Creation of internal points in Voronoi's type method. Control adaptation

George, Paul‐Louis; Hecht, Frédéric; Vallet, Marie-Gabrielle

doi:10.1016/0961-3552(91)90034-2

Cited by 40 publications

(34 citation statements)

References 7 publications

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“…In an adaptive process the tangential and normal spacing could be adapted using a generalized metric approach [8,9,15,17] by treating each separately. In a typical complex aerospace configuration the elements at the edge of the BL region often have considerable anisotropy from the normal spacing not having reached outer region length scales.…”

Section: Boundary Layer Meshing Algorithmmentioning

confidence: 99%

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Enhanced Viscous Mesh Generation with Metric-Based Blending

Marcum

Alauzet

2015

SEMA SIMAI Springer Series

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In this work we describe a unified approach that blends the best characteristics of both a near body pseudo-structured boundary-layer (BL) and generalized anisotropic metric approaches. Specifically, near-body physics with anisotropy are resolved using an a priori pseudo-structured process and off-body or field features are resolved using an adaptive generalized approach. In particular the metric field of the adaptive approach is derived from the BL region of the pseudo-structured approach. The derived metric is based on local aspect ratio and geometry. This metric is then blended from the BL region into the overall field to allow for a smooth transition to the generalized field. The result is a flexible and optimal overall mesh generation process that can be used with or without adaptation. Metricbased formulations for quality functions and other geometric quantities require for mesh generation are presented. Results are presented that demonstrate the overall approach in the context of blending between the near body pseudo-structured region and the outer tetrahedral field region. These results point out that the metric-based transition can be used to improve mesh quality and density for configurations with anisotropic surface meshes and BL regions that do not reach outer region length scale.

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Section: Boundary Layer Meshing Algorithmmentioning

confidence: 99%

“…Specifically, near-body physics with anisotropy are resolved using an a priori pseudo-structured process [19,21] and off-body or field features are resolved using an adaptive generalized approach [8,9,15,17]. In Fig.…”

Section: Introductionmentioning

confidence: 99%

Enhanced Viscous Mesh Generation with Metric-Based Blending

Marcum

Alauzet

2015

SEMA SIMAI Springer Series

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“…The main idea of the metric-based mesh adaptation, initially introduced in [21], is to generate a unit mesh in the prescribed Riemannian metric space, e.g. a mesh of ⊂ R 3 such that each edge has a unit length and each tetrahedron is regular for (M(x)) x∈ :…”

Section: Metric-based Generation Of Anisotropic Adapted Meshesmentioning

confidence: 99%

An L^∞–L^p mesh‐adaptive method for computing unsteady bi‐fluid flows

Guégan

Allain

Dervieux

et al. 2010

Numerical Meth Engineering

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SUMMARYThis paper discusses the contribution of mesh adaptation to high-order convergence of unsteady multifluid flow simulations on complex geometries. The mesh adaptation relies on a metric-based method controlling the L p -norm of the interpolation error and on a mesh generation algorithm based on an anisotropic Delaunay kernel. The mesh-adaptive time advancing is achieved, thanks to a transient fixedpoint algorithm to predict the solution evolution coupled with a metric intersection in the time procedure. In the time direction, we enforce the equidistribution of the error, i.e. the error minimization in L ∞ norm. This adaptive approach is applied to an incompressible Navier-Stokes model combined with a level set formulation discretized on triangular and tetrahedral meshes. Applications to interface flows under gravity are performed to evaluate the performance of this method for this class of discontinuous flows.

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“…The total error committed on our stochastic QoI j(ξ) for the Euler model is the summation of the stochastic error estimate, the integrand of (16) and the deterministic error estimate (23). These error terms are approximated as weighted interpolation errors.…”

Section: Total Error Estimatementioning

confidence: 99%

“…The use of Riemannian metric spaces is an elegant and efficient way to achieve this goal. The main idea of metric-based mesh adaptation, initially introduced in [23], is to generate a unit mesh in a prescribed Riemannian metric space. Consequently, the generated mesh will be uniform and isotropic in the Riemannian metric space while it will be anisotropic and adapted in the usual, Euclidean space.…”

Section: Total Error Estimatementioning

confidence: 99%

Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations

Langenhove

Lucor

Alauzet

et al. 2018

Journal of Computational Physics

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The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling error and parametric uncertainty, this may be achieved by combining goal-oriented error estimates and adaptive anisotropic spatial mesh refinements. To this end, an elegant and efficient framework is the one of (Riemannian) metric-based adaptation where a goal-based a priori error estimation is used as indicator for adaptivity. This work proposes a novel extension of this approach to the case of aforementioned system approximations bearing a stochastic component. In this case, an optimisation problem leading to the best control of the distinct sources of errors is formulated in the continuous framework of the Riemannian metric space. Algorithmic developments are also presented in order to quantify and adaptively adjust the error components in the deterministic and stochastic approximation spaces. The capability of the proposed method is tested on various problems including a supersonic scramjet inlet subject to geometrical and operational parametric uncertainties. It is demonstrated to accurately capture discontinuous features of stochastic compressible flows impacting pressure-related quantities of interest, while balancing computational budget and refinements in both spaces.

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Creation of internal points in Voronoi's type method. Control adaptation

Cited by 40 publications

References 7 publications

Enhanced Viscous Mesh Generation with Metric-Based Blending

Enhanced Viscous Mesh Generation with Metric-Based Blending

An L^∞–L^p mesh‐adaptive method for computing unsteady bi‐fluid flows

Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations

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Creation of internal points in Voronoi's type method. Control adaptation

Cited by 40 publications

References 7 publications

Enhanced Viscous Mesh Generation with Metric-Based Blending

Enhanced Viscous Mesh Generation with Metric-Based Blending

An L∞–Lp mesh‐adaptive method for computing unsteady bi‐fluid flows

Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations

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An L^∞–L^p mesh‐adaptive method for computing unsteady bi‐fluid flows