Solve double laplacian (laplacian of laplacian) equation

t.oliveira · January 5, 2016, 21:07

Hi,

I can successfully solve $\nabla^2 p =0$ using

Code:

solve(fvm::laplacian(p));

How can I solve $\nabla^4 u =0$ ?

Besides that, would mixed boundary conditions for

be enough?

Thanks!

blais.bruno · January 13, 2016, 15:17

You can solve by carrying out a double laplacian with a mute variable

Code:

mute= solve(fvm::laplacian(p));
solve(fvm::laplacian(mute));

And then solve iteratively until convergence. For periodic boundary conditions, this preserves second order (or whatever order your scheme is)

The solution contained in mute will be the solution to
$\nabla^4 u =0$ ?

The problem is that this requires boundary condition for both p and mute, thus you need to have 2 boundary conditions for mute, which is not generally the case if you are trying to solve $\nabla^4 u =0$ .

However, solving a fourth degree equation straight away with openfoam is not possible as far as I know.

Quote:

Originally Posted by t.oliveira

Hi,

I can successfully solve $\nabla^2 p =0$ using

Code:

solve(fvm::laplacian(p));

How can I solve $\nabla^4 u =0$ ?

Besides that, would mixed boundary conditions for

be enough?

Thanks!

t.oliveira · February 1, 2016, 09:49

Thanks, Bruno. This answers my questions.

January 5, 2016, 21:07	Solve double laplacian (laplacian of laplacian) equation	#1
t.oliveira Senior Member Thomas Oliveira Join Date: Apr 2015 Posts: 114 Rep Power: 12	Hi, I can successfully solve $\nabla^2 p =0$ using Code: solve(fvm::laplacian(p)); How can I solve $\nabla^4 u =0$ ? Besides that, would mixed boundary conditions for be enough? Thanks!

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Help with if statement	CHARLES	OpenFOAM Programming & Development	17	August 22, 2021 03:14
CFD by anderson, chp 10.... supersonic flow over flat plate	varunjain89	Main CFD Forum	18	May 11, 2018 07:31
Parallel User Defined Real Gas Model	aeroman	FLUENT	4	July 1, 2015 06:09
solve an implicit equation in UDF	Rui_27	Fluent UDF and Scheme Programming	0	September 8, 2014 10:12
Constant velocity of the material	Sas	CFX	15	July 13, 2010 08:56

February 1, 2016, 09:49		#3
t.oliveira Senior Member Thomas Oliveira Join Date: Apr 2015 Posts: 114 Rep Power: 12	Thanks, Bruno. This answers my questions.