High-Order Unstructured Essentially Nonoscillatory and Weighted Essentially Nonoscillatory Schemes for Aerodynamic Flows

Wolf, William; Azevedo, João Luiz F.

doi:10.2514/1.19373

Cited by 17 publications

(18 citation statements)

References 20 publications

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“…In the present work, the formulation is extended for the SFV method. The extension here reported applies some ideas from previous work on ENO and WENO schemes [8] in the calculation of the limited properties. It should be emphasized that there are other approaches that implement a similar hierarchical moment limiter formulation for the SFV scheme [26], but with slight differences, in comparison to the present approach, on the calculation of the derivatives for the limited reconstruction.…”

Section: F Limited Reconstructionmentioning

confidence: 99%

“…The nb1 to nb5 subscripts represent the neighbors of SV i that form the computational stencil to compute the averaged derivatives. This stencil is determined by an ENO based search, as in [8], for the smoothest SV set. Since only a small number of SVs is selected for limited reconstruction, the overhead of this search does not adversely affect the overall performance of the scheme.…”

Section: F Limited Reconstructionmentioning

confidence: 99%

“…The main advantages of such an approach are that it is easy to implement and the memory requirements are quite modest. The code uses a three-stage TVD Runge-Kutta scheme for explicit time integration [8], i.e.,…”

Section: Temporal Discretizationmentioning

confidence: 99%

“…This observation has motivated the group to study and to implement essentially nonoscillatory (ENO) and weighted essentially nonoscillatory (WENO) schemes in the past [8]. However, as the intrinsic reconstruction model of these schemes relies on gathering neighboring cells for polynomial reconstructions for each cell at each time step, both were found to be very demanding on computational resources for resolution orders greater than 3 in 2-D or anything greater than second order in 3-D.…”

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confidence: 99%

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Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

et al. 2010

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The present work has the objective of demonstrating the capabilities of a spectral finite volume scheme implemented in a cell-centered finite volume context for unstructured meshes. The two-dimensional Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution for flow problems governed by hyperbolic conservation laws. Roe's flux difference splitting method is used as the numerical approximate Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature and also compared to an weighted essentially nonoscillatory scheme. There is good agreement with the comparison data, and efficiency improvements over the weighted essentially nonoscillatory method are observed. The features of the present methodology include an implicit timemarching algorithm; second-, third-, and fourth-order spatial resolution; exact high-order domain boundary representation; and a hierarchical moment limiter to treat flow solution discontinuities.

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Section: F Limited Reconstructionmentioning

confidence: 99%

Section: F Limited Reconstructionmentioning

confidence: 99%

Section: Temporal Discretizationmentioning

confidence: 99%

mentioning

confidence: 99%

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Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

et al. 2010

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“…Furthermore, several research groups extended the original schemes to handle unstructured [18][19][20][21][22]a sw e l la sm i x e d -e l e m e n tu n s t r u c t u r e dg r i d s [ 3,[23][24][25][26], furthermore WENO methods are also utilised within the DG framework [27,28].…”

Section: Introductionmentioning

confidence: 99%

Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations

2017

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This version is available at https://strathprints.strath.ac.uk/59947/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Assessment of High-Order Finite Volume Methods on Unstructured Meshes for RANS Solutions of Aeronautical Configurations.Antonis F. Antoniadis a, * ,P a n a g i o t i sT s o u t s a n i s referenced data and discussed in terms of accuracy, grid dependence and computational budget.

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Application of Richardson extrapolation to the numerical solution of partial differential equations

Burg

Erwin

2008

Numerical Methods Partial

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Richardson extrapolation is a methodology for improving the order of accuracy of numerical solutions that involve the use of a discretization size h. By combining the results from numerical solutions using a sequence of related discretization sizes, the leading order error terms can be methodically removed, resulting in higher order accurate results. Richardson extrapolation is commonly used within the numerical approximation of partial differential equations to improve certain predictive quantities such as the drag or lift of an airfoil, once these quantities are calculated on a sequence of meshes, but it is not widely used to determine the numerical solution of partial differential equations. Within this article, Richardson extrapolation is applied directly to the solution algorithm used within existing numerical solvers of partial differential equations to increase the order of accuracy of the numerical result without referring to the details of the methodology or its implementation within the numerical code. Only the order of accuracy of the existing solver and certain interpolations required to pass information between the mesh levels are needed to improve the order of accuracy and the overall solution accuracy. Using the proposed methodology, Richardson extrapolation is used to increase the order of accuracy of numerical solutions of the linear heat and wave equations and of the nonlinear St. Venant equations in one‐dimension. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009

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High-Order Unstructured Essentially Nonoscillatory and Weighted Essentially Nonoscillatory Schemes for Aerodynamic Flows

Cited by 17 publications

References 20 publications

Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations

Application of Richardson extrapolation to the numerical solution of partial differential equations

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