SLEIPNNIR: a multiscale, particle level set method for Newtonian and non-Newtonian interface flows. (English) Zbl 1436.76033
Summary: 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.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M28 | Particle methods and lattice-gas methods |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 74A50 | Structured surfaces and interfaces, coexistent phases |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
multiscale; micro-macro; semi-Lagrangian; particle level set; radial basis functions; viscoelasticReferences:
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