Laplace flow

Anna Tian · December 13, 2013, 05:14

Hi,

May I ask what is Laplace flow? Is it like an inviscid flow? What is a Laplace flow CFD?

siw · December 13, 2013, 11:51

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.

cfdnewbie · December 13, 2013, 14:21

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.

Anna Tian · December 16, 2013, 03:22

Quote:

Originally Posted by siw

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.

I didn't find this concept in the book of Fundamentals of Aerodynamics by J. Anderson. Shall we say it is steady-state incompressible flow?

siw · December 16, 2013, 10:09

I've got a copy of the 3rd edition and it's on page 206.

Anna Tian · December 16, 2013, 11:26

Quote:

Originally Posted by siw

I've got a copy of the 3rd edition and it's on page 206.

Sorry. I'm using the fifth edition. Could you please tell me it is at which chapter and which section?

siw · December 16, 2013, 11:52

Chapter 3: Fundamentals of Inviscid, Incompressible Flow, Section 3.7 Governing Equation for Irrotational, Incompressible Flow: Laplace's Equation.

adrin · December 18, 2013, 22:15

"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

December 13, 2013, 05:14	Laplace flow	#1
Anna Tian Senior Member Meimei Wang Join Date: Jul 2012 Posts: 494 Rep Power: 15	Hi, May I ask what is Laplace flow? Is it like an inviscid flow? What is a Laplace flow CFD? __________________ Best regards, Meimei

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December 13, 2013, 11:51		#2
siw Senior Member Stuart Join Date: Jul 2009 Location: Portsmouth, England Posts: 733 Rep Power: 25	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.

December 13, 2013, 14:21		#3
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	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.

December 16, 2013, 10:09		#5
siw Senior Member Stuart Join Date: Jul 2009 Location: Portsmouth, England Posts: 733 Rep Power: 25	I've got a copy of the 3rd edition and it's on page 206.

December 16, 2013, 11:52		#7
siw Senior Member Stuart Join Date: Jul 2009 Location: Portsmouth, England Posts: 733 Rep Power: 25	Chapter 3: Fundamentals of Inviscid, Incompressible Flow, Section 3.7 Governing Equation for Irrotational, Incompressible Flow: Laplace's Equation.

December 18, 2013, 22:15		#8
adrin Senior Member adrin Join Date: Mar 2009 Posts: 115 Rep Power: 17	"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