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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 24 (1973), S. 473-487 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Zeitabhängige Störungen in einem mit Gas gefüllten offenen Rohr werden beschrieben mit Hilfe einer nicht-linearen Theorie, welche sowohl Amplituden-Dispersion wie auch gegenseitige Beeinflussung von Wellenzügen berücksichtigt. Für Reflektionen am offenen Ende muss die Theorie die nicht-linearen Korrekturen zweiter Ordnung zu den Charakteristiken berücksichtigen, um lineare und nicht-lineare Laufzeiten unterscheiden zu können. Die Anfangswertaufgabe wird auf die Lösung einer Funktional-Differenzen-Gleichung reduziert, welche das Signal am Rohrende bestimmt. Wenn das Signal gedämpft wird durch Zulassung von Abstrahlung am Rohrende, kann die Stossbildung vermieden werden.
    Notes: Summary Transient disturbances in a column of gas in an open tube are described using a nonlinear theory which includes both amplitude dispersion and wave interactions. For reflection from an open end, the theory must include the second nonlinear correction to the characteristic to distinguish the linear and nonlinear travel times. The initial value problem is reduced to solving a functional difference equation which determines the signal on a boundary. When the signal is damped by allowing radiation of energy at the boundaries, it may be possible to prevent shock formation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 27 (1976), S. 49-59 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé En fonction du signal appliqué, on dérive les équations qui régissent la propagation de chocs faibles dans des milieux inhomogènes, ou dont les propriétés dépendent de la force du signal. Il s'avère d'abord nécessaire d'obtenir une solution du deuxième ordre de géométrie acoustique nonlinéaire à l'extérieur du choc. On démontre ensuite que pour ces systèmes dissipatifs la vitesse de choc, au premier ordre d'amplitude, est égale à le moyenne arithmétique des vitesses caractéristiques devant et derrière le choc. Ce résultat est démontré de deux façons dont l'une, chose assez surprenante, se révèle indépendante des détails de la solution du deuxième ordre.
    Notes: Abstract The equations governing the propagation of weak shocks in nonuniform or rate dependent media are derived in terms of the applied signal function. It is first necessary to find, the second order nonlinear geometrical acoustics solution outside the shock. It is shown that for such dissipative systems, the shock speed, to first order in the amplitude, is the arithmetic mean of the characteristic speed in the front and back of the shock. This result is found by two methods one of which, surprisingly, is independent of the details of the second order solution.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 39 (1988), S. 861-873 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The standard mapping arises in many physical applications, including the analysis of nonlinear resonant acoustic oscillations in a closed tube. A perturbation expansion, in powers of the amplitude parameter, is given for the calculation of the fixed points of various orders and the associated separatrices. It is shown how exact homoclinic orbits can be calculated numerically. Explicit analytic expressions are given for the separatrices associated with the first four resonances when the perturbation parameter is small.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of scientific computing 15 (2000), S. 265-292 
    ISSN: 1573-7691
    Keywords: finite differences ; corner singularities ; incompressible flows ; adaptive grids ; asymptotic error analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Two problems that include corner singularities are considered. The first concerns the flow of a viscous fluid in a channel driven by a constant pressure gradient, when the velocity satisfies a two-dimensional Poisson equation. The second is Stokes flow in a two-dimensional region when the stream-function satisfies the biharmonic equation. For both problems the boundaries of the domains contain corners. For corner angles greater than some critical value, the stress or the vorticity is singular. Using both a formal analysis and numerical results, we show that numerical approximations for the stream-function and velocity, obtained by using standard second-order finite difference methods, still converge to the exact solutions despite the corner singularities. However, the convergence rate is lower than second-order and the deterioration in the accuracy is not local, i.e., not confined to the corner. On the other hand, even though the vorticity solution of the Stokes problem does not converge, it diverges only locally. At a finite distance from the corner, the vorticity converges with the same rate as the stream-function. Adaptive methods for improving the accuracy are also discussed.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 713-729 
    ISSN: 0271-2091
    Keywords: finite difference ; boundary conditions ; Navier-Stokes equations ; convergence analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference method for the Navier-Stokes equations in vorticity -streamfunction formulation is proposed to resolve the difficulty of the lack of a vorticity boundary condition at a no-slip boundary. It is particularly suitable for flows in regions with complicated geometries. Convergence with second-order accuracy in vorticity and velocity is established. In numerical experiments the convergence rates agree with theoretical predictions. Test results for the two-dimensional driven cavity problem and for the flow in expansion and contraction channels are given.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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