Continuous Mesh Framework Part II: Validations and Applications

Loseille, Adrien; Alauzet, Frédéric

doi:10.1137/10078654x

Cited by 145 publications

(94 citation statements)

References 17 publications

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“…where |H ρ | is derived from H ρ by taking the absolute value of the eigenvalues and π M ρ is the continuous interpolate defined in [14] and [15]. Minimizing ρ − Π h ρ L p (Ω) for a given number N of vertices can be recast in the continuous setting as minimizing ρ − π M ρ L p (Ω) for a complexity C(M) = N , which is the continuous counter part of the number of vertices.…”

Section: Generate Meshmentioning

confidence: 99%

3D Parallel Anisotropic Unsteady Mesh Adaptation for the High-Fidelity Prediction of Bubble Motion

Menier

2015

ESAIM: Proc.

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Abstract. Anisotropic unsteady mesh adaptation is applied to the high-fidelity prediction of bubble motion, which has applications in the framework of safety evaluations for nuclear reactors. A prescribed advection of the bubble is performed, which lacks any physical sense but is representative of the reality and makes it possible to precisely measure the diffusion caused by the numerical model. The model is described, and results are presented in 2D and 3D, with comparisons in terms of mesh convergence, CPU time, and propagation of the interface.Résumé. L'adaptation de maillage instationnaire anisotropique est appliquéeà la prédiction hautefidélité de la propagation de l'interface d'une bulle, dont les applications existent notamment dans le cadre desévaluations de sureté des réacteurs nucléaires. Une advection de la bulle est prescrite, qui n'est pas physique mais représente bien la réalité tout en permettant une mesure précise de la diffusion causée par le modéle numérique. Ce dernier est décrit et des résultats sont présentés en 2D et 3D avec comparaisons des convergences en maillage, des temps CPU et de la propagation de l'interface de la bulle.

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Section: Generate Meshmentioning

confidence: 99%

3D Parallel Anisotropic Unsteady Mesh Adaptation for the High-Fidelity Prediction of Bubble Motion

Menier

2015

ESAIM: Proc.

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“…For L p methods, Loseille and Alauzet (2011) found p = 2 to be the optimal value and incorporate more influence from dynamics of smaller magnitudes. Experience has shown this metric formation to be very effective for gravity current simulations (Hiester et al, 2011(Hiester et al, , 2014.…”

Section: Metric Formationmentioning

confidence: 99%

Direct numerical simulations of particle-laden density currents with adaptive, discontinuous finite elements

2014

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Abstract. High-resolution direct numerical simulations (DNSs) are an important tool for the detailed analysis of turbidity current dynamics. Models that resolve the vertical structure and turbulence of the flow are typically based upon the Navier-Stokes equations. Two-dimensional simulations are known to produce unrealistic cohesive vortices that are not representative of the real three-dimensional physics. The effect of this phenomena is particularly apparent in the later stages of flow propagation. The ideal solution to this problem is to run the simulation in three dimensions but this is computationally expensive. This paper presents a novel finite-element (FE) DNS turbidity current model that has been built within Fluidity, an open source, general purpose, computational fluid dynamics code. The model is validated through re-creation of a lock release density current at a Grashof number of 5 × 10 6 in two and three dimensions. Validation of the model considers the flow energy budget, sedimentation rate, head speed, wall normal velocity profiles and the final deposit. Conservation of energy in particular is found to be a good metric for measuring model performance in capturing the range of dynamics on a range of meshes. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. The use of adaptive mesh optimisation is shown to reduce the required element count by approximately two orders of magnitude in comparison with fixed, uniform mesh simulations. This leads to a substantial reduction in computational cost. The computational savings and flexibility afforded by adaptivity along with the flexibility of FE methods make this model well suited to simulating turbidity currents in complex domains.

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“…We propose to work in the continuous mesh framework introduced in [10,11]. The main idea of this framework is to model discrete meshes by Riemannian metric fields.…”

Section: Continuous Mesh Model and Adaptationmentioning

confidence: 99%

“…Given a continuous mesh M , we shall say, following [10,11], that a discrete mesh H of the same domain Ω is a unit mesh with respect to M , if each triangle K ∈ H , defined by its list of edges (e i ) i=1...3 , verifies:…”

Section: Continuous Mesh Model and Adaptationmentioning

confidence: 99%

“…Given a smooth function u, to each unit mesh H with respect to M corresponds a local interpolation error |u − Π H u|. In [10,11], it is shown that all these interpolation errors are well represented by the so-called continuous interpolation error related to M , which is locally expressed in terms of the Hessian H u of u as follows:…”

Section: Continuous Mesh Model and Adaptationmentioning

confidence: 99%

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Adaptive metric-based multigrid for a Poisson problem with discontinuous coefficients,

Brèthes

2014

ESAIM: ProcS

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Abstract. In order to solve the linear partial differential equation Au = f , we combine two methods: FullMultigrid method and Hessian-based mesh adaptation. First, we define independently an Hessian-based mesh adaptation loop and a FMG algorithm where, at each phase, the equation is solved by a preconditioned GMRES with multigrid as preconditioner. Then we insert the adaptive loop between the FMG phases. We use this new algorithm and we compare its results with those obtained with non-adaptive FMG.Résumé. On se propose de résoudre uneéquation différentielle linéaire aux dérivées partielles Au = f en combinant deux méthodes : la méthode FMG et la méthode d'adaptation basée hessien. Tout d'abord, on définit, indépendamment l'un de l'autre, une boucle d'adaptation de maillage basée sur des hessiens et un algorithme FMG où dans chaque phase, l'équation est résolue par un GMRES préconditionné par les multigrilles. Puis, on insère la boucle adaptative entre les phases FMG. On utilise le nouvel algorithme ainsi obtenu et on compare ses résultats avec ceux obtenus avec le FMG non adaptatif.

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Continuous Mesh Framework Part II: Validations and Applications

Cited by 145 publications

References 17 publications

3D Parallel Anisotropic Unsteady Mesh Adaptation for the High-Fidelity Prediction of Bubble Motion

3D Parallel Anisotropic Unsteady Mesh Adaptation for the High-Fidelity Prediction of Bubble Motion

Direct numerical simulations of particle-laden density currents with adaptive, discontinuous finite elements

Adaptive metric-based multigrid for a Poisson problem with discontinuous coefficients,

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