Periodic boundary conditions and conditional terms

[Sihe Chen]

I am trying to setup a 2D square computational domain that is doubly periodic. Do I have to impose the tau method in this case? I could not find a similar case in the tutorial.

Also, I want to put in a conditional term in the equation. By conditional term I mean the term that takes effect in some conditions only, e.g. only some distance from the boundaries.

Many thanks in advance for the help :)

[Guangpu Zhu]

Hi, Sihe,

     You don't need to impose the tau method. 

Best,

E-mail: zhug...@gmail.com

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[Sihe Chen]

Thanks Guangpu. Any suggestions on the conditional terms? Is there something functions like Heaviside step function? I could not find it in the documentation...

[Guangpu Zhu]

Hi, Shihe,

   I suggest you read the tutorial carefully, you will find the answer.

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[MANISH KUMAR]

Hello Dedalus Users, 

 I am trying to implement double periodic boundary conditions in Dedalus v3 using Fourier modes in both the x and y directions for a 2D flow. The following is the portion of the code:

~~~~~~~~~

problem = d3.LBVP([u, p, tau_p], namespace=locals())

problem.add_equation("-grad(p) + lap(u) = f", condition = "(nx != 0) or (ny != 0)")

problem.add_equation("u = 0", condition = "(nx == 0) and (ny == 0)")

problem.add_equation("div(u) + tau_p = 0")

problem.add_equation("integ(p) = 0") # Pressure gauge

~~~~~~~~~~

Without any condition on the momentum equation, it gives the error, "RuntimeError: Factor is exactly singular".

When I apply the condition shown in the code, it gives the error, "NameError: name 'ny' is not defined. Did you mean: 'nx'?".

I wonder if anyone has faced a similar problem.

Thanks in advance for any help.

Best regards,

Manish Kumar

[Calum Skene]

Hi Manish,

You can avoid using condition altogether by introducing another tau term, tau_u created in the same way as tau_p. Something like

problem = d3.LBVP([u, p, tau_p, tau_u], namespace=locals())

problem.add_equation("-grad(p) + lap(u) + tau_u = f")

problem.add_equation(integ(u) = 0")

problem.add_equation("div(u) + tau_p = 0")

problem.add_equation("integ(p) = 0") # Pressure gauge

should work. The tau_u term absorbs the nx=ny=0 average, and introduces another degree of freedom which allows you to specify integ(u)=0.

Best,

Calum

[MANISH KUMAR]

Thanks, Calum. Yes, It works.

Best regards

Manish Kumar