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Mathematics Module: Coupled Simulation: How to access dependent variable at certain point?

Posted 08.02.2012, 11:04 GMT-5 Version 4.2a, Version 4.3a 7 Replies

Thomas Steinbacher
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Hello!

I want to couple a time dependent PDE with an ODE. The dependent variable of the PDE system is u1, the one for the ODE is v1. Now I want the value u1x(x_s) (i.e. the value of u1x at position x_s) to be included in the ODE. How could I possibly realise this?



Minimal example:

PDE: f(u1,u1x,u1t,t)=0
ODE: g(v1,u1x(x=x_s))=0

with u1=u1(x,t) and v1=v1(t)

(For me the ODE is only a transcendental equation without any derivatives of the dependent variable)

Thanks for your help!
7 Replies Last Post 12.11.2012, 09:19 GMT-5
John H.
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Posted: 1 decade ago 09.02.2012, 03:49 GMT-5
You have to define a coupling operator, of the "integration" or "average" type, that acts only on the point x_s of your geometry. Since it integrates only over a point, you can thus probe any variable/expression at that point and use it however you want in your equation system. If you haven't already, you may have to modify the geometry sequence so that x_s is assigned a vertex number.
You have to define a coupling operator, of the "integration" or "average" type, that acts only on the point x_s of your geometry. Since it integrates only over a point, you can thus probe any variable/expression at that point and use it however you want in your equation system. If you haven't already, you may have to modify the geometry sequence so that x_s is assigned a vertex number.
Thomas Steinbacher
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Posted: 1 decade ago 09.02.2012, 06:41 GMT-5
That was good hint, thanks. But now I want to extract my value at a moving point x_s(t). Here I cannot define a geometric point since its position would be fixed. Any suggestions for this case?
That was good hint, thanks. But now I want to extract my value at a moving point x_s(t). Here I cannot define a geometric point since its position would be fixed. Any suggestions for this case?
John H.
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Posted: 1 decade ago 09.02.2012, 07:29 GMT-5
Off the top of my head, I can't think of a straightforward way to do this in Comsol. (That obviously doesn't mean there is no straightforward way. Maybe I'm missing something and someone else can say more...)

However, though I've never had to deal with a problem like yours, I could think of a possible way around it. Maybe you could define, again, an integration coupling operator, but this time over the whole domain (or interval – I guess your problem is 1D). Then integrate the expression ("u1x" in your case) multiplied by a suitably defined Dirac delta function centered around x_s(t). By "suitably defined" I mean a delta function that is about as wide as the mesh size. You can use a combination of one of the built-in Heaviside functions – such as flc1hs(...) – to construct the delta function. Not sure if and how this will work out, but it might be worth a shot.
Off the top of my head, I can't think of a straightforward way to do this in Comsol. (That obviously doesn't mean there is no straightforward way. Maybe I'm missing something and someone else can say more...) However, though I've never had to deal with a problem like yours, I could think of a possible way around it. Maybe you could define, again, an integration coupling operator, but this time over the whole domain (or interval – I guess your problem is 1D). Then integrate the expression ("u1x" in your case) multiplied by a suitably defined Dirac delta function centered around x_s(t). By "suitably defined" I mean a delta function that is about as wide as the mesh size. You can use a combination of one of the built-in Heaviside functions – such as flc1hs(...) – to construct the delta function. Not sure if and how this will work out, but it might be worth a shot.
Thomas Steinbacher
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Posted: 1 decade ago 09.02.2012, 08:39 GMT-5
Yes that worked! Thanks again.

For those who are interested: I defined a small eps and used two Heaviside step functions which set the whole integration area to zero except from my small 2*eps zone around my x-value of interest. Then I multiplied the step functions by my variable field u1x and integrated this as defined in my operator definition (intop1). Furthermore I had to divide this by the length of the interval, which is 2*eps:

intop1(u1x*(x>x_s-eps)*(x<x_s+eps))/(2*eps)
Yes that worked! Thanks again. For those who are interested: I defined a small eps and used two Heaviside step functions which set the whole integration area to zero except from my small 2*eps zone around my x-value of interest. Then I multiplied the step functions by my variable field u1x and integrated this as defined in my operator definition (intop1). Furthermore I had to divide this by the length of the interval, which is 2*eps: intop1(u1x*(x>x_s-eps)*(x
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 09.02.2012, 09:20 GMT-5
Hi

As "eps" is already defined in COMSOL, is it the internal one or your own "eps" you are using ?
--
Good luck
Ivar
Hi As "eps" is already defined in COMSOL, is it the internal one or your own "eps" you are using ? -- Good luck Ivar
Thomas Steinbacher
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Posted: 1 decade ago 09.02.2012, 10:07 GMT-5
Yes you are right, I renamed it to epsT.
Yes you are right, I renamed it to epsT.
Tamir Epstein
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Posted: 1 decade ago 12.11.2012, 09:19 GMT-5
Hi,

I’m a new user in Comsol and would like to solve similar set of equations (PDE coupled to an ODE).
My question is how did you define the moving point variable x_s that you integrate on?

Thanks,
Tamir.
Hi, I’m a new user in Comsol and would like to solve similar set of equations (PDE coupled to an ODE). My question is how did you define the moving point variable x_s that you integrate on? Thanks, Tamir.

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