Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles

Habashi, Wagdi G.; Dompierre, Julien; Bourgault, Yves; Ait‐Ali‐Yahia, D.; Fortin, Michel; Vallet, Marie-Gabrielle

doi:10.1002/(sici)1097-0363(20000330)32:6<725::aid-fld935>3.0.co;2-4

Cited by 202 publications

(126 citation statements)

References 25 publications

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“…Numerous examples have shown that long and thin elements are useful in computation of problems with boundary or internal layers [1,2,14,15,19,22]. A practical question is in what direction an element should be long and how long and thin it should be.…”

Section: Introductionmentioning

confidence: 99%

An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives

Cao

2008

Math. Comp.

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Abstract. In this paper, we introduce the magnitude, orientation, and anisotropic ratio for the higher order derivative ∇ k+1 u (with k ≥ 1) of a function u to characterize its anisotropic behavior. The magnitude is equivalent to its usual Euclidean norm. The orientation is the direction along which the absolute value of the k + 1-th directional derivative is about the smallest, while along its perpendicular direction it is about the largest. The anisotropic ratio measures the strength of the anisotropic behavior of ∇ k+1 u. These quantities are invariant under translation and rotation of the independent variables. They correspond to the area, orientation, and aspect ratio for triangular elements. Based on these measures, we derive an anisotropic error estimate for the piecewise polynomial interpolation over a family of triangulations that are quasi-uniform under a given Riemannian metric. Among the meshes of a fixed number of elements it is identified that the interpolation error is nearly the minimum on the one in which all the elements are aligned with the orientation of ∇ k+1 u, their aspect ratios are about the anisotropic ratio of ∇ k+1 u, and their areas make the error evenly distributed over every element.

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Section: Introductionmentioning

confidence: 99%

An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives

Cao

2008

Math. Comp.

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“…Considering a linear interpolation of the metric tensor, the integration of Eq. 25 is evaluated by [17]:…”

Section: Metric Estimatesmentioning

confidence: 99%

“…The upper and lower error threshold values η U and η L are assumed as 1.4 and 0.6, respectively [17]. As the investigated flows are compressible and turbulent, the continuous function u chosen for the adaptation is the intersection of all conservative flow field variables, with φ = ρ ∩ u i ∩ E for the error estimation in Eq.…”

Section: Adaptation Algorithmmentioning

confidence: 99%

Large Eddy Simulation of Turbulent Compressible Flows Using the Characteristic Based Split Scheme and Mesh Adaptation

Linn¹,

Awruch²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The simulation of high-speed turbulent compressible flows using a numerical method of Large Eddy Simulation (LES) combined with the Characteristic-Based Split scheme (CBS) and anisotropic mesh adaptation is presented in this work. The CBS scheme is a unified approach for Computational Fluid Dynamics (CFD) with capability of covering a wide range of flow speeds and types with good stability and accuracy compared with other numerical schemes of the same order [1]. Although LES of incompressible flows combined with the CBS scheme has already been successfully addressed, the compressible extension is not yet covered, been the main contribution of this work. The CBS scheme is employed in a Finite Element Method (FEM) context for space and time discretization using unstructured meshes with adaptation [2], allowing the representation of complex geometries with accuracy. The anisotropic mesh adaptation is performed with mesh refinement, mesh coarsening and edge swapping procedures. A compressible dynamic Smagorinsky model is employed for the compressible LES model. The developed code is used to investigate a complex turbulent transonic flow around a circular cylinder in a two-dimensional approach. Several complex flow features such as lamda-shock-waves, viscous interactions and Von Kármán vortex sheet effects are correctly captured by the mesh adaptation strategy and the computed aerodynamic coefficients are close to the experimental reported values.

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“…Therefore, a high residual in one region may generate a high algebraic error in another where the residual itself is small. On the other hand there is no point in reducing the residual far 6 below the truncation error, as (3.14) and (3.15) indicate: The algebraic error h * -h *k would reduce, but the exact error h -h *k would not. Again, usually the discrete systems of finite volume methods are such that the quantity ΔΩP rh k ,P is more easily attainable for each CV.…”

Section: Truncation Error Estimatementioning

confidence: 99%

Estimate of the truncation error of finite volume discretization of the Navier-Stokes equations on colocated grids

Syrakos

Goulas

2005

Int. J. Numer. Meth. Fluids

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A methodology is proposed for the calculation of the truncation error of finite volume discretisations of the incompressible Navier -Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier -Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretisations of the incompressible Navier -Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure-part of the mass fluxes is not dependent on the coefficients of the linearised momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two-dimensional flows, but extension to three-dimensional cases should not pose problems.

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Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles

Cited by 202 publications

References 25 publications

An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives

An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives

Large Eddy Simulation of Turbulent Compressible Flows Using the Characteristic Based Split Scheme and Mesh Adaptation

Estimate of the truncation error of finite volume discretization of the Navier-Stokes equations on colocated grids

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