Aspects of linear stability analysis for higher-order finite-difference methods

Zingg, David W.

doi:10.2514/6.1997-1939

Cited by 8 publications

(10 citation statements)

References 16 publications

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“…Figure 4 shows eigenvalues on a uniform mesh for DRP, suggesting that the most unstable eigenvalues are independent of N. All eigenvalues are on the left half plane, indicating that the DRP scheme used in this experiment is asymptotic stable. Eigenvalue analysis only provides sufficient stability conditions for a normal matrix [24]. Unfortunately, the matrix M M M is not normal.…”

Section: Stability Analysismentioning

confidence: 98%

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High-order schemes for predicting computational aeroacoustic propagation with adaptive mesh refinement

Peers

Huang

2013

Acta Mech Sin

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High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic (CAA) problems with an aim at improving computational efficiency. A number of numerical issues associated with high-order schemes on an adaptively refined mesh, such as stability and accuracy are addressed. Several CAA benchmark problems are used to demonstrate the feasibility and efficiency of the approach.

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Section: Stability Analysismentioning

confidence: 98%

“…Small perturbations in M M M could lead to large divergences in the resultant eigenvalues. For a nonnormal matrix, -pseudospectra analysis should examine stability margin [24]. The -pseudospectra is defined in terms of eigenvalues of perturbed matrices, that is…”

Section: Stability Analysismentioning

confidence: 99%

High-order schemes for predicting computational aeroacoustic propagation with adaptive mesh refinement

Peers

Huang

2013

Acta Mech Sin

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“…This was found by increasing the stencil of the numerical boundary scheme one node beyond the stencil needed to achieve fifth-order accuracy (and hence sixth-order global accuracy). The resulting free parameter values, α = 3/20, β = 1/10, in (14) and (15) were selected by trial and error to obtain the eigenvalue spectrum displayed in Fig. 1.…”

Section: Discussionmentioning

confidence: 99%

On Linear Stability Analysis of High-Order Finite-Difference Methods

Zingg

Lederle

2005

17th AIAA Computational Fluid Dynamics Conference

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In order to produce the desired global order of accuracy, high-order finite-difference methods require suitably accurate stable boundary schemes. Various tools can be helpful in providing insight into the stability of numerical boundary schemes, including spectra, pseudospectra, and the singular value decomposition. In this paper, these tools are applied to several different discretizations of the linear convection equation which display various types of instability. Pseudospectra are seen to be a convenient and effective means of detecting instabilities. The same instabilities can also be revealed by either the spectrum or the spectrum of the associated circulant matrix resulting from the assumption of periodic boundary conditions. Finally, the singular value decomposition is shown to be a good indicator of the cause of the instability.

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“…For the sake of brevity they are omitted. , where M * is the conjugate transpose of M [139,140]. However, M of any high-order spatial scheme used in this work is non-normal.…”

Section: Stability Analysismentioning

confidence: 99%

“…However, M of any high-order spatial scheme used in this work is non-normal. For a non-normal matrix, -pseudospectra analysis has been used to measure the stability margin of high-order methods [139]. It was also applied to analyse a wave equation [141].…”

Section: Stability Analysismentioning

confidence: 99%

Adaptive Mesh Refinement for Computational Aeroacoustics

Huang

Zhang

2005

11th AIAA/CEAS Aeroacoustics Conference

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This thesis describes a parallel block-structured adaptive mesh refinement (AMR) method that is employed to solve some computational aeroacoustic problems with the aim of improving the computational efficiency. AMR adaptively refines and coarsens a computational mesh along with sound propagation to increase grid resolution only in the area of interest.While sharing many of the same features, there is a marked difference between the current and the established AMR approaches. Rather than low-order schemes generally used in the previous approaches, a high-order spatial difference scheme is employed to improve numerical dispersion and dissipation qualities. To use a highorder scheme with AMR, a number of numerical issues associated with fine-coarse block interfaces on an adaptively refined mesh, such as interpolations, filter and artificial selective damping techniques and accuracy are addressed. In addition, the asymptotic stability and the transient behaviour of a high-order spatial scheme on an adaptively refined mesh are also studied with eigenvalue analysis and pseudospectra analysis respectively. In addition, the fundamental AMR algorithm is simplified in order to make the work of implementation more manageable.Particular emphasis has been placed on solving sound radiation from generic aero-engine bypass geometry with mean flow. The approach of AMR is extended to support a body-fitted multi-block mesh. The radiation from an intake duct is modelled by the linearised Euler equations, while the radiation from an exhaust duct is modelled by the extended acoustic perturbation equations to suppress hydrodynamic instabilities generated in a sheared mean flow. After solving the near-field sound solution, the associated far-field sound directivity is estimated by solving the Ffowcs Williams-Hawkings equation. The overall results demonstrate the accuracy and the efficiency of the presented AMR method, but also reveal some limitations. The possible methods to avoid these limitations are given at the end of this thesis.

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Aspects of linear stability analysis for higher-order finite-difference methods

Cited by 8 publications

References 16 publications

High-order schemes for predicting computational aeroacoustic propagation with adaptive mesh refinement

High-order schemes for predicting computational aeroacoustic propagation with adaptive mesh refinement

On Linear Stability Analysis of High-Order Finite-Difference Methods

Adaptive Mesh Refinement for Computational Aeroacoustics

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