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The Bernoulli Equation in PDE form modelling Interfacial Fluid Flows


Brideson, M and Forbes, L, The Bernoulli Equation in PDE form modelling Interfacial Fluid Flows, Proceedings of the 49th ANZIAM Conference, 3-7 February 2013, Newcastle, Australia, pp. 47. ISBN 978-0-9873276-1-1 (2013) [Conference Extract]

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We consider two inviscid, immiscible, and incompressible uids separated by a sharp interface. The outer uid ows in a so-called straining pattern about the inner uid, which contains a source. When the inner uid exhibits cylindrical symmetry (line source) or spherical symmetry (point source), the shape of the interface is described by a non-linear rst order PDE. For both geometries the PDE resembles the famous non-linear rst order ODE, the Bernoulli Equation. Remarkably, the power law variable substitution technique used in the single variable case is also e ective in this multivariable case, and allows us to obtain closed-form solutions to these nonlinear PDEs. The examples presented may have applications in astrophysics.

Item Details

Item Type:Conference Extract
Keywords:Bernoulli equation, straining flow
Research Division:Engineering
Research Group:Fluid mechanics and thermal engineering
Research Field:Fluid mechanics and thermal engineering not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Brideson, M (Dr Michael Brideson)
UTAS Author:Forbes, L (Professor Larry Forbes)
ID Code:90361
Year Published:2013
Deposited By:Mathematics and Physics
Deposited On:2014-04-01
Last Modified:2014-06-10

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