High-Order Finite-Element Framework for the Efficient Simulation of Multifluid Flows

In this paper, we present a comprehensive framework for the simulation of Multifluid flows based on the implicit level-set representation of interfaces and on an efficient solving strategy of the Navier-Stokes equations. The mathematical framework relies on a modular coupling approach between the le...

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Bibliographic Details
Published in:Mathematics (Basel) 2018-10, Vol.6 (10), p.203
Main Authors: Metivet, Thibaut, Chabannes, Vincent, Ismail, Mourad, Prud’homme, Christophe
Format: Article
Language:English
Subjects:
Analysis of PDEs
Boundary conditions
Computational fluid dynamics
Computer Science
Computer simulation
Curvature
Discretization
Finite element method
finite-element toolbox
Fluid mechanics
Fluid-structure interaction
high-order finite elements
level-set method
Mathematical analysis
Mathematics
Mechanics
Methods
Modeling and Simulation
Multifluid flows
Navier-Stokes equations
Numerical Analysis
parallel computing
Physics
Preconditioning
Simulation
Software
Velocity
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Summary:In this paper, we present a comprehensive framework for the simulation of Multifluid flows based on the implicit level-set representation of interfaces and on an efficient solving strategy of the Navier-Stokes equations. The mathematical framework relies on a modular coupling approach between the level-set advection and the fluid equations. The space discretization is performed with possibly high-order stable finite elements while the time discretization features implicit Backward Differentation Formulae of arbitrary order. This framework has been implemented within the Feel++ library, and features seamless distributed parallelism with fast assembly procedures for the algebraic systems and efficient preconditioning strategies for their resolution. We also present simulation results for a three-dimensional Multifluid benchmark, and highlight the importance of using high-order finite elements for the level-set discretization for problems involving the geometry of the interfaces, such as the curvature or its derivatives.
ISSN:2227-7390
2227-7390
DOI:10.3390/math6100203