The LS-STAG immersed boundary method modification for viscoelastic flow computations

The LS-STAG immersed boundary cut-cell method modification for viscoelastic flow computations is presented. Rate type viscoelastic flow models (linear and quasilinear) are considered. Formulae for differential types of convected time derivatives the LS-STAG discretization was obtained. Normal non-newtonian stresses are computed at the centers of base LS-STAG mesh cells and shear non-newtonian stresses are computed at the cell corners. The LS-STAG-discretization of extra-stress equations for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson–Segalman fluids was developed. Time-stepping algorithm is defined by the following three steps. Firstly, a prediction of the velocity and pressure correction are computed by means of semi-implicit Euler scheme. Secondly, the provisional velocity is corrected to get a solenoidal velocity and the corresponding pressure field. After this the extra-stress equations are solved. Applications to popular benchmarks for viscoelastic flows with stationary boundaries and comparisons with experimental and numerical studies are presented. The results show that the developed LS-STAG method modification demonstrates an accuracy comparable to body-fitted methods. The obtained modification is implemented in the “LS-STAG” software package developed by the author. This software allows to simulate viscous incompressible flows around a moving airfoil of arbitrary shape or airfoils system with one or two degrees of freedom. For example, it allows to simulate rotors autorotation and airfoils system wind resonance. Intel\textsuperscript{\textregistered} Cilk\texttrademark Plus, Intel\textsuperscript{\textregistered} TBB and OpenMP parallel programming technologies are used in the “LS-STAG”.