High-Order Methods for Incompressible Fluid Flow

Deville, Michel; Fischer, P. F.; Mund, EH; Gartling, D. K.

doi:10.1115/1.1566402

Cited by 184 publications

(208 citation statements)

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“…Those practising ℎ-type refinement consider high-order expansions to be anything up to fifth-order [7,16] while at the other end of the spectrum, the global spectral community would consider expansion orders in the region of 100 to be relatively modest [5]. In contrast, the spectral/ℎ element community [8,3] would place high order in the region of 15th-order. Spectral/ℎ discretisations offer a broad performance-tuning capacity, not only through choice of element shape, element density and expansion order, but through a choice of different implementations for evaluating operators.…”

Section: Introductionmentioning

confidence: 99%

From h to p Efficiently: Selecting the Optimal Spectral/hpDiscretisation in Three Dimensions

Cantwell

Sherwin

Kirby

2011

Math. Model. Nat. Phenom.

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Abstract. There is a growing interest in high-order finite and spectral/ℎ element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of ℎ-and -type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations for evaluating operators over the space of discretisations with a desired solution tolerance, we demonstrate how the optimal discretisation and operator implementation may be selected for a specified problem. Furthermore, this demonstrates the need for codes to support both low-and high-order discretisations.

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Section: Introductionmentioning

confidence: 99%

From h to p Efficiently: Selecting the Optimal Spectral/hpDiscretisation in Three Dimensions

Cantwell

Sherwin

Kirby

2011

Math. Model. Nat. Phenom.

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“…This feature makes them very good candidates for data compression, especially on spectral grids which are widely used in direct numerical simulations (DNS) of turbulent flows [17]. Additional benefits, such as high computational efficiency due to tensor-product implementations on hexahedral grids [18], further increase their advantage due to the fact that data compression should be designed to be of negligible computational cost and low accuracy loss.…”

Section: Mathematical Formulation Of Data Compression Algorithmmentioning

confidence: 99%

“…The partial differential equation Lu = f is solved in weak form via a continuous Galerkin approach by minimizing the projection of the residual on a space of test functions v, details can be found in e.g. [17]. The approach ensures C 0 continuity between elements, i.e.…”

Section: Mathematical Formulation Of Data Compression Algorithmmentioning

confidence: 99%

Lossy Data Compression Effects on Wall-bounded Turbulence: Bounds on Data Reduction

Otero

Vinuesa

Marin

et al. 2018

Flow Turbulence Combust

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Postprocessing and storage of large data sets represent one of the main computational bottlenecks in computational fluid dynamics. We assume that the accuracy necessary for computation is higher than needed for postprocessing. Therefore, in the current work we assess thresholds for data reduction as required by the most common data analysis tools used in the study of fluid flow phenomena, specifically wall-bounded turbulence. These thresholds are imposed a priori by the user in L 2 -norm, and we assess a set of parameters to identify the minimum accuracy requirements. The method considered in the present work is the discrete Legendre transform (DLT), which we evaluate in the computation of turbulence statistics, spectral analysis and resilience for cases highly-sensitive to the initial conditions. Maximum acceptable compression ratios of the original data have been found to be around 97%, depending on the application purpose. The new method outperforms downsampling, as well as the previously explored data truncation method based on discrete Chebyshev transform (DCT).

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“…Also various relevant textbooks are available, including those by Barth and Deconinck [6] and Deville, Fischer, and Mund [29], both of which present a general overview of high-order methods, as well as the textbook by Karniadakis and Sherwin [72], which is primarily focused on high-order FE methods, and the textbooks by Cockburn, Karniadakis, and Shu [18], and Hesthaven and Warburton [51], which focus on DG methods. Given the existence of this literature, a detailed review of various unstructured high-order schemes is omitted from this article.…”

Section: Overviewmentioning

confidence: 99%

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

Vincent

Jameson

2011

Math. Model. Nat. Phenom.

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Abstract. Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order techniques in both academia (where the use of low-order schemes remains widespread) and industry (where the use of low-order schemes is ubiquitous). In this short review, issues that have hitherto prevented the use of high-order methods amongst a non-specialist community are identified, and current efforts to overcome these issues are discussed. Attention is focused on four areas, namely the generation of unstructured high-order meshes, the development of simple and efficient time integration schemes, the development of robust and accurate shock capturing algorithms, and finally the development of high-order methods that are intuitive and simple to implement. With regards to this final area, particular attention is focused on the recently proposed flux reconstruction approach, which allows various well known high-order schemes (such as nodal discontinuous Galerkin methods and spectral difference methods) to be cast within a single unifying framework. It should be noted that due to the experience of the authors the review is directed somewhat towards aerodynamic applications and compressible flow. However, many of the discussions have a wider applicability. Moreover, the tone of the review is intended to be generally accessible, such that an extended scientific community can gain insight into factors currently pacing the adoption of unstructured high-order methods.

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High-Order Methods for Incompressible Fluid Flow

Cited by 184 publications

References 0 publications

From h to p Efficiently: Selecting the Optimal Spectral/hpDiscretisation in Three Dimensions

From h to p Efficiently: Selecting the Optimal Spectral/hpDiscretisation in Three Dimensions

Lossy Data Compression Effects on Wall-bounded Turbulence: Bounds on Data Reduction

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

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