Anisotropic Level Set Adaptation for Accurate Interface Capturing

Ducrot, Vincent; Frey, Pascal

doi:10.1007/978-3-540-87921-3_10

Cited by 5 publications

(5 citation statements)

References 33 publications

(29 reference statements)

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“…According to and , the geometric error and the approximation error associated with the level‐set function are conveniently bounded if the mesh is generated under the intersection of the metrics (see the work of Frey and George) associated with ϕ , ϕ 0 , and u . Then, at each step, the new mesh is generated from this metric by using a Delaunay‐based local mesh modification procedure (see the work of Ducrot and Frey as well as sections 4 and 5.2 in the work of Dapogny et al for more details).…”

Section: Numerical Toolsmentioning

confidence: 99%

An adaptive numerical scheme for solving incompressible 2-phase and free-surface flows

Frey

Kazerani

2018

Int J Numer Meth Fluids

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Summary In this paper, we present a numerical scheme for solving 2‐phase or free‐surface flows. Here, the interface/free surface is modeled using the level‐set formulation, and the underlying mesh is adapted at each iteration of the flow solver. This adaptation allows us to obtain a precise approximation for the interface/free‐surface location. In addition, it enables us to solve the time‐discretized fluid equation only in the fluid domain in the case of free‐surface problems. Fluids here are considered incompressible. Therefore, their motion is described by the incompressible Navier‐Stokes equation, which is temporally discretized using the method of characteristics and is solved at each time iteration by a first‐order Lagrange‐Galerkin method. The level‐set function representing the interface/free surface satisfies an advection equation that is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level‐set function (redistancing) as well as the construction of a convenient flow for the level‐set advection equation. Numerical results are presented for both bifluid and free‐surface problems.

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Section: Numerical Toolsmentioning

confidence: 99%

An adaptive numerical scheme for solving incompressible 2-phase and free-surface flows

Frey

Kazerani

2018

Int J Numer Meth Fluids

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“…A large literature is devoted to this topic; interested reader is referred to other works. [39][40][41][42][43][44][45][46][47] The adaptation strategy that is considered here is relying on the metric tensor proposed by Coupez. 48,49 This approach is based on the level set representation of the interface and ensures a proper representation of this surface with a minimum number of elements.…”

Section: Introductionmentioning

confidence: 99%

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Legrain

Moës

2018

Numerical Meth Engineering

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Summary A novel integration scheme is proposed for fictitious domain finite element methods. It relies on the use of a surface tracking strategy based on anisotropic mesh adaptation. Thanks to an error estimator, the method builds iteratively an adapted anisotropic mesh that is refined near the geometrical interface and elongated in the direction of a small curvature. This strategy allows to decrease the integration cost, which can be problematic for high‐order fictitious domain methods. In addition, it opens the possibility for the creation of unfitted solid shell strategies that can be used for the treatment of thin structures. Numerical studies show that the method leads to promising results for both integration cost and behavior with respect to locking.

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“…A first answer to these issues has already been proposed [3,22,25,41]. It is based on a control of the space-time interpolation error in L ∞ norm, the subdivision of the time interval into large sub-intervals on which the mesh is kept constant and on a local fixed-point algorithm to address the prediction of the solution and the convergence of the non-linear mesh adaptation problem.…”

Section: Introductionmentioning

confidence: 99%

Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries

Barral

Olivier

Alauzet

2017

Journal of Computational Physics

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Anisotropic metric-based mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. However, its extension to time-dependent problems with body-fitted moving geometries is far from straightforward. This paper establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space-time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, three dimensional adaptive simulations with moving boundaries are presented to validate the proposed approach.

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Anisotropic Level Set Adaptation for Accurate Interface Capturing

Cited by 5 publications

References 33 publications

An adaptive numerical scheme for solving incompressible 2-phase and free-surface flows

An adaptive numerical scheme for solving incompressible 2-phase and free-surface flows

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries

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