| Author | Message | ||||
     Archie Campbell (amc1) Member Username: amc1 Post Number: 6 Registered: 03-2008 |
Dear Nelsons Like at least one previous correspondent I would like to be able to plot lines of force or streamlines for a 2D vector field with zero divergence. The adjoint equation in ‘Fieldmap’ cannot be used in many non-linear problems , but I thought the following should work. If the current density is J then we want a solution of the equation curl(M) =J where J is a known vector field. This is two equations for one variable Mz, but we know a solution exists, so solving one of the equations should produce a solution which satisfies the other. I therefore solve dM/dy=Jx and contour M. This works well for eddy currents which do not cross the boundary as in the attached ‘ex1-eddy.pde’. However it causes an error or instability if the vector crosses the boundary as in ‘fieldmap-ex2.pde’ . I have put ! in front of this equation and tried curl(curl(M))=D which produces a solution, but not the correct one although I think the solution should be unique. Is there a way of making either of these equations produce a general solution in the general case? A happy and prosperous New Year to all at FLEXpde. Archie Campbell
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1208 Registered: 06-2003 |
Interestingly, this approach results in the same equations as a streamline/vorticity model of fluid flow. We have used this method in the past to trace field lines. But it seems to work only if eps is constant. I have to assume that there is some kind of boundary correction that has to be applied at the interior material interface, but I don't know what it is. If you use D/magnitude(D) as the vector field, it gets close to the right solution. But not exactly. The field lines are not quite perpendicular to the potential contours. |
ex1-eddy.pde eddy current streamlines