Discontinuous Galerkin Method for Incompressible Two-Phase Flows

DOI10.1007/978-3-030-43651-3_64zbMath1454.65116arXiv2003.12373OpenAlexW3142703782MaRDI QIDQ5117495

Janick Gerstenberger, Samuel Burbulla, Dietmar B. Kröner

Publication date: 25 August 2020

Published in: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.12373

zbMATH Keywords

incompressible Navier-Stokes equationstwo-phase flowdiscontinuous Galerkin

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Iterative numerical methods for linear systems (65F10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Capillarity (surface tension) for incompressible viscous fluids (76D45) Liquid-gas two-phase flows, bubbly flows (76T10) Preconditioners for iterative methods (65F08) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Uses Software

• DUNE-FEM

Cites Work

• A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module
• Reconstructing volume tracking
• A stable and high-order accurate discontinuous Galerkin based splitting method for the incompressible Navier-Stokes equations
• An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells
• Qualitative Behaviour of Incompressible Two-Phase Flows with Phase Transitions: The Case of Non-Equal Densities
• Stable Discontinuous Galerkin FEM Without Penalty Parameters
• Quantitative benchmark computations of two-dimensional bubble dynamics
• A locally conservative LDG method for the incompressible Navier-Stokes equations
• Discontinuous Galerkin finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations

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