Multi-scale Simulation of Newtonian and Non-Newtonian Multi-phase Flows

Abstract

This work is devoted to the multi-scale simulation of Newtonian and non-Newtonian multi-phase flows using a level-set method to capture the fluid interface along with Brownian Dynamics simulations to account for the viscoelastic effects of the fluid. The Navier-Stokes equations are solved by a second order accurate semi-Lagrangian scheme, evolving the level-set function along the characteristic curves of the flow. Marker particles are added to correct the shape of the free surface, using a Semi-Lagrangian Particle Level-Set method taking into account viscous and surface tension effects. Non-Newtonian flows are modeled by means of a micro-macro, multi-scale approach in which stochastic, partial differential equations are solved using a variance-reduced technique on a number of ensembles of dumbbells scattered over the domain, with the Finitely Extensible Non-linear Elastic (FENE) kinetic model. Several benchmark problems for Newtonian and non-Newtonian fluids are presented, ranging from imposed flows to complex, high density and viscosity ratio flows featuring highly viscoelastic effects. The results highlight the versatility, accuracy and robustness of the proposed technique.