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Anna Tian December 13, 2013 06:14

Laplace flow
 
Hi,

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

siw December 13, 2013 12:51

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 15:21

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 04:22

Quote:

Originally Posted by siw (Post 466307)
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 11:09

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

Anna Tian December 16, 2013 12:26

Quote:

Originally Posted by siw (Post 466677)
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 12:52

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

adrin December 18, 2013 23:15

"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


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