computation

A modification of the immersed boundary method LS-STAG with level functions has been developed to simulate flows of non-Newtonian viscous fluids. The viscosity of these fluids is completely determined by the intensity of the strain rate tensor at each point at any time. The LS-STAG method modification was previously developed for another class of non-Newtonian fluids (viscoelastic fluids). The modification demonstrated high accuracy even for viscoelactic flows characterized by high values of the Weissenberg number. Therefore, it is of interest to generalize the LS-STAG method for non-Newtonian viscous fluids. Note that although the LS-STAG method can be successfully used to simulate flows with moving immersed boundaries, this paper focuses only on flows with fixed ones. The developed numerical method can be used both for viscoplastic fluids and for generalized Newtonian fluids that do not have a yield point. For viscoplastic fluids, the Ofoli-Morgan-Steffe, Mizrahi-Burk, Casson, and Herschel-Bulkley models used with the Bercovier-Engelmann and Papanastasiou regularization models are considered, and for fluids that do not have a yield point, the Ellis, Cross, Carreau, Yasuda (Carreau-Yasuda) models, as well as the Ostwald-de Waele power model are considered. To verify the numerical method developed and implemented in the author's software package, a well-studied problem of power-law flow past a stationary circular airfoil was used at different values of the Reynolds number and flow index. The obtained results are in good agreement with the known in the literature computational data of other researchers. In the future, it is planned to generalize the developed modification of the LS-STAG method for non-Newtonian viscous fluids simulation for the case of moving immersed boundaries.

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