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Unable to modify Laplace equation to satisfaction

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Hello, I am trying to find the Pressure distribution within the eye by using the laplace equation.

The equation for this is

K*d(d(Pressure,x))

I have 4 domains inside the eye and they all have different K values.

The equation I have mentioned above is to find the pressure distribution throughout the eye across varying K value in different domains. My problem lies with the fact that COMSOL is not allowing me to break up the whole of eye into 4 different domains and then define the pressure in x direction for the different domains.

For example instead of having the equation K*d(P,x) for pressure in x-direction

I want to use the following equation:

[K1d(P1,x)+K2d(P2,x)+K3d(P3,x)+K4d(P4,x)] as the change in pressure in x direction.

Where K1, K2, K3 and K4 are just constant values for the material and P1, P2, P3, P4 are the pressures in different domains.

I do not have the values of P1-P4. But I have dirichlet boundary conditions for the entire surface of the eye.

If comsol is able to do a simple laplacian like d(P,x) throughout a single domain using boundary conditions, I see no reasons, why cant it do the same thing across multiple domains where:

Kd(P,x)=[K1d(P1,x)+K2d(P2,x)+K3d(P3,x)+K4*d(P4,x)].

How do I resolve this?


4 Replies Last Post 2018年10月5日 GMT-4 09:47
Gunnar Andersson COMSOL Employee

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Posted: 6 years ago 2018年10月2日 GMT-4 04:38
Updated: 6 years ago 2018年10月2日 GMT-4 04:39

Instead of splitting P into P1-P4 you can define K in different ways in different domains:

  • Component > Definitions: Add a Variables node.

  • Change Geometry entity level to Domain.

  • Select domain 1.

  • Enter K in the Name column and the value K1 in the Expression column.

  • Repeat the steps above for domains 2-4. You should end up with four Variables nodes that each provide the definition of K in one domain.

Instead of splitting P into P1-P4 you can define K in different ways in different domains: - Component > Definitions: Add a Variables node. - Change Geometry entity level to Domain. - Select domain 1. - Enter K in the Name column and the value K1 in the Expression column. - Repeat the steps above for domains 2-4. You should end up with four Variables nodes that each provide the definition of K in one domain.

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Posted: 6 years ago 2018年10月2日 GMT-4 05:41

I just tried that and it doesnt seem to bring any change to the result. The left column in equation view has a warning sign inside it now. I have attached an image showing how I modified the Laplace equation. Thank you for your help

I just tried that and it doesnt seem to bring any change to the result. The left column in equation view has a warning sign inside it now. I have attached an image showing how I modified the Laplace equation. Thank you for your help


Magnus Ringh COMSOL Employee

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Posted: 6 years ago 2018年10月3日 GMT-4 11:51

Hi,

It seems that you are using the Laplace Equation interface, which really just solves . To get K into the equation, I would use the Coefficient Form PDE interface with c = K and all other coefficients set to 0. The warning sign indicates that you are changing the built-in definitions of those variables, which you can do, but you should then be aware that you affect the results. If you plot them, you can see that the K values set up as suggested in the previous reply do have an effect, but they will not affect the solution to the Laplace equation.

Best regards, Magnus Ringh, COMSOL

Hi, It seems that you are using the Laplace Equation interface, which really just solves \bigtriangleup u = 0. To get K into the equation, I would use the Coefficient Form PDE interface with c = K and all other coefficients set to 0. The warning sign indicates that you are changing the built-in definitions of those variables, which you can do, but you should then be aware that you affect the results. If you plot them, you can see that the K values set up as suggested in the previous reply do have an effect, but they will not affect the solution to the Laplace equation. Best regards, Magnus Ringh, COMSOL

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Posted: 6 years ago 2018年10月5日 GMT-4 09:47

Hi Magnus that worked wonderfully. Thanks!

Hi Magnus that worked wonderfully. Thanks!

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