[Getdp] Non-linear magnetodynamics with a superconducting tape

[Frederic Trillaud Pighi]

Dear Guillaume,

I have completed a run of the code I sent you (I should have checked it
before sending it!!). Even though it runs, It does not seem to work
correctly. Indeed, it does not seem to converge. I will look through it
in my spare time.

Best,

Frederic


On Wed, 2015-10-21 at 14:14 +0000, DILASSER Guillaume wrote:
> Good evening,
> 
>  
> 
> I am writing this Email to hopefully get some advice on how to
> implement in GetDP a non-linear material law corresponding to the
> behavior of a HTS superconductor. I have recently started to use GetDP
> with the aim of simulating superconducting electromagnets but for now
> I am still learning how to use the software. I chose to work first on
> an example available here (HTS modelling workgroup website, it is
> example 1 at the top of the page) to be able to compare my results to
> those of the community. The scenario implies a simple strand of
> superconductor with a rectangular cross-section to which is applied an
> AC current, everything is then surrounded by air. For the benchmark,
> the aim is mostly to compute the AC losses in the material during the
> current cycle.
> 
>  
> 
> Since I have much to learn, I tackled the problem step by step by
> first considering a linear case in which I have resistive material in
> place of the superconductor. I enclose the files I have been working
> on for those who want to have a look at them (sadly it is mostly
> written in French…). The outline of what I tried is following : I
> considered the 2D case to resolve the problem in the cross-section but
> did not implement yet the use of symmetries. I wrote the A-Phi
> formulation with constant parameters nu and sigma. The resolution of
> the magnetodynamic problem is fairly trivial as everything is linear.
> I guess the solution shown in the enclosed files is about to be
> correct yet I still have some unanswered questions :
> 
> ·        Is the way I implemented the shell-to-infinite-domain
> transformation correct ? I had some error like “the Jacobian x is not
> in the range [a,b]” which I did not understand when messing with the
> VolSphShell Jacobian, is there a specific documentation on the
> topic ? 
> 
> ·        When I try to drop the thickness of the tape down to about 1
> µm (the width of the tape is about 4 mm), Gmsh gives an error as “some
> points are coincident”. I tried the solutions to prevent that, namely
> decrease the size of the mesh elements in the conductor and/or
> increase the mesh.RandomFactor but without success. What did I miss ?
> 
> ·        I tried to compute the AC losses in the material in the
> post-process but unfortunately I must have done something wrong as I
> always find 0… Where does it come from ?
> 
>  
> 
> Those were the issues I still have with my first (resistive) scenario
> but to switch now to the original example I need to add the E-J
> material law for the superconductor. My plan is to begin with a simple
> non-linear power law E = e0 * (|J|/jc)^N * (J/jc), e0 = 10-4 V/m, jc =
> 108 A/m², N about 10. For the A-Phi formulation I have to implement a
> sigma(E) = sigma(dA/dt + gradPhi) relation in the equations but what
> is precisely to do remains unclear.
> 
> ·        The helix.pro example gave me an idea of what I could do even
> if it is not the same formulation. However, if I am unsure on how I
> can linearize the expressions involving sigma. If I understood well,
> it is forbidden to write a term such as [ DtDof[ sigma[Dof[{a}],{v}] *
> Dof[{a}], {a} ].
> 
> ·        Or, is this possible to use some of the Built-in functions
> like IterativeLoop[] with non-linear term like the one above ?
> 
> I would really appreciate your advice on how I can (and should)
> implement this material power-law behavior. I realize that A-Phi was
> probably not the best formulation to work with as the sigma appears a
> lot in the equation and is a function of two variables… 
> 
>  
> 
> Faithfully yours,
> 
>  
> 
> Guillaume DILASSER
> 
> Doctorant SACM / LEAS
> 
> CEA - Centre de Saclay - Bât.123 - PC 319c
> 
> 91191 Gif sur Yvette Cedex - France -
> 
>  
> 
> guillaume.dilasser at cea.fr
> 
>  
> 
> 
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