Summary
A finite element formulation is developed for the analysis of a general discontinuous potential field (with multiply connected regions) and leads to the solution of the Dirichlet, Neumann and Mixed Boundary Value Problems. Subcritical compressibility effects are included. The finite element model is presented in detail for the two-dimensional and axisymmetric case, but may readily be extended to the general three-dimensional case. For the representation of general boundary conditions (linear interdependencies between the unknown variables) two alternative methods are formulated. Several typical examples including compressibility, circulatory (lifting) flow and the analysis of infinite cascades demonstrate the wide applicability and accuracy of the method.
Übersicht
Für die Berechnung von allgemeinen diskontinuierlichen Potentialfeldern mit mehrfach zusammenhängenden Bereichen wird eine Formulierung für die Methode der finiten Elemente entwickelt. Dies führt zur einfachen Lösung von Randwertproblemen erster, zweiter und dritter Art, wobei auch Kompressibilitätseffekte im unterkritischen Bereich berücksichtigt werden können. Ein Finite-Element-Typ wird im Detail für den zweidimensionalen und rotationssymmetrischen Fall abgeleitet, jedoch kann die Darstellung leicht auf den allgemeinen dreidimensionalen Fall ausgedehnt werden. Für die Verwirklichung allgemeiner Randbedingungen (d. h. Berücksichtigung von linear abhängigen unbekannten Variablen) werden zwei Methoden formuliert.
Mehrere typische Beispiele, welche Kompressibilität, Auftrieb und die Berechnung unendlicher Kaskadenströmung behandeln, zeigen dic Vielfalt der Anwendungsmöglichkeiten und die Genauigkeit der Methode.
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References
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Argyris, J.H., Mareczek, G. Potential flow analysis by finite elements. Ing. arch 42, 1–25 (1972). https://doi.org/10.1007/BF00533282
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DOI: https://doi.org/10.1007/BF00533282