Spectral Methods for the Small Disturbance Equation of Transonic Flows

Fishelov, Dalia

doi:10.1137/0909015

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…In addition, the time-dependent equation is a model for other problems in two space variables approximated by spectral methods, for which we examine stability and convergence to a steady state solution. The purpose of this paper is to give theoretical support to the schemes, presented here and in [6], for solving the small disturbance equation, using Chebyshev spectral methods. Numerical results are given in [6] and [5].…”

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The spectrum and the stability of the Chebyshev collocation operator for transonic flow

Fishelov¹

1988

Math. Comp.

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Abstract.The extension of spectral methods to the small disturbance equation of transonic flow is considered.It is shown that the real parts of the eigenvalues of its spatial operator are nonpositive. Two schemes are considered; the first is spectral in the x and y variables, while the second is spectral in x and of second order in y. Stability for the second scheme is proved. Similar results hold for the two-dimensional heat equation.

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confidence: 99%

The spectrum and the stability of the Chebyshev collocation operator for transonic flow

Fishelov¹

1988

Math. Comp.

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“…The purpose of this paper is to give theoretical support to the schemes, presented here and in [6], for solving the small disturbance equation, using Chebyshev spectral methods. Numerical results are given in [6] and [5]. The present paper contains eight sections.…”

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confidence: 99%

“…The extension of these schemes and numerical results for high Mach numbers are given in [6] and [5]. It is shown that one may still use these schemes when shocks are present (high Mach numbers) by filtering the results.…”

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The Spectrum and the Stability of the Chebyshev Collocation Operator for Transonic Flow

Fishelov¹

1988

Mathematics of Computation

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“…We finally arrive the following scheme for discretizating (2.1) in time According to [15], this scheme is second order accurate in time, is accurate up to order two in the time variable, even in the nonlinear case. The same time discretization w~s used also in [14].…”

Section: Time Discretizationmentioning

confidence: 99%