A Directionally Adaptive Methodology Using an Edge-Based Error Estimate on Quadrilateral Grids

Ait‐Ali‐Yahia, D.; Habashi, Wagdi G.; Tam, A.; Vallet, Marie-Gabrielle; Fortin, Michel

doi:10.1002/(sici)1097-0363(19961015)23:7<673::aid-fld471>3.0.co;2-p

Cited by 52 publications

(23 citation statements)

References 12 publications

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“…The edge-based error estimate is based on the work of Ait- Ali-Yahia et al (1996). A node-moving scheme is then implemented, re-allocating grid points along those directions where the error is high.…”

Section: Adaptive Methodsmentioning

confidence: 99%

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A Mesh Adaption Method by Node Re-Allocation Using an Edge-Based Error Measure

Bono¹,

Awruch²

2005

RET

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A mesh adaptation technique implemented in an algorithm to simulate compressible flows characterized by the presence of strong shocks, using the finite element method (FEM), is presented in this work. The initial mesh is continuously adapted during the solution process using a node movement technique, keeping as much as possible mesh smoothness and local orthogonality with an unconstrained optimization method. The error is estimated as a function of the Hessian tensor, containing second derivatives of the specific mass, and a Riemann metric projected on the element edges is obtained in order to determine node movements. Time and spatial discretization of the governing equations are carried out using an explicit Taylor-Galerkin scheme and an isoparametric hexahedrical element with eight nodes. An Arbitrary Lagrangean Eulerian (ALE) description is used to take into account mesh movement. Finally, some two-dimensional examples involving transonic and supersonic flows are presented to validate the algorithm.

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Section: Adaptive Methodsmentioning

confidence: 99%

“…In order to obtain the second derivative of at a node I, a weak formulation was employed (similar to that of Ait-Ali- Yahia et al, 1996) and the following expression was obtained:…”

Section: Error Estimationmentioning

confidence: 99%

A Mesh Adaption Method by Node Re-Allocation Using an Edge-Based Error Measure

Bono¹,

Awruch²

2005

RET

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“…The determinant of the Hessian matrix has been widely used in computer vision [15] (e.g. the 'blob detection') and shock wave detection in computational fluid dynamics [2,20]. axes for more complex geometries.…”

Section: Feature Detection Criteriamentioning

confidence: 99%

Distance Solutions for Medial Axis Transform

Xia

Tucker

2009

Proceedings of the 18th International Meshing Roundtable

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Abstract.A method towards robust and efficient medial axis transform (MAT) of arbitrary domains using distance solutions is presented. The distance field, d, is calculated by solving the hyperbolic-natured Eikonal (or Level Set) equation. The solution is obtained on Cartesian grids. Both the fast-marching method and fast-sweeping method are used to calculate d. Medial axis point clouds are then extracted based on the distance solution via a simple criteria: the Laplacian or the Hessian determinant of d. These point clouds in 2D-pixel and 3D-voxel space are further thinned to curves and surfaces through binary image thinning algorithms. This results in an overall hybrid approach. As an alternative to other methods, the current d−MAT procedure bypasses difficulties that are usually encountered by pure geometric methods (e.g. the Voronoi approach), especially in 3D, and provides better accuracy than pure thinning methods. It is also shown that the d−MAT approach provides the potential to sculpt/control the MAT form for specialized solution purposes. Various examples are given to demonstrate the current approach.

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“…The approach for moving nodes uses the spring analogy, similar to the techniques presented by Gnoffo 2 and Ait-Ali-Yahia et al 20 The springs are taken to be the mesh edges. The spring constants are the edge error estimates.…”

Section: Curvature Clusteringmentioning

confidence: 99%

“…This sort of clustering is intended to reduce the interpolation error in a piecewise-linear data representation, 18,19 but is not necessarily driven by the flow physics, and can lead to excessive clustering or conflicting requirements in certain regions, such as a bow shock or stagnation point. Figure 1 presents an illustrative pictorial based on the results of AitAli-Yahia et al, 20 where 18 cells were driven into the bow shock by gradient based clustering. A shock is pictured on the left side of the figure with an ideal mesh for a three-point stencil.…”

Section: Introductionmentioning

confidence: 99%

On multi-dimensional unstructured mesh adaption

Wood

Kleb

1999

14th Computational Fluid Dynamics Conference

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Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

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A Directionally Adaptive Methodology Using an Edge-Based Error Estimate on Quadrilateral Grids

Cited by 52 publications

References 12 publications

A Mesh Adaption Method by Node Re-Allocation Using an Edge-Based Error Measure

A Mesh Adaption Method by Node Re-Allocation Using an Edge-Based Error Measure

Distance Solutions for Medial Axis Transform

On multi-dimensional unstructured mesh adaption

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