A reformulation of the conservative level set reinitialization equation for accurate and robust simulation of complex multiphase flows

Chiodi, Robert; Desjardins, Olivier

doi:10.1016/j.jcp.2017.04.053

Cited by 73 publications

(60 citation statements)

References 21 publications

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“…Otherwise, some error indicators for the coarser mesh ( δ =

\sqrt{2}

) suggest that this characteristic element length is not sufficient to reach minimum size for a competent usage of reinitialization tools in long‐term calculations. Responses of very HO schemes for this test reveal that the intermediate grid size ( δ =

\frac{\sqrt{2}}{2}

) is sufficient to achieve same order of errors as the high order scheme in the work of Chiodi and Desjardins with the coarse mesh ( δ =

\sqrt{2}

).…”

Section: Numerical Testsmentioning

confidence: 89%

“…As a result, oscillations of the phase function appear during reinitialization . Several procedures were proposed to alleviate spurious values during reinitialization as, for instance, use of fast marching methods combined with remapping of compressive fluxes and a modified reinitialization equation (eg, see the work of Chiodi and Desjardins and references therein). To get rid of these wiggles, a simple approach is proposed to complement a reinitialization process.…”

Section: A Conservative Flux‐corrected Finite Element Methods For Intementioning

confidence: 99%

“…Efficient diffusion/antidiffusion action during this stage is critically dependent on an accurate determination of normals. To enhance the calculation of normals, some procedures have been recently published . The main target of the enhancement is to avoid indeterminacy far from interface, where the phase function is nearly constant.…”

Section: Introductionmentioning

confidence: 99%

“…To enhance the calculation of normals, some procedures have been recently published. 16,17 The main target of the enhancement is to avoid indeterminacy far from interface, where the phase function is nearly constant. This paper advocates a fast and simple methodology, by restricting computation of normals only for a few element layers surrounding interface position.…”

Section: Introductionmentioning

confidence: 99%

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A conservative flux‐corrected continuous finite element method for fluid interface dynamics

Molina

Ortiz

2019

Numerical Methods in Fluids

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Summary This paper presents a continuous finite element solution for fluid flows with interfaces. The method is founded on the sign‐preserving flux correction transport methodology and extends nonoscillatory finite element algorithm capabilities to predict interface motion efficiently. The procedure is composed of three main stages, along the lines of the conservative level set method: transport of phase function, reconstruction of phase function, and solution of equations of motion of two incompressible fluids. The flux correction technique takes action on the three steps. Limiting process incorporates a straightforward refinement to remove global mass residuals present in the earliest version of the algorithm. This is of particular importance in the transport step. Moreover, new method retains the efficacy of the original. To reconstruct the phase function after transport, a novel nonlinear (and conservative) streamlined diffusion equation is proposed, with an anisotropic diffusivity comprising artificial compression and diffusive fluxes along interface displacements direction. A substantial reduction of unphysical overshoots along the interface is reached by an improved bound estimation that includes interface information. Complete operation of the correction algorithm for two incompressible fluids flows requires two pressure solutions. We explore a reduced form to circumvent this extra burden. Numerical experiments verify the formulation by reproducing stringent benchmarks both for transport/reinitialization and for two‐fluid interface propagation.

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“…Otherwise, some error indicators for the coarser mesh ( δ =

\sqrt{2}

\frac{\sqrt{2}}{2}

) is sufficient to achieve same order of errors as the high order scheme in the work of Chiodi and Desjardins with the coarse mesh ( δ =

\sqrt{2}

).…”

Section: Numerical Testsmentioning

confidence: 89%

Section: A Conservative Flux‐corrected Finite Element Methods For Intementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A conservative flux‐corrected continuous finite element method for fluid interface dynamics

Molina

Ortiz

2019

Numerical Methods in Fluids

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show abstract

“…Even though the 3D and 2D cases cannot be directly compared, it suggests that the model could be improved to obtain a better mass conservation. Moreover, there is a broad scientific literature on the implementation of conservative advection schemes for the Level-Set method (e.g., Kees et al, 2011;Owkes and Desjardins, 2013;Chiodi and Desjardins, 2017), that could benefit to the mass conservation capacity of our model in the future.…”

Section: Mass Conservationmentioning

confidence: 99%

A Micro-Mechanical Model for the Transformation of Dry Polar Firn Into Ice Using the Level-Set Method

et al. 2020

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Interpretation of greenhouse gas records in polar ice cores requires a good understanding of the mechanisms controlling gas trapping in polar ice, and therefore of the processes of densification and pore closure in firn (compacted snow). Current firn densification models are based on a macroscopic description of the firn and rely on empirical laws and/or idealized geometries to obtain the equations governing the densification and pore closure. Here, we propose a physically-based methodology explicitly representing the porous structure and its evolution over time. In order to handle the complex geometry and topological changes that occur during firn densification, we rely on a Level-Set representation of the interface between the ice and the pores. Two mechanisms are considered for the displacement of the interface: (i) mass surface diffusion driven by local pore curvature and (ii) ice dislocation creep. For the latter, ice is modeled as a viscous material and the flow velocities are solutions of the Stokes equations. First applications show that the model is able to densify firn and split pores. Using the model in cold and arid conditions of the Antarctic plateau, we show that gas trapping models do not have to consider the reduced compressibility of closed pores compared to open pores in the deepest part of firns. Our results also suggest that the mechanism of curvature-driven surface diffusion does not result in pore splitting, and that ice creep has to be taken into account for pores to close. Future applications of this type of model could help quantify the evolution and closure of firn porous networks for various accumulation and temperature conditions.

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A framework to perform high‐order deconvolution for finite‐volume method on simplicial meshes

Bernard

Lartigue

Balarac

et al. 2020

Numerical Methods in Fluids

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In this article, a new framework to design high-order approximations in the context of node-centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High-performance computing context. This method is based on deconvolution between nodal and volume-average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh-to-mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high-rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third-order expansion. This method, although tightly connected to the k-exact schemes theory, does not rely on successive corrections: the high-order property is obtained in a single operation, which makes them more attractive in terms of performances.

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A reformulation of the conservative level set reinitialization equation for accurate and robust simulation of complex multiphase flows

Cited by 73 publications

References 21 publications

A conservative flux‐corrected continuous finite element method for fluid interface dynamics

A conservative flux‐corrected continuous finite element method for fluid interface dynamics

A Micro-Mechanical Model for the Transformation of Dry Polar Firn Into Ice Using the Level-Set Method

A framework to perform high‐order deconvolution for finite‐volume method on simplicial meshes

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