div and laplacian

gooya_kabir · November 22, 2013, 09:18

Hi friends,

I want to generate some equations in open foam. My interest is to generate (d2v/dx2)+(d2v/dy2). But in openfoam there is "div" and "laplacian" commands which make equations in x, y and z directions and I want just in x and y directions. What can I do?

Thank you in advance for your help and comments.
Kind Regards

Bernhard · November 22, 2013, 09:32

Use a 2D mesh, i.e. flat and parallel front and back planes, with only one cell. Set the boundary conditions to empty.

gooya_kabir · November 22, 2013, 09:40

Quote:

Originally Posted by Bernhard

Use a 2D mesh, i.e. flat and parallel front and back planes, with only one cell. Set the boundary conditions to empty.

thanks for your response

. But my geometry is 3D, and just I want to apply an equation which has gradient in x and y directions.?!

ngj · November 23, 2013, 07:12

Hallo,

This basically means that you are solving a system in 3D, which is of the form:

$1\cdot\frac{\partial^2 v}{\partial x^2} + 1\cdot\frac{\partial^2 v}{\partial y^2} + 0\cdot\frac{\partial^2 v}{\partial z^2} = 0$

I believe that the Laplacian operator in OpenFoam does support a diffusivity as a tensor of rank two, which basically means that the above equation could be re-written as:

$\nabla\boldsymbol{\cdot}\mathbf{\Gamma}\nabla v = 0$

where

$\mathbf{\Gamma} = \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&0\end{array}\right]$

and $\nabla=(\partial/\partial x,\,\partial/\partial y,\,\partial/\partial y)$ .

Good luck,

Niels

gooya_kabir · November 25, 2013, 04:28

thank you. I think I could not transform my words. I want to apply the below equation, what's the mathematical description of this equation in open foam?

-∂p/∂x=μ((∂^2 v)/(∂y^2 )+(∂^2 v)/(∂z^2 ))

Quote:

Originally Posted by ngj

Hallo,

This basically means that you are solving a system in 3D, which is of the form:

$1\cdot\frac{\partial^2 v}{\partial x^2} + 1\cdot\frac{\partial^2 v}{\partial y^2} + 0\cdot\frac{\partial^2 v}{\partial z^2} = 0$

I believe that the Laplacian operator in OpenFoam does support a diffusivity as a tensor of rank two, which basically means that the above equation could be re-written as:

$\nabla\boldsymbol{\cdot}\mathbf{\Gamma}\nabla v = 0$

where

$\mathbf{\Gamma} = \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&0\end{array}\right]$

and $\nabla=(\partial/\partial x,\,\partial/\partial y,\,\partial/\partial y)$ .

Good luck,

Niels

November 22, 2013, 09:18	div and laplacian	#1
gooya_kabir Member Reza Join Date: Feb 2012 Posts: 67 Rep Power: 14	Hi friends, I want to generate some equations in open foam. My interest is to generate (d2v/dx2)+(d2v/dy2). But in openfoam there is "div" and "laplacian" commands which make equations in x, y and z directions and I want just in x and y directions. What can I do? Thank you in advance for your help and comments. Kind Regards

November 22, 2013, 09:32		#2
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	Use a 2D mesh, i.e. flat and parallel front and back planes, with only one cell. Set the boundary conditions to empty. gooya_kabir likes this.

November 23, 2013, 07:12		#4
ngj Senior Member Niels Gjoel Jacobsen Join Date: Mar 2009 Location: Copenhagen, Denmark Posts: 1,900 Rep Power: 37	Hallo, This basically means that you are solving a system in 3D, which is of the form: $1\cdot\frac{\partial^2 v}{\partial x^2} + 1\cdot\frac{\partial^2 v}{\partial y^2} + 0\cdot\frac{\partial^2 v}{\partial z^2} = 0$ I believe that the Laplacian operator in OpenFoam does support a diffusivity as a tensor of rank two, which basically means that the above equation could be re-written as: $\nabla\boldsymbol{\cdot}\mathbf{\Gamma}\nabla v = 0$ where $\mathbf{\Gamma} = \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&0\end{array}\right]$ and $\nabla=(\partial/\partial x,\,\partial/\partial y,\,\partial/\partial y)$ . Good luck, Niels gooya_kabir likes this. __________________ Please note that I do not use the Friend-feature, so do not be offended, if I do not accept a request.

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