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Journal Articles Mathematics Year : 2018

High-order finite-element framework for the efficient simulation of multifluid flows

Abstract

We present in this paper 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.
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Dates and versions

hal-01865602 , version 1 (31-08-2018)

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Thibaut Métivet, Vincent Chabannes, Mourad Ismail, Christophe Prud'Homme. High-order finite-element framework for the efficient simulation of multifluid flows. Mathematics , 2018, 6 (10), ⟨10.3390/math6100203⟩. ⟨hal-01865602⟩
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