Numerical comparison of some Hessian recovery techniques

Vallet, Marie-Gabrielle; Manole, C.‐M.; Dompierre, Julien; Dufour, Steven; Guibault, François

doi:10.1002/nme.2036

Cited by 59 publications

(47 citation statements)

References 23 publications

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“…Thus, it is necessary to recover a discrete approximation to the true Hessian. Different recovery schemes such as quadratic fitting (Vallet et al 2007), superconvergent patch recovery (Zienkiewicz & Zhu 1992), integration by parts (Buscaglia & Dari 1997) and double Galerkin projection (Pain et al 2001) have been suggested. These schemes vary in cost, accuracy and robustness; a number of comparisons of Hessian recovery schemes have recently been published (e.g.…”

Section: (E) Hessian Recoverymentioning

confidence: 99%

See 1 more Smart Citation

Anisotropic mesh adaptivity for multi-scale ocean modelling

Piggott

Farrell²,

Wilson³

et al. 2009

Phil. Trans. R. Soc. A.

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Research into the use of unstructured mesh methods in oceanography has been growing steadily over the past decade. The advantages of this approach for domain representation and non-uniform resolution are clear. However, a number of issues remain, in particular those related to the computational cost of models produced using unstructured mesh methods compared with their structured mesh counterparts. Mesh adaptivity represents an important means to improve the competitiveness of unstructured mesh models, where high resolution is only used when and where necessary. In this paper, an optimizationbased approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics. Comparisons are made between the results obtained with uniform isotropic resolution, isotropic adaptive resolution and fully anisotropic adaptive resolution.

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Section: (E) Hessian Recoverymentioning

confidence: 99%

“…These schemes vary in cost, accuracy and robustness; a number of comparisons of Hessian recovery schemes have recently been published (e.g. Lipnikov & Vassilevski 2006;Vallet et al 2007). Here, the double Galerkin projection approach described in Pain et al (2001) is used.…”

Section: (E) Hessian Recoverymentioning

confidence: 99%

Anisotropic mesh adaptivity for multi-scale ocean modelling

Piggott

Farrell²,

Wilson³

et al. 2009

Phil. Trans. R. Soc. A.

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“…Two different strategies can be devised to further enhance accuracy of the transverse normal stress and guarantee its convergence in any case (see the paper by Vallet et al (2007) for some details on Hessian recovery techniques). The first strategy is to apply a second superconvergent recovery procedure, inspired by the RCP procedure, to improve transverse shear stresses before reconstructing the transverse normal stress using threedimensional equilibrium.…”

Section: Reconstruction Of the Transverse Normal Stressmentioning

confidence: 99%

A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory

Daghia

Miranda

Ubertini

et al. 2008

International Journal of Solids and Structures

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This paper presents a hybrid stress approach for the analysis of laminated composite plates. The plate mechanical model is based on the so called First-order Shear Deformation Theory, rationally deduced from the parent three-dimensional theory. Within this framework, a new quadrilateral four-node finite element is developed from a hybrid stress formulation involving, as primary variables, compatible displacements and elementwise equilibrated stress resultants. The element is designed to be simple, stable and locking-free. The displacement interpolation is enhanced by linking the transverse displacement to the nodal rotations and a suitable approximation for stress resultants is selected, ruled by the minimum number of parameters. The transverse stresses through the laminate thickness are reconstructed a posteriori by simply using three-dimensional equilibrium. To improve the results, the stress resultants entering the reconstruction process are first recovered using a superconvergent patch-based procedure called Recovery by Compatibility in Patches, that is properly extended here for laminated plates. This preliminary recovery is very efficient from the computational point of view and generally useful either to accurately evaluate the stress resultants or to estimate the discretization error. Indeed, in the present context, it plays also a key role in effectively predicting the shear stress profiles, since it guarantees the global convergence of the whole reconstruction strategy, that does not need any correction to accommodate equilibrium defects. Actually, this strategy can be adopted together with any plate finite element. Numerical testing demonstrates the excellent performance of both the finite element and the reconstruction strategy.

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“…with h max and h min as the maximum and minimum allowed edge size in the mesh and the Hessian matrix is evaluated by a double projection scheme using a weak formulation [19].…”

Section: Metric Estimatesmentioning

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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Numerical comparison of some Hessian recovery techniques

Cited by 59 publications

References 23 publications

Anisotropic mesh adaptivity for multi-scale ocean modelling

Anisotropic mesh adaptivity for multi-scale ocean modelling

A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory

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

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