Tau method for Cavity flows

[Guangpu Zhu]

Dear Dedalus Developers and Community members,

          I am trying to use the Dedalus to reproduce the classic cavity flow.

x and z basis are defined as follows:

xbasis = d3.ChebyshevT(coords['x'], size=Nx, bounds=(0, Lx), dealias=dealias) zbasis = d3.ChebyshevT(coords['z'], size=Nz, bounds=(0, Lz), dealias=dealias)

 

Following the generalized tau method introduced here, I rewrite the dimensionless Navier-Stokes equation as

I am not sure if my understanding of the tau method is correct.

If the above note is right, tau can be defined as 'dist.Field(name='tau_1', bases=xbasis)'

or  'dist.Field(name='tau_1', bases=zbasis)'

Great thanks in advance.

[Daniel Lecoanet]

Hi,

It is possible to solve such problems in Dedalus, but it requires great sophistication with the tau method. If you are interested in trying to work it out, I would suggest starting with this paper: https://arxiv.org/abs/2211.17259 . Note however that the hydrodynamics problem is even more subtle due to the incompressibility condition.

Daniel

On Nov 1, 2023, at 3:13 AM, Guangpu Zhu <zhug...@gmail.com> wrote:

Dear Dedalus Developers and Community members,

          I am trying to use the Dedalus to reproduce the classic cavity flow.

x and z basis are defined as follows:

xbasis = d3.ChebyshevT(coords['x'], size=Nx, bounds=(0, Lx), dealias=dealias) zbasis = d3.ChebyshevT(coords['z'], size=Nz, bounds=(0, Lz), dealias=dealias)

 

Following the generalized tau method introduced here, I rewrite the dimensionless Navier-Stokes equation as

<QQ截图20231101160532.jpg>

I am not sure if my understanding of the tau method is correct.

If the above note is right, tau can be defined as 'dist.Field(name='tau_1', bases=xbasis)'

or  'dist.Field(name='tau_1', bases=zbasis)'

Great thanks in advance.

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<QQ截图20231101160532.jpg>

[Guangpu Zhu]

Hi,  Daniel,

 Thanks for your kind suggestion, I will check the manuscript you recommend. 

Best,