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September 9, 2010 9:02am UTC

Problem with Neumann boundary condition definition

Hi,

I am simulating a Helmholtz equation (using the PDE mode module) with a Neumann boundary condition. Some days ago, we decided to update our Comsol version from 3.4 to 4.0. In the new version we saw a few changes about the definition of Neumann boundary condition (now called flux/source condition):

While in the older version the equation was:

n•(c?u)+qu=g

in the actual one it is:

-n•(-c?u-?u+?)=g

Does anyone know if both equations are equivalent?

I have been reading the documentation I have (modeling guide for both versions) but I did not find out any clue.

Besides, for the older version I realised that although in the manual it is said that Neumann equation is

n•(c?u+?u-?)+qu=g-h^T ?

the program interface only shows n•(c?u)+qu=g.

I do not think both equations are the same. I am trying to understand why the definition of the manual does not correspond to the equation shown in the program (when using Helmholtz PDE).

I would be very pleased if someone give me any idea about this topic.

Thank you very much,

Cristina

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September 14, 2010 9:50am UTC in response to Alessandro Ricci

Re: Problem with Neumann boundary condition definition

Hi,

First of all, thank you very much Alessando Ricci for your quick reply. As you suggested me I have been reading the manuals for both versions and I got some conclusions (lets see if I am right or not):

1) Regarding the Neumann boundary condition, the main difference between both versions (3.4 and 4.0) is that in 3.4 the Neumann boundary condition is more general because of the term qu (in fact, as it is said in the manual, this generalized Neumann condition is often called mixed boundary condition).

2) If we focus in 4.0 version, I think there should be a mistake in the way the boundary condition is shown in the "question tab" of the program interface.

The manual says the boundary condition (for a scalar coefficient PDE equation) is:
n•(cgradient(u)+ ?u-?)=g

We are using the predefined Helmholtz equation so ?= ?=0 and therefore the boundary condition should be:
n•(cgradient(u))=g

However, in the equation tab of the program it appears: -n•(-cgradient(u)-au+ ?)=g, so for the Helmholtz PDE we have (?= ?=0) :
-n•(-cgradient(u)-au)=g

with a=absorption coefficient (which should be defined in Helmholtz PDE).

I suppose there is a typo (it should be written ? instead of a), so I assume that the program is not considering the absorption coefficient in Neumann condition. Besides, the “dot product” would not be right because au is a scalar number not a vector. Does anyone agree with me?

I hope this time all the symbols in the equations are shown properly.

Regards,

Cristina

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September 15, 2010 8:22am UTC in response to Ivar Kjelberg

Re: Problem with Neumann boundary condition definition

Hi Ivar,

I am really sorry about the problem with the special characters, to avoid that I use this time words instead of those characters. Just to make it clear:

alfa= conservative flux convection coefficient
gamma= conservative flux source term
c= diffusion coefficient
g= boundary source term
a= absorption coefficient
n= unit normal vector

The manual says the boundary condition (for a scalar coefficient PDE equation) is:
n•(cgradient(u)+ alfau-gamma)=g

We are using the predefined Helmholtz equation so alfa= gamma=0 and therefore the boundary condition should be:
n•(cgradient(u))=g

However, in the equation tab of the program it appears: -n•(-cgradient(u)-au+ gamma)=g, so for the Helmholtz PDE we have (alfa= gamma=0) :
-n•(-cgradient(u)-au)=g

I suppose there is a typo (it should be written alfa instead of a), so I assume that the program is not considering the absorption coefficient in Neumann condition. Besides, the “dot product” would not be right because au is a scalar number not a vector.
I would like to know if I am right or not because maybe there is something that I am missing or that I just do not understand.

Hopefully this time no “?” symbols appear.

Regards,

Cristina

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