Exact Newton method with third-order convergence to model the dynamics of bubbles in incompressible flow

DOI10.1016/J.AML.2017.01.012zbMath1393.76067OpenAlexW2582142997MaRDI QIDQ2407750

Aymen Laadhari

Publication date: 6 October 2017

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2017.01.012

zbMATH Keywords

finite element methodsurface tensionthird-order convergencenonlinear problemNewtonNavier-Stokes flow

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

• A short note on Navier-Stokes flows with an incompressible interface and its approximations
• A modification of Newton method with third-order convergence
• A continuum method for modeling surface tension
• Fully implicit methodology for the dynamics of biomembranes and capillary interfaces by combining the level set and Newton methods
• Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics
• A numerical model for the trans-membrane voltage of vesicles
• A simple modification of Newton's method to achieve convergence of order \(1+\sqrt 2\)
• Third-order modification of Newton's method
• Quantitative benchmark computations of two-dimensional bubble dynamics
• Numerical simulation of a single rising bubble by VOF with surface compression

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