[jinhua2015]

Hi all,

I'm new to the forum. It's a really nice place to discuss fluid mechanics.

I recently got a pseudo-spectral code (Fourier*Chebyshev*Fourier for the spatial discretization) for simulating a turbulence channel flow. But the code is old and I was told not to take it for granted. So I would like to validate the code first to see if it can run correctly.

In this regard, I would like to ask

(1) how to generate a consistent and proper initial condition (ic) field for the turbulence channel flow? The ic should satisfy the nonslip boundary conditions for the velocities and the divergence-free condition at the same time.

(2) what is a simple way to check the code? Is there any analytical solution in the channel flow setting to NS equation? I guess probably not. From the reference, I see that people usually check the mean velocity profile around the wall, i.e., the law of the wall. But that will be in a too late stage, I mean, I should take the statistics of the generated flow data to check the law of the wall. Is there any simpler and easier to check the code?

Thanks a lot for your suggestions. Any comments will be appreciated.

jinhua

[FMDenaro]

Originally Posted by jinhua2015

Hi all,

I'm new to the forum. It's a really nice place to discuss fluid mechanics.

I recently got a pseudo-spectral code (Fourier*Chebyshev*Fourier for the spatial discretization) for simulating a turbulence channel flow. But the code is old and I was told not to take it for granted. So I would like to validate the code first to see if it can run correctly.

In this regard, I would like to ask

(1) how to generate a consistent and proper initial condition (ic) field for the turbulence channel flow? The ic should satisfy the nonslip boundary conditions for the velocities and the divergence-free condition at the same time.

(2) what is a simple way to check the code? Is there any analytical solution in the channel flow setting to NS equation? I guess probably not. From the reference, I see that people usually check the mean velocity profile around the wall, i.e., the law of the wall. But that will be in a too late stage, I mean, I should take the statistics of the generated flow data to check the law of the wall. Is there any simpler and easier to check the code?

Thanks a lot for your suggestions. Any comments will be appreciated.

jinhua

Hi,
I suggest to test the code first for the laminar steady Poiseuille solution... I suppose you have periodic condition in streamwise and spanwise condition, so you could check for the 4 combinations of pressure gradient. An initial condition could be simply the plug flow.

Then, if you want to use the code for turbulent conditions you should distinguish between DNS and LES formulations that drive to different grid resolution. The initial condition cna be generated from the Poiseuille solution with a superimposed fluctuations. However, you need to run the code until the solution loose memory of the initial condition.
Many database for DNS are available, for example here

http://turbulence.ices.utexas.edu/MKM_1999.html

[jinhua2015]

Originally Posted by FMDenaro

Hi,
I suggest to test the code first for the laminar steady Poiseuille solution... I suppose you have periodic condition in streamwise and spanwise condition, so you could check for the 4 combinations of pressure gradient. An initial condition could be simply the plug flow.

Then, if you want to use the code for turbulent conditions you should distinguish between DNS and LES formulations that drive to different grid resolution. The initial condition cna be generated from the Poiseuille solution with a superimposed fluctuations. However, you need to run the code until the solution loose memory of the initial condition.
Many database for DNS are available, for example here

http://turbulence.ices.utexas.edu/MKM_1999.html

Thanks. I'm currently reading and trying to understand the code. I will report the questions I may have later. Thanks again.

[jinhua2015]

Originally Posted by FMDenaro

Hi,
I suggest to test the code first for the laminar steady Poiseuille solution... I suppose you have periodic condition in streamwise and spanwise condition, so you could check for the 4 combinations of pressure gradient. An initial condition could be simply the plug flow.

Then, if you want to use the code for turbulent conditions you should distinguish between DNS and LES formulations that drive to different grid resolution. The initial condition cna be generated from the Poiseuille solution with a superimposed fluctuations. However, you need to run the code until the solution loose memory of the initial condition.
Many database for DNS are available, for example here

http://turbulence.ices.utexas.edu/MKM_1999.html

Hi,

I take your suggestion to run the code with steady Poiseuille flow (initial condition is u=1-y^2 without background turbulence and the flow is driven by a constant streamwise pressure gradient -2/Re, solved from the steady NS equation). Now even for this simple setting, I have some problems. I expect that the flow would remain the same before the numerical error takes over, but it's very soon that I spot the trend of the flow filed is going to blow up. The maximum velocity keeps increasing. I plot the flow field, it seems that there are check-board errors (for example, I plot the u at the boundary y=1, the velocity there should be zero, but when I run for less than 1 time unit, the error shows a check-board pattern.). I know that this could be avoided in the finite difference scheme by using staggered grid, but the code I have do not solve pressure explicitly (see Kim, Moin Moser 1987). Do you know what may be the cause of this error in spectral method?

The code was using FFTPACK for the FFT. I actually have also tried FFTW as I suspect that FFTPACK might be worse in the performance, but this error is still there....

Thanks for any comments.

Jinhua

[FMDenaro]

first, your plot show a vanishing velocity u ! You can see oscillations but their magnitude order is 10^-13 ....

second, have you set Re=1? the height of the channel is 1 in non dimensional unit?

third, do you run the code within the numerical stabilty constraints? you should get a steady solution (check the magnitude of max time derivative)

[jinhua2015]

Originally Posted by FMDenaro

first, your plot show a vanishing velocity u ! You can see oscillations but their magnitude order is 10^-13 ....

second, have you set Re=1? the height of the channel is 1 in non dimensional unit?

third, do you run the code within the numerical stabilty constraints? you should get a steady solution (check the magnitude of max time derivative)

Hi FMDenaro,

Thanks for your reply. At the initial time, the velocity amplitude at the boundary (y=1) is indeed zero, but then it increases slowly to 10^-13. If I run for a longer time, the flow field will blow up.

The nondimensional length is the half channel flow, so yes, y=1 is the boundary of the channel.

I constrain the CFL number.

I tried this morning, and I did get a steady solution. I will run for a real flow with some turbulence. Hope it will get right. Thanks a lot. Have a nice day.

Jinhua

[FMDenaro]

Originally Posted by jinhua2015

Hi FMDenaro,

Thanks for your reply. At the initial time, the velocity amplitude at the boundary (y=1) is indeed zero, but then it increases slowly to 10^-13. If I run for a longer time, the flow field will blow up.

The nondimensional length is the half channel flow, so yes, y=1 is the boundary of the channel.

I constrain the CFL number.

I tried this morning, and I did get a steady solution. I will run for a real flow with some turbulence. Hope it will get right. Thanks a lot. Have a nice day.

Jinhua

however, the velocity at the walls must be prescribed, not computed...so, see the part in your code that fix the BC.s.

what about the steady solution you get?

[kaya]

Originally Posted by jinhua2015

Hi FMDenaro,

Thanks for your reply. At the initial time, the velocity amplitude at the boundary (y=1) is indeed zero, but then it increases slowly to 10^-13. If I run for a longer time, the flow field will blow up.

The nondimensional length is the half channel flow, so yes, y=1 is the boundary of the channel.

I constrain the CFL number.

I tried this morning, and I did get a steady solution. I will run for a real flow with some turbulence. Hope it will get right. Thanks a lot. Have a nice day.

Jinhua

which time scheme do you have?

do you do dealiasing? actually with such a low re it shouldn't be a problem

you can save your velocity field and take the spatial spectrum in each time snapshot and see how it changes before your code blows. than can enlighten a bit