Question related to fill in boundary conditions in comsol

[overgift]

Firstly I really feel so lucky to find this forum. Since I don't have a strong physics background but now dealing with many problems directly related to physics.

I'm now doing some simulation in comsol and need to solve some PDEs. I'm using this PDE coefficient form in comsol. The equations need to be solved are:

-[tex]\rho[/tex][tex]\omega[/tex]²[tex]\vec{u}[/tex]- [tex]\nabla[/tex]T=0
[tex]\nabla \vec{D}[/tex] = 0
[tex]\vec{E}[/tex] = -[tex]\nabla V[/tex]
T=c^ES-eE_i
D_i=[tex]\epsilon[/tex]S

The equations specify the behavior of a piezoelectric substrate when subjected to an electric field. In these equations the variable need to be solved is [tex]\vec{u}[/tex]=[tex]\vec{u}[/tex](u,v,w,V).

Then PDE coefficient form in comsol is: -[tex]\nabla[/tex][tex]\cdot[/tex](C[tex]\nabla[/tex][tex]\vec{u}[/tex]+[tex]\alpha[/tex][tex]\vec{u}[/tex]-[tex]\gamma[/tex])+a[tex]\vec{u}[/tex]+[tex]\beta[/tex][tex]\cdot[/tex][tex]\nabla[/tex][tex]\vec{u}[/tex]=[tex]\vec{f}[/tex]

in this step I need to transfer my equations to this PDE coefficient form.

Then I need to specify the boundary condition:

The neumann boundary condition in comsol coefficient form specifies:
n[tex]\cdot[/tex](C[tex]\nabla[/tex][tex]\vec{u}[/tex]+[tex]\alpha[/tex][tex]\vec{u}[/tex]-[tex]\gamma[/tex])+q[tex]\vec{u}[/tex]=[tex]\vec{g}[/tex]

The mixed boundary condition in comsol coefficient form specifies:
n[tex]\cdot[/tex](C[tex]\nabla[/tex][tex]\vec{u}[/tex]+[tex]\alpha[/tex][tex]\vec{u}[/tex]-[tex]\gamma[/tex])+q[tex]\vec{u}[/tex]=[tex]\vec{g}[/tex]-h^T[tex]\mu[/tex]
h[tex]\vec{u}[/tex]=[tex]\vec{r}[/tex]

q, g,h,r are coefficients I need to fill in according to my specicial case.

one of the boundary conditions writes V=V_p, n[tex]\cdot[/tex]=0. And I really not sure how to define this in the mixed boundary condition and decide the value of q,g,h,r. Could anyone with comsol experience give me some hint?

 

[PerennialII]

Hi overgift,

I was first wondering is there some specific reason you're using the PDE form rather than the MEMS/piezoelectric application modes? Those would build you the coupling "automatically" and specifying for example the electric potential boundary condition would be a fairly straightforward task? Or perhaps you're doing something which is beyond the capabilities of those implementations.

 

[sir-pinski]

Thank you for sharing your question with us. It's great to hear that you have found this forum helpful for your physics-related problems.

Regarding your question about fill in boundary conditions in comsol, I can understand that it can be a bit confusing to transfer your equations to the PDE coefficient form and then specify the boundary conditions. But don't worry, with some guidance, you will be able to do it successfully.

Firstly, let's take a look at the PDE coefficient form in comsol that you have mentioned. This form includes the PDE coefficients C, \alpha, \gamma, a, and \beta. These coefficients represent the material properties and the coefficients in your PDE equations, and they need to be specified according to your specific case. You can find more information about these coefficients in the comsol documentation or by using the help function in comsol.

Now, let's focus on the boundary conditions. The Neumann boundary condition in comsol coefficient form specifies the normal derivative of your solution variable \vec{u}. In your case, this would be the normal derivative of \vec{u} with respect to the boundary condition. Similarly, for the mixed boundary condition, you would need to specify the normal derivative of \vec{u} as well as the value of \vec{u} itself on the boundary. The coefficients q, g, h, and r would depend on your specific case and can be determined by considering the physical meaning of your boundary condition and the material properties of your system.

For the boundary condition V=Vp, n\cdot=0, you would need to specify the value of \vec{u} as Vp on the boundary, and the normal derivative of \vec{u} would be zero. This would mean that there is no flux of \vec{u} across that boundary.

I would suggest looking at some examples or tutorials provided by comsol to get a better understanding of how to specify boundary conditions in comsol. You can also reach out to their support team for further assistance.

I hope this helps you in solving your problem. Good luck with your simulations!