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Two mathematically identical equations draw diffrent graphs!
Posted Jun 19, 2012, 4:04 p.m. EDT Studies & Solvers Version 4.2a 2 Replies
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I am trying to solve a dimensionless transient problem with PDE solver.
I had an issue in solving
dtheta/dt + grad cdot (- grad theta) = 0
, which should be identical to
dtheta/dt = d2theta/dx2
in 1-dimension with the PDE solver in COMSOL: these two have different
results!
I attached two mph files showing the difference.
I want any comment. I hope I made some syntax error.
I had an issue in solving
dtheta/dt + grad cdot (- grad theta) = 0
, which should be identical to
dtheta/dt = d2theta/dx2
in 1-dimension with the PDE solver in COMSOL: these two have different
results!
I attached two mph files showing the difference.
I want any comment. I hope I made some syntax error.
Attachments:
2 Replies Last Post Jul 11, 2012, 11:57 p.m. EDT
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Posted:
1 decade ago
Hi Sun Ung Kim,
I did not go through your model files but what you are observing might be related to the fact that mathematical equations which are equivalent on the continuous level, i.e., in their analytic form, may show a different behaviour/solution if you a apply a discrete numeric scheme. In particular, the discretized equations are usually no longer equivalent.
It's been a while but I worked on very similar problems a couple of years ago. Maybe this one can give you some idea on how much a solution may vary depending on the actual formulation used for the implementation.
www.comsol.com/papers/4887/download/Weddemann.pdf
I did not go through your model files but what you are observing might be related to the fact that mathematical equations which are equivalent on the continuous level, i.e., in their analytic form, may show a different behaviour/solution if you a apply a discrete numeric scheme. In particular, the discretized equations are usually no longer equivalent.
It's been a while but I worked on very similar problems a couple of years ago. Maybe this one can give you some idea on how much a solution may vary depending on the actual formulation used for the implementation.
www.comsol.com/papers/4887/download/Weddemann.pdf
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Posted:
1 decade ago
Thank you for your reply. Probably my problem is different from what you were looking at.
My problem is solved by changing quadratic Lagrange shape function to Hermite shape functions.
Thanks anyway, and have a good day!
Best,
Sun Ung Kim
Received message from COMSOL:
Dear Sun Ung,
The difference in results is because second-order derivative terms in the f
coefficient are not accurately represented when using quadratic Lagrange
shape functions. One workaround is to change the discretization to use
Hermite shape functions instead, see attached model.
With best regards,
My problem is solved by changing quadratic Lagrange shape function to Hermite shape functions.
Thanks anyway, and have a good day!
Best,
Sun Ung Kim
Received message from COMSOL:
Dear Sun Ung,
The difference in results is because second-order derivative terms in the f
coefficient are not accurately represented when using quadratic Lagrange
shape functions. One workaround is to change the discretization to use
Hermite shape functions instead, see attached model.
With best regards,