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Propagation of simple non-linear waves in gas filled tubes with friction

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Summary

The propagation of simple nonlinear waves in tubes is investigated. It is seen that both continuous and discontinuous asymptotic waves exist for which the nonlinear distortion and the viscous effect owing to the boundary layer just balance. Both types of solutions can be collapsed into one normalized asymptotic solution. A numerical method is given to compute time-dependent solutions. The evolution of continuous and discontinuous waves is illustrated with two examples.

Zusammenfassung

Untersucht wird die Fortpflanzung einfacher nichtlinearer Wellen in Rohren. Es wird gezeigt, daß asymptotische Wellen mit und ohne Diskontinuität existieren, für welche sich Grenzschichteffekte und nichtlineare Aufsteilung gerade die Waage halten. Die Lösungen beider Arten können auf eine einzige normalisierte asymptotische Lösung zurückgeführt werden. Es wird ein numerisches Verfahren angegeben, mit welchem zeitabhängige Lösungen berechnet werden können. Die Evolution von Wellen mit und ohne Diskontinuität wird mit zwei Beispielen illustriert.

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Authors and Affiliations

  1. Brown Boveri Research Center, Baden, Switzerland

    Jakob J. Keller

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  1. Jakob J. Keller
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Keller, J.J. Propagation of simple non-linear waves in gas filled tubes with friction. Z. angew. Math. Phys. 32, 170–181 (1981). https://doi.org/10.1007/BF00946746

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  • DOI: https://doi.org/10.1007/BF00946746

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