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December 13, 2013, 05:14 |
Laplace flow
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#1 |
Senior Member
Meimei Wang
Join Date: Jul 2012
Posts: 494
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Hi,
May I ask what is Laplace flow? Is it like an inviscid flow? What is a Laplace flow CFD?
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Best regards, Meimei |
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December 13, 2013, 11:51 |
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#2 |
Senior Member
Stuart
Join Date: Jul 2009
Location: Portsmouth, England
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Steady incompressible, irrotational flow is governed by the Laplace equation.
Some references for reading up on this: Fundamentals of Aerodynamics by J. Anderson. https://en.wikipedia.org/wiki/Laplace_equation. |
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December 13, 2013, 14:21 |
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#3 |
Senior Member
cfdnewbie
Join Date: Mar 2010
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The Laplace Operator is of particular interest for incompressible Navier-Stokes equations, as the diffusion term can be written in Laplace form. Also, the divergence-free constraint requires the solution of a Poisson equation. So for an incompressible flow solver (and viscosity dominated problems), the solution to the Laplace equation is central.
Thus, studying Laplace flow (and the associated solution strategies) is fundamental for incompressible solvers. |
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December 16, 2013, 03:22 |
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#4 | |
Senior Member
Meimei Wang
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Quote:
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Best regards, Meimei |
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December 16, 2013, 10:09 |
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#5 |
Senior Member
Stuart
Join Date: Jul 2009
Location: Portsmouth, England
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I've got a copy of the 3rd edition and it's on page 206.
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December 16, 2013, 11:26 |
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#6 |
Senior Member
Meimei Wang
Join Date: Jul 2012
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Sorry. I'm using the fifth edition. Could you please tell me it is at which chapter and which section?
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Best regards, Meimei |
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December 16, 2013, 11:52 |
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#7 |
Senior Member
Stuart
Join Date: Jul 2009
Location: Portsmouth, England
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Chapter 3: Fundamentals of Inviscid, Incompressible Flow, Section 3.7 Governing Equation for Irrotational, Incompressible Flow: Laplace's Equation.
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December 18, 2013, 22:15 |
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#8 |
Senior Member
adrin
Join Date: Mar 2009
Posts: 115
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"Shall we say it is steady-state incompressible flow?"
No! As the name suggests, Laplace flow (or more commonly, potential flow) is governed (only) by the Laplace equation. Incompressible flow includes non-linear convection, pressure gradient and viscosity terms (only du/dt=0 in the steady case, where d/dt is partial derivative). I strongly recommend that you open up any introductory book on fluid mechanics. Without understanding very basic fluid mechanics, your attempts at performing CFD will be futile - guaranteed! Adrin |
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