Question about the Tau Method

[MinYu Li]

Hi everyone,

I am working with the following set of partial differential equations.

iαu + Dv = 0

-iωu + iαUu + U'v = -iαp

-iωv + iαUv = -Dp

where D = d/dy

This set of partial differential equations requires two boundary conditions. According to the documentation, applying these two conditions involves adding two tau terms. However, I am unsure which equations the tau terms should be applied to in my case.

Based on the example in the documentation, should I add the tau terms to each y-differential equation, that is, the first and third equations?

Any guidance would be greatly appreciated!

Minyu Li

[Keaton Burns]

Hi Minyu,

Yes I would try doing everything here implicitly (move the pressure terms to the LHS) and add a tau term to each equation with a Chebyshev derivative, and then add your two boundary conditions (presumably Dirichlet conditions on v?).

Best,

-Keaton

--
You received this message because you are subscribed to the Google Groups "Dedalus Users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to dedalus-user...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/dedalus-users/3a58697e-a461-4669-99cd-48cf220fb526n%40googlegroups.com.

[MinYu Li]

Hi Keaton,

Thanks for your response, it was really helpful.

Best regards,  
Minyu