A coupled PDE/ODE IVP system

[James Taylor]

Dear Dedalus Users,

I'd like to solve a 1D IVP problem formulated in the attached PDF file. The problem is described by a coupled PDE/ODE system and involves a time-dependent boundary condition. An analytical solution exists. I'd like to recover this solution numerically.

I'm trying to implement the problem in Dedalus. My attempt is in the attached script. I've defined 's' as a field with only an ξ-basis (since it doesn't depend on t). The script produces the following error message:

ValueError: Pencil () has 3 constant equations for 1 constant variables plus 1 differential equations / tau terms.

Can you provide guidance or suggest modifications to my script that would make it work?

Thanks in advance for all your help!  

James

[Keaton Burns]

Hi James,

In Dedalus v2, the differential order of the system is inferred from the number of derivatives on the LHS. You can overwrite this, and mark equations as differential, with the tau=True keyword.  I’d suggest doing this the dt(u) equation. However, I’d also suggest switching to Dedalus v3, since we’re phasing out support for v2 going forward. 

Best,

-Keaton

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