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The Bernoulli Equation in PDE form modelling Interfacial Fluid Flows
conference contribution
posted on 2023-05-24, 12:38 authored by Michael BridesonMichael Brideson, Lawrence ForbesLawrence ForbesWe 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.
History
Publication title
Proceedings of the 49th ANZIAM ConferenceEditors
D Allingham et alPagination
47ISBN
978-0-9873276-1-1Department/School
School of Natural SciencesPublisher
The University of Newcastle and ANZIAMPlace of publication
AustraliaEvent title
The 49th ANZIAM ConferenceEvent Venue
Newcastle, AustraliaDate of Event (Start Date)
2013-02-03Date of Event (End Date)
2013-02-07Repository Status
- Restricted