The Modified LS-STAG Method Application for Planar Viscoelastic Flow Computation in a 4:1 Contraction Channel

In this study we present the modification of the LS-STAG immersed boundary cut-cell method. This modification is designed for viscoelastic fluids. Linear and quasilinear viscoelastic fluid models of a rate type are considered. The obtained numerical method is implemented in the LS-STAG software package developed by the author. This software is created for viscous incompressible flows simulation both by the LS-STAG method and by it developed modifications. Besides of this, the software package is designed to compute extra-stresses for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson --- Segalman fluids on the LS-STAG mesh. The construction of convective derivatives discrete analogues is described for Oldroyd, Cotter --- Rivlin, Jaumann --- Zaremba --- Noll derivatives. The centers of base LS-STAG mesh cells are the locations for shear non-Newtonian stresses computation. The corners of these cells are the positions for normal non-Newtonian stresses computation. The first order predictor--corrector scheme is the basis for time-stepping numerical algorithm. Benchmark solutions for the planar flow of Oldroyd-B fluid in a 4:1 contraction channel are presented. A critical value of Weissenberg number is defined. Computational results are in good agreement with the data known in the literature

This work was supported by the Russian Science Foundation (RSF project no. 17-79-20445)

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