Towards very high‐order accurate schemes for unsteady convection problems on unstructured meshes

Abgrall, Rémi; Andrianov, Nikolai; Mezine, Mohamed

doi:10.1002/fld.870

Cited by 17 publications

(22 citation statements)

References 3 publications

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“…After the description of the test problems, a short overview about the different approaches that are used by the different partners for shock-capturing is given in Sect. 3.…”

Section: Refinement (P- H-and Hp-adaption)mentioning

confidence: 95%

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Synthesis Report on Shock Capturing Strategies

Taube

Munz

2010

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Abstract. One key problem in higher-order methods is the preservation of monotonicity across discontinuities such as shock waves. This synthesis report gives an overview about the different approaches adopted by the ADIGMA partners, IN-RIA, NJU, SERAM, UNBG, UNPR, UNST and VKI, who are all involved in the shock capturing workpackage. It shows the current state-of-the-art of the shock capturing capabilities. After a brief description of the different methods, these are compared based on the results for two two-dimensional test cases, one unsteady strong Ma = 10 shock (DMR) and one steady solution of a transonic flow around a NACA0012 profile (MTC 2). The focus is put on a thin shock profile and the least dissipative representation of the small scale instabilities for the DMR problem and the accurate computation of the aerodynamic coefficients with the least entropy error in the smooth flow region for the MTC 2 case.

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“…After the description of the test problems, a short overview about the different approaches that are used by the different partners for shock-capturing is given in Sect. 3.…”

Section: Refinement (P- H-and Hp-adaption)mentioning

confidence: 95%

“…The proof requires the problem to be steady. Unsteady problems can be rephrased into steady ones and the same line of arguments applies, see [1,4,3].…”

Section: Residual Distribution Approachmentioning

confidence: 98%

Synthesis Report on Shock Capturing Strategies

Taube

Munz

2010

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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“…The extension to quadrilateral meshes poses some difficulties, although some advances towards the extension of the residual distribution ideas to quadrilaterals have been recently published [12,77].…”

Section: Residual Distribution Schemesmentioning

confidence: 99%

“…Higher order generalizations have been constructed, based on subtriangulations and extensions of the basic distribution strategy for second order schemes [9,12]. The extension to quadrilateral meshes poses some difficulties, although some advances towards the extension of the residual distribution ideas to quadrilaterals have been recently published [12,77].…”

Section: Residual Distribution Schemesmentioning

confidence: 99%

High-order Finite Volume Methods and Multiresolution Reproducing Kernels

Cueto‐Felgueroso

Colominas

2008

Arch Computat Methods Eng

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This paper presents a review of some of the most successful higher-order numerical schemes for the compressible Navier-Stokes equations on unstructured grids. A suitable candidate scheme would need to be able to handle potentially discontinuous flows, arising from the predominantly hyperbolic character of the equations, and at the same time be well suited for elliptic problems, in order to deal with the viscous terms. Within this context, we explore the performance of Moving Least-Squares (MLS) approximations in the construction of higher order finite volume schemes on unstructured grids. The scope of the application of MLS is threefold: 1) computation of high order derivatives of the field variables for a Godunov-type approach to hyperbolic problems or terms of hyperbolic character, 2) direct reconstruction of the fluxes at cell edges, for elliptic problems or terms of elliptic character, and 3) multiresolution shock detection and selective limiting. The proposed finite volume method is formulated within a continuous spatial representation framework, provided by the MLS approximants, which is "broken" locally (inside each cell) into piecewise polynomial expansions, in order to make use of the specialized finite volume technology for hyperbolic problems. This approach is in contrast with the usual practice in the finite volume literature, which proceeds bottomup, starting from a piecewise constant spatial representa-L. Cueto-Felgueroso ( ) tion. Accuracy tests show that the proposed method achieves the expected convergence rates. Representative simulations show that the methodology is applicable to problems of engineering interest, and very competitive when compared to other existing procedures.

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“…This approach has been considered in [3], then extended to flow problems (unpublished). A much more interesting approach, because it is explicit and very cheap, as well as needing very little modifications of the computer code has been proposed in [31], only for second order space-time schemes so far with triangular meshes.…”

Section: Unsteady Problemsmentioning

confidence: 99%

A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

Abgrall

2012

Commun. comput. phys.

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Abstract. We describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil. We provide their connections with standard stabilized finite element and discontinuous Galerkin schemes, show that their are really non oscillatory. We also discuss the extension to these methods to parabolic problems. We also draw some research perspectives.

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Towards very high‐order accurate schemes for unsteady convection problems on unstructured meshes

Cited by 17 publications

References 3 publications

Synthesis Report on Shock Capturing Strategies

Synthesis Report on Shock Capturing Strategies

High-order Finite Volume Methods and Multiresolution Reproducing Kernels

A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

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