Finite element simulation of nonlinear fluids

Více o knize

This thesis focuses on developing new numerical and algorithmic tools for flows with pressure and shear-dependent viscosity, alongside the foundational concepts of the generalized Navier-Stokes equations. Viscosity can depend on density in compressible flows, and if the pressure-density relationship is reversible, viscosity may also depend on pressure. However, in incompressible powder flow, viscous stresses can vary with pressure changes while density remains nearly constant. Additionally, viscosity can change with varying shear rates, as seen in Bingham flow. These dependencies often coexist in nonflowing or slow-flowing materials, such as smaller-sized bulk powders. The Navier-Stokes equations in primitive variables (velocity-pressure) are considered the optimal framework for addressing these phenomena. Modifying viscous stresses leads to generalized Navier-Stokes equations, which extend their applicability to such flows. These equations are mathematically more complex than the traditional Navier-Stokes equations. Several numerical challenges arise, including the difficulty of approximating incompressible velocity fields, poor conditioning, potential lack of differentiability in nonlinear functions due to material laws, and the possible dominance of convective effects.