Solve double laplacian (laplacian of laplacian) equation

t.oliveira · January 5, 2016, 22:07

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, 16:17

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, 10:49

Thanks, Bruno. This answers my questions.

January 5, 2016, 22:07	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!

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February 1, 2016, 10:49		#3
t.oliveira Senior Member Thomas Oliveira Join Date: Apr 2015 Posts: 114 Rep Power: 12	Thanks, Bruno. This answers my questions.