Diffusivity tensor

Hi,

I am using the convection-diffusion module in 2D but I would like to specify a 2 x 2 diffusivity tensor D instead of a single coefficient. So for example Dxx is the diffusivity that controls flow in the x-direction in response to gradients in the x-direction, Dxy is the diffusivity controlling flow in the x-direction in response to gradients in the y-direction and so on...

Can this be done in FEATool?

Thanks

Mikel

mdiez wrote

I am using the convection-diffusion module in 2D but I would like to specify a 2 x 2 diffusivity tensor D instead of a single coefficient. So for example Dxx is the diffusivity that controls flow in the x-direction in response to gradients in the x-direction, Dxy is the diffusivity controlling flow in the x-direction in response to gradients in the y-direction and so on...

Yes, similar to the orthotropic heat conduction example you can edit the equation to account for fully anisotropic diffusion as

... - (Dxx*cx_x + Dxy*cx_y + Dyx*cy_x + Dyy*cy_y) ...

Thank you!

In my 2D convection-diffusion model I have two adjacent subdomains: in one I set the diffusivity in tensor form as you suggest, and in the other subdomain I intend to set the diffusivity as a single coefficient, but when I edit the equation it sets the same equation form for both subdomains.

Is there a way to specify the diffusivity for each subdomain independently?

Thanks again!

Regards

Mikel

mdiez wrote

In my 2D convection-diffusion model I have two adjacent subdomains: in one I set the diffusivity in tensor form as you suggest, and in the other subdomain I intend to set the diffusivity as a single coefficient, but when I edit the equation it sets the same equation form for both subdomains.

Currently the design is such as you must have the same equation for all subdomains (for each dependent variable). However, you can make your coefficients (Dxx, Dxy ...) different in each subdomain, so if you enter an anisotropic system as above. And define your coefficients using the "Model Constants and Expressions" dialog as (space separated between different subdomain values):

  Name:   Expression:
   Dxx     D1  Dxx2
   Dxy     0   Dxy2
   Dyx     0   Dyx2
   Dyy     D1  Dyy2

you will get the isotropic diffusion with coefficient D1 in subdomain 1, and use a corresponding anisotropic diffusion tensor in subdomain 2.