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Journal ArticleDOI

A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations

30 Mar 2009-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 228, Iss: 5, pp 1447-1465
TL;DR: A shock-capturing methodology is developed for non-linear computations using low-dissipation schemes and centered finite differences that allows in particular to distinguish shocks from linear waves, and from vortices when it is performed from dilatation rather than from pressure.
About: This article is published in Journal of Computational Physics.The article was published on 2009-03-30. It has received 329 citations till now. The article focuses on the topics: Filter (signal processing) & Spatial filter.
Citations
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Journal ArticleDOI
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

Journal ArticleDOI
TL;DR: In this paper, the authors review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock waves.
Abstract: We review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock waves. Ideal numerical methods should be accurate and free from numerical dissipation in smooth parts of the flow, and at the same time they must robustly capture shock waves without significant Gibbs ringing, which may lead to nonlinear instability. Adapting to these conflicting goals leads to the design of strongly nonlinear numerical schemes that depend on the geometrical properties of the solution. For low-dissipation methods for smooth flows, numerical stability can be based on physical conservation principles for kinetic energy and/or entropy. Shock-capturing requires the addition of artificial dissipation, in more or less explicit form, as a surrogate for physical viscosity, to obtain nonoscillatory transitions. Methods suitable for both smooth and shocked flows are discussed, and the potential for hybridization is highlighted. Examples of the application of advanced algorithms to DNS/LES of turbulent, compressible flows are presented.

381 citations


Cites methods from "A shock-capturing methodology based..."

  • ...The idea of adaptively filtering the numerical solution for shock-capturing also underlies the work of Visbal & Gaitonde (2005) and Bogey et al. (2009), who developed computational strategies based on high-accuracy central discretization of spatial derivatives, supplemented with selective filtering…...

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Journal ArticleDOI
TL;DR: In this paper, the effects of the nozzle-exit conditions on the flow and sound fields of initially laminar jets are computed by large-eddy simulations (LES) to investigate the effects.
Abstract: Round jets originating from a pipe nozzle are computed by large-eddy simulations (LES) to investigate the effects of the nozzle-exit conditions on the flow and sound fields of initially laminar jets. The jets are at Mach number 0.9 and Reynolds number 105, and exhibit exit boundary layers characterized by Blasius velocity profiles, maximum root-mean-square (r.m.s.) axial velocity fluctuations between 0.2 and 1.9% of the jet velocity, and momentum thicknesses varying from 0.003 to 0.023 times the jet radius. The far-field noise is determined from the LES data on a cylindrical surface by solving the acoustic equations. Jets with a thinner boundary layer develop earlier but at a slower rate, yielding longer potential cores and lower centreline turbulent intensities. Adding random pressure disturbances of low magnitude in the nozzle also increases the potential core length and reduces peak r.m.s. radial velocity fluctuations in the shear layer. In all the jets, the shear-layer transition is dominated by vortex rolling-ups and pairings, which generate strong additional acoustic components, but also amplify the downstream-dominant low-frequency noise component when the exit boundary layer is thick. The introduction of inlet noise however results in weaker pairings, thus spectacularly reducing their contributions to the sound field. This high sensitivity to the initial conditions is in good agreement with experimental observations.

250 citations

Journal ArticleDOI
TL;DR: In this paper, large-eddy simulations of isothermal round jets at a Mach number of 09 and a diameter-based Reynolds number ReD of 105 originating from a pipe are performed using low-dissipation schemes in combination with relaxation filtering.
Abstract: Large-eddy simulations (LESs) of isothermal round jets at a Mach number of 09 and a diameter-based Reynolds number ReD of 105 originating from a pipe are performed using low-dissipation schemes in combination with relaxation filtering The aim is to carefully examine the capability of LES to compute the flow and acoustic fields of initially nominally turbulent jets As in experiments on laboratory-scale jets, the boundary layers inside the pipe are tripped in order to obtain laminar mean exit velocity profiles with high perturbation levels At the pipe outlet, their momentum thickness is δθ(0)=0018 times the jet radius, yielding a Reynolds number Reθ=900, and peak turbulence intensities are around 9% of the jet velocity Two methods of boundary-layer tripping and five grids are considered The results are found to vary negligibly with the tripping procedure but appreciably with the grid resolution Based on analyses of the LES quality and on comparisons with measurements at high Reynolds numbers, fine d

186 citations

References
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Book
01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.

8,808 citations

Journal ArticleDOI
TL;DR: In this article, the authors present finite-difference schemes for the evaluation of first-order, second-order and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes.

5,832 citations

Book
01 Jan 2002
TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

5,791 citations


"A shock-capturing methodology based..." refers background in this paper

  • ...Later, however, when the two fronts are well separate, the shock-capturing filtering does not apply around the linear contact discontinuities [48], because of the shock detection performed from the dilatation....

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Journal ArticleDOI
TL;DR: A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the caser= 3, instead of the fourth-order with the original smoothness measurement by Liuet al.

5,649 citations


"A shock-capturing methodology based..." refers background in this paper

  • ...Shock-tube problems Two standard shock-tube problems, namely Sod’s and Lax’s problems [18,45], are now considered....

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Journal ArticleDOI
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.

5,292 citations