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Lösung der Navier-Stokes-Gleichungen: Teil 1

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Numerische Strömungsmechanik

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Zusammenfassung

Die zusätzliche Komplexität der Navier-Stokes-Gleichungen und besondere Merkmale für inkompressible Strömungen werden in diesem und im nächsten Kapitel betrachtet; hier behandeln wir grundlegende Fragen, die Merkmale der Gleichungen und die Lösungsmethoden. Die versetzten und nichtversetzten Anordnungen von Variablen, die Druckgleichung und die Druck-Geschwindigkeits-Kopplung für inkompressible Strömungen unter Verwendung der Teilschritt- und SIMPLE-Algorithmen werden ausführlich beschrieben. Andere Ansätze (der PISO-Algorithmus, Stromfunktion-Wirbelstärke und künstliche Kompressibilität) werden ebenfalls kurz beschrieben. Die Anfangs- und Randbedingungen für die Navier-Stokes-Gleichungen und ihre Implementierung bei kartesischen Gittern werden ebenfalls behandelt.

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Notes

  1. 1.

    Strömungen, in denen die Dichte des Fluids mit der Höhe in einem Gravitationsfeld variiert, werden als geschichtet oder stratifiziert bezeichnet, und die Strömung kann schweres Fluid nach oben und leichtes Fluid nach unten tragen, sodass es nun eine andere Dichte als seine Umgebung hat; das Fluid hat dann nicht nur kinetische Energie, sondern auch Energie als Folge seiner Position, genannt Potentialenergie. Das Ergebnis sind Auftriebskräfte, die später in diesem Kapitel angesprochen werden und sowohl in der Meteorologie als auch in der Ozeanographie sehr wichtig sind.

  2. 2.

    In diesem Fall wird die Extrapolation \(p^{n+1}=(3/2) p^{n+1/2}-(1/2) p^{n-1/2}\) verwendet.

  3. 3.

    Gekoppelte (oder monolithische) Löser sind ebenfalls verfügbar und die meisten kommerziellen Programme bieten sie inzwischen an; die Diskussion über Solver-Alternativen findet man in der Programmdokumentation und in der Literatur, z. B. Heil et al. (2008) oder Malinen (2012). Siehe auch Kap. 11 für eine kurze Beschreibung einer solchen Methode.

  4. 4.

    Diese Beziehung wurde zuerst von Raithby und Schneider (1979) hergeleitet und später von Perić (1985) mit unterschiedlichen Argumenten wiederentdeckt.

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Author information

Authors and Affiliations

  1. Stanford University, Stanford, CA, USA

    Joel H. Ferziger

  2. Institut für Schiffstechnik, Meerestechnik und Transportsysteme (ISMT), Universität Duisburg-Essen, Erlangen, Deutschland

    Milovan Perić

  3. School of Engineering, Stanford University, Stanford, CA, USA

    Robert L. Street

Authors
  1. Joel H. Ferziger
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  2. Milovan Perić
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  3. Robert L. Street
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Correspondence to Milovan Perić .

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Ferziger, J.H., Perić, M., Street, R.L. (2020). Lösung der Navier-Stokes-Gleichungen: Teil 1. In: Numerische Strömungsmechanik. Springer Vieweg, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46544-8_7

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