Author |
Message |
Olexiy Orel (scorpion)
Member Username: scorpion
Post Number: 11 Registered: 03-2007
| Posted on Tuesday, February 24, 2009 - 11:28 am: | |
Hello friends. Please explain me a few moments about constraints. "CONSTRAINTS should not be used with steady state systems which are unambiguously defined by their boundary conditions, or in time-dependent systems." Is a simple diffusion equation system "unambiguously defined by its boundary conditions"? For example: del2(C)=0. C equals 1 on one peace of the boundary, 0 on another, natural(C)=0 on the rest. Is this system defined unambiguously? What do I do when enabling constraints (like charge conservation)? Does it mean that the solution will not satisfy the equation and BC's strictly any more? Thanks.
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Jerry Brown (jerrybrown11743)
Member Username: jerrybrown11743
Post Number: 53 Registered: 03-2004
| Posted on Tuesday, February 24, 2009 - 05:19 pm: | |
If you look in the folder of sample problems that come with FlexPDE you will find a folder named "constraints". It's a sub-folder of "misc". Also Prestube in the "Samples\steady_state\stress" folder shows how constraints are used to eliminate rigid body motion in an elasticity problem. |
Archie Campbell (amc1)
Member Username: amc1
Post Number: 8 Registered: 03-2008
| Posted on Wednesday, March 04, 2009 - 03:40 pm: | |
THe question of whether a solution is unambiguously defined is far from straightforward and leads to problems with constraints, as I have found, (see previous postings). The easisest way of trying to determine this is to think of the physical situation, heat flow is particularly useful. In this case value(C) defines a uniform temperature boundary and natural(C)=0 an insulator. What your problem describes is a box with one section at one temperature and a second at another temperature with the remaining surfaces insulators. This is clearly a well defined system with a single steady state solution. Methematical uniqueness theorems which define unique solutions are more general, but much more difficult to understand by anyone except mathematicians. |