SLEIPNNIR: A multiscale, particle level set method for Newtonian and non-Newtonian interface flows

Abstract

We present in this paper a multiscale, micro–macro, particle level set method for Newtonian and non-Newtonian interface flows. The technique, termed SLEIPNNIR (‘Semi-Lagrangian Ensemble Implementation of Particle level set for Newtonian and non-Newtonian Interfacial Rheology’), uses the finite element method in a semi-Lagrangian framework for the discretization of the governing equations, capturing the free surface by means of a particle level set strategy where all involved magnitudes are computed sharply. Surface tension effects are considered via the Laplace–Beltrami operator using a fully-explicit or semi-implicit technique, with a second-order accurate reinitialization procedure to ensure the signed distance property. Non-Newtonian fluids are tackled by means of a stochastic, variance-reduced, kinetic modeling approach in which the polymer stress tensor is retrieved making use of Compactly-Supported Radial Basis Functions for randomly scattered data interpolation.We carry out numerical tests to highlight the versatility, robustness and accuracy of the proposed scheme through a series of bubble dynamics experiments in a 2D setup, for large density and viscosity ratios, and featuring strong, purely elastic effects relevant to Engineering applications.