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

Thibaut Metivet, Vincent Chabannes, Mourad Ismail and Christophe Prud’homme
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Thibaut Metivet: IRMA-UMR 7501, Cemosis-Center of Modeling and Simulation, Université de Strasbourg/CNRS, F-67000 Strasbourg, France
Vincent Chabannes: IRMA-UMR 7501, Cemosis-Center of Modeling and Simulation, Université de Strasbourg/CNRS, F-67000 Strasbourg, France
Mourad Ismail: LIPhy-UMR 5588 Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes/CNRS, F-38041 Grenoble, France
Christophe Prud’homme: IRMA-UMR 7501, Cemosis-Center of Modeling and Simulation, Université de Strasbourg/CNRS, F-67000 Strasbourg, France

Mathematics, 2018, vol. 6, issue 10, 1-25

Abstract: 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.

Keywords: Multifluid flows; level-set method; high-order finite elements; Navier-Stokes equations; finite-element toolbox; parallel computing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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