Continuous metrics and mesh adaptation

Courty, Francois; Leservoisier, David; George, Paul‐Louis; Dervieux, Alain

doi:10.1016/j.apnum.2005.03.001

Cited by 23 publications

(15 citation statements)

References 10 publications

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“…Minimizing the L p ( ) norm of the interpolation error is an active field of research [5,[22][23][24]. We follow now the continuous mesh formulation introduced in [25] and used in [8,11,26].…”

Section: Multi-scale Mesh Adaptationmentioning

confidence: 99%

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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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Section: Multi-scale Mesh Adaptationmentioning

confidence: 99%

“…[5,[22][23][24]) but taking it would imply that the space-time mesh can be updated only after the computation of the whole simulation time frame.…”

Section: Representativity Of the Spatial Interpolation Errormentioning

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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“…To improve the efficiency and accuracy of the numerical solution, a higher density of points would be expected in these regions than in the rest of the physical domain. For this purpose many different mesh adaptation schemes have been developed [1,7,30,32,37,36,38,39,40]. Essential to mesh adaptation is the ability to control the size, shape and orientation of mesh elements throughout the domain.…”

Section: Introductionmentioning

confidence: 99%

Target-Edge Based Orthogonal Anisotropic Mesh

Vazquez

Ollivier‐Gooch

2015

22nd AIAA Computational Fluid Dynamics Conference

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We present a new procedure to adaptively produce anisotropic metric-orthogonal meshes. The approach is based in optimization techniques: point insertion is designed to improve mesh alignment as well as conforming to a metric, swapping is performed in the metric space, point movement is defined by target elements from a metric, and point deletion is based on quality and metric length. These techniques are intended to produce a quasi-structured mesh, since these meshes have the advantage of the flexibility for complex geometries of unstructured meshes and the directional accuracy of structured meshes. This combination produces a reliable alignment for anisotropic meshes, reducing our previous work's reliance on smoothing for good alignment. Examples of analytical metrics and error estimation metrics from numerical flow simulation are shown. NomenclatureC Dν Drag coefficient due to viscosity C Dp Drag coefficient due to pressure C f Skin friction factorlength λ eigenvalue ϒ Quality metric criteria V eigenvector A Jacobian matrix C Cell E Edge of a cell M metric tensor Ma Mach number Q Cell quality T weighted Jacobian matrix V Vertex of a cell W target matrix x,y,z cartesian coordinates

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“…In this paper, we use the multiscale continuous metric concept, introduced by [12,14,13], which is suitable for the detection of structures of different sizes. Hence, following the methodology developed by Loseille [23], we define an optimal continuous metric that minimizes the interpolation error in the L p norm and read into MeshAdapt [25] which is a commercially available mesh adaptation software.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, elements constructed in this way are deformed to enable them to adapt more effectively to the gradients of the solution. Control of the distribution of calculation nodes is combined with an error estimation method and a continuous metric [12][13][14] that allows the elements to be stretched and aligned in the calculation domain.…”

Section: Introductionmentioning

confidence: 99%