Analysis of WENO Schemes for Full and Global Accuracy

Aràndiga, Francesc; Baeza, Antonio; Belda, A. M.; Mulet, Pep

doi:10.1137/100791579

Cited by 98 publications

(138 citation statements)

References 15 publications

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“…In this investigation, we aim to perform a sensitivity analysis for p to quantify its effect on our solutions. A mathematical analysis of the role of the smoothness indicator and the parameter can be found in [67].…”

Section: Weno Reconstructionsmentioning

confidence: 99%

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Maulik

San

2017

Fluids

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Solving two-dimensional compressible turbulence problems up to a resolution of 16, 384 2 , this paper investigates the characteristics of two promising computational approaches: (i) an implicit or numerical large eddy simulation (ILES) framework using an upwind-biased fifth-order weighted essentially non-oscillatory (WENO) reconstruction algorithm equipped with several Riemann solvers, and (ii) a central sixth-order reconstruction framework combined with various linear and nonlinear explicit low-pass spatial filtering processes. Our primary aim is to quantify the dissipative behavior, resolution characteristics, shock capturing ability and computational expenditure for each approach utilizing a systematic analysis with respect to its modeling parameters or parameterizations. The relative advantages and disadvantages of both approaches are addressed for solving a stratified Kelvin-Helmholtz instability shear layer problem as well as a canonical Riemann problem with the interaction of four shocks. The comparisons are both qualitative and quantitative, using visualizations of the spatial structure of the flow and energy spectra, respectively. We observe that the central scheme, with relaxation filtering, offers a competitive approach to ILES and is much more computationally efficient than WENO-based schemes.

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Section: Weno Reconstructionsmentioning

confidence: 99%

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Maulik

San

2017

Fluids

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“…where R is a reconstruction procedure (a function whose cell-averages coincide with the given ones; we use the WENO technique proposed in [1,13] for five points stencils). We can thus discretize the spatial derivative in (1) as:…”

Section: Finite Difference Weno Schemesmentioning

confidence: 99%

High Order Boundary Extrapolation Technique for Finite Difference Methods on Complex Domains with Cartesian Meshes

2015

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The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the numerical methods and mesh type. In this paper we present a technique for the extrapolation of information from the interior of the computational domain to ghost cells designed for structured Cartesian meshes (which, as opposed to non-structured meshes, cannot be adapted to the morphology of the domain boundary). This technique is based on the application of Lagrange interpolation with a filter for the detection of discontinuities that permits a data dependent extrapolation, with higher order at smooth regions and essentially non oscillatory properties near discontinuities.

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“…Although we can apply this algorithm with any nonlinear prediction [7,10,13], for simplicity, we only describe here a particular type of linear prediction operators, constructed using 2D polynomial interpolants, and two nonlinear predictions procedures, ENO and WENO.…”

Section: Predictionmentioning

confidence: 99%

“…Weighted essentially nonoscillatory (WENO) reconstructions, introduced by Liu, Osher, and Chan in [24] are based on the idea of increasing the order of accuracy of the method (al least in smooth regions) by considering a reconstruction given by a convex combination of the different reconstruction candidates of the ENO method with weights designed to increase the accuracy of each individual reconstruction to obtain the same order of accuracy as linear prediction (P k k−1f k−1 ) s 2i−n,2j −m (29) (see [7,24]) for details).…”

Section: Wenomentioning

confidence: 99%

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Cell average image transform algorithms with exact error control

2014

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In this paper we present non-separable two-dimensional multi-resolution algorithms based on Harten's cell average framework for multi-resolution which guarantee a priori prescribed quality in the reconstructed image, hence being suitable for applications where quality control is most important, yet performing economically in terms of storage and speed of computation. Moreover, after applying the algorithm the exact error between the original and the decoded images measured in the L 2 discrete norm is known without being necessary to decode the image.

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Analysis of WENO Schemes for Full and Global Accuracy

Cited by 98 publications

References 15 publications

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence

High Order Boundary Extrapolation Technique for Finite Difference Methods on Complex Domains with Cartesian Meshes

Cell average image transform algorithms with exact error control

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