Development of Computational Techniques for Transonic Flows: An Historical Perspective

Caughey, David A.; Jameson, Antony

doi:10.1007/978-94-010-0017-8_29

Cited by 3 publications

(3 citation statements)

References 60 publications

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“…They adopted a relaxation-like method along with type-dependent finite difference stencils. For an account of the impact of the Murman-Cole method in aerodynamics, and a review of more modern CFD approaches towards transonic flow, see the historical perspective of [25]. While the aerodynamic scenario is the most widely known, special examples of mixed-type equations arise in fields as diverse as plasma physics [26] and windshield design [27].…”

Section: Brief Review Of Mixed-type Problemsmentioning

confidence: 99%

“…For m = 1, the matrix A = A T 1 is given by Eq. (25). More generally the entries of A Tm may be gathered from the identity [40,42] …”

Section: Basic Formulas For Chebyshev Polynomialsmentioning

confidence: 99%

Section: Brief Review Of Mixed-type Problemsmentioning

confidence: 99%

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Multidomain spectral method for the helically reduced wave equation

Lau

Price²

2007

Journal of Computational Physics

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We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the "eigenspectral method." Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.

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Section: Brief Review Of Mixed-type Problemsmentioning

confidence: 99%

“…For m = 1, the matrix A = A T 1 is given by Eq. (25). More generally the entries of A Tm may be gathered from the identity [40,42] …”

Section: Basic Formulas For Chebyshev Polynomialsmentioning

confidence: 99%

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Multidomain spectral method for the helically reduced wave equation

Lau

Price²

2007

Journal of Computational Physics

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Transonic Nonlinear Aeroelasticity

Dowell

Bendiksen

Edwards

et al. 2010

Encyclopedia of Aerospace Engineering

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A review of the state of the art of transonic nonlinear aeroelasticity is presented. The discussion begins with a description of the generic nonlinear aeroelastic behavior that may occur followed by a summary of lessons learned from flight experience. Physical sources of nonlinear behavior are identified in both the aerodynamic fluid flow and the structure. Methods for the efficient computation of unsteady aerodynamic forces are summarized and then the chapter concludes with a discussion of correlation of theory and experiment for flutter boundaries in transonic flow and limit cycle oscillations (LCOs) arising from a variety of physical sources for several distinct aeroelastic configurations.

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Implicit gas-kinetic BGK scheme with multigrid for 3D stationary transonic high-Reynolds number flows

Jiang

Yue

2012

Computers & Fluids

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Development of Computational Techniques for Transonic Flows: An Historical Perspective

Cited by 3 publications

References 60 publications

Multidomain spectral method for the helically reduced wave equation

Multidomain spectral method for the helically reduced wave equation

Transonic Nonlinear Aeroelasticity

Implicit gas-kinetic BGK scheme with multigrid for 3D stationary transonic high-Reynolds number flows

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