2018
DOI: 10.3390/math6100203
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High-Order Finite-Element Framework for the Efficient Simulation of Multifluid Flows

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 ar… Show more

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Cited by 8 publications
(12 citation statements)
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References 36 publications
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“…The equations and integrals introduced above are solved or evaluated within a finite-element framework, using the Feel++-finite-element C++ library [45,44], and in particular the LevelSet framework from the Feel++ toolboxes [42], which features a comprehensive and seamless parallel set of tools for this kind of surface tracking methods.…”
Section: Finite Element Librarymentioning
confidence: 99%
See 1 more Smart Citation
“…The equations and integrals introduced above are solved or evaluated within a finite-element framework, using the Feel++-finite-element C++ library [45,44], and in particular the LevelSet framework from the Feel++ toolboxes [42], which features a comprehensive and seamless parallel set of tools for this kind of surface tracking methods.…”
Section: Finite Element Librarymentioning
confidence: 99%
“…To assess the accuracy of our diffusion-redistanciation scheme, we first simulate an initial two-dimensional circular interface evolving according to the Willmore flow, which can also be computed analytically. As it evolves with the flow, the interface should remains circular, and increase it radius r as r(t) = (r 0 + 2 t) 1/4 (42) with r 0 the initial radius. Note that this law, which comes from the analytic flow equation dr dt = H 3 2 = 12r 3 provides a good test of our algorithm, since the right hand side is actually obtained through a delicate compensation between the second-order term w (c.f.…”
Section: D Willmore Flow Of a Circlementioning
confidence: 99%
“…Different 3D versions of the single bubble rise benchmark have been proposed in the literature [61,62,63,26].…”
Section: Single Bubble Rise (3d)mentioning
confidence: 99%
“…Equating (10) and (11) to zero, leads to Equations (6) and (7). Assuming Equation 12is non-negative gives Equation (8).…”
Section: Approximation Of Modelmentioning
confidence: 99%
“…It can easily be estimated from the increasing publishing trend of research articles over the last few decades that FEM has proved itself a well programmed and commonly used method in an extensive range of engineering applications in general, for example in structural analysis, heat transfer and fluid mechanics etc. Different mathematicians have presented FEM for PDEs as well as for OCPs [5][6][7][8][9][10][11][12].…”
Section: Introductionmentioning
confidence: 99%