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Problem with solving for unstructured mesh

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Old   November 22, 2006, 09:03
Default Hi, people! I wrote my own
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Efimenko Evgenii
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Hi, people!

I wrote my own solver to solve electromagnetic problems. This program solves set of curl Maxwell equations. and now I am testing it solving problems for resonators. I used it for quite complicated geometry as cross-like volume, it works fine even for quite coarse mesh.

Then I decided to test it for cylindrical geometry, but I failed. I got really unstructured mesh and for this mesh solution exponentionally grows to infinity. Everything that I changed is structured ortogonal mesh to unstructured non-ortogonal mesh.

Could anyone give me advice or any assumption how this problem can be solved?

Thank in advance.
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Old   November 22, 2006, 09:49
Default I don't know much about using
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Michael Prinkey
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I don't know much about using finite volume solvers for coupled EM, but I have written a solver (not in OpenFOAM) to solve electric fields coupled to reacting flow. I don't think that you can count on the segregated solution approach to always be stable, at least not without some underrelaxation. The reason is simple. You have (at least) six fields...the D-vector and B-vector fields that all couple strongly to each other. D is based on the curl of B. B is based on the curl of D. That coupling is all external. So the linear system of an equation for D or B is only going to have a diagonal and right-hand side.

d(D0)/dt = function(B0,B1,B2)
...
d(B0)/dt = function(D0,D1,D2)
...

So there is no linear system to solve. You are stuck either doing explicit timestepping or an iterative scheme based only on successive substitution. Both are potentially unstable depending on your choice of timestep and/or underrelaxation factors. As a rule, unstructured problems are usually more difficult to solve and less stable than structured problems. Vector components aligned with grid faces, no skew terms...all nice things that vanish with the grid structure. Moving to unstructured meshes may simply have moved your solver out of the basin of convergence you were enjoying before. You can try underrelaxing the solution more or reducing the timestep.

A better solution to this stability problem is to solve the fully coupled system. I.e., solve for all components of D and B from a block structured system. However, that capability does not currently exist in OpenFOAM.
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Old   November 24, 2006, 10:17
Default Which form of Maxwell's equati
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E. David Huckaby
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Which form of Maxwell's equations have you implemented ?
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