Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor

摘要: We propose a numerical scheme for simulation of transient flows incompressible non-Newtonian fluids characterised by non-monotone relation between the symmetric part velocity gradient (shear rate) and Cauchy stress tensor stress). The main difficulty in dealing with governing equations such is that constitutive allows several values to be associated same value gradient. This issue handled via reformulation equations. are reformulated as system triple pressure-velocity-apparent viscosity, where apparent viscosity given scalar implicit equation. prove proposed has---on discrete level---a solution, using we numerically solve flow problems.