[sjwon1991]

Hi, I have a question in my current simulation code which is normalized by central velocity.

I develop flow field from laminar flow containing initial perturbation without initial pressure field (which is set as zero).

Time advancement scheme is Hybrid Runge-Kutta 3rd order scheme proposed by Rai and Moin in 1991. In my case, pressure gradient terms are added to G.E. with RK coefficient, 2*alpha.

To satisfy the constant mass flow rate, I adjust the updated velocity based on delta flow rate,actual-target, and add it to the next time step's pressure term as damper.

Current simulation, I did not add mean pressure gradient which is -1 in u_tau normlized case.

My senior said, I just solve the fluctuating pressure component of governing equation, if I don't add mean pressure gradient term.

I want to figure out the balance between global pressure gradient and the total shear stress of the domain.

How could I get or add the mean pressure gradient terms in my present simulation?

Is it okay to simulate channel flow without mean pressure gradient? (Actually, I have well performed statistics without mean pressure gradient).

Thank you.

[FMDenaro]

Generally, you find two approaches, the first is fixing a constant pressure gadient in the momentum (as you wrote, is -1 when normalized by rho*u_tau^2), the second is adjust dynamically the forcing term to take into account the shear stress at the walls.
The pressure equation is solved with periodic bc.s along streamwise and spanwise directions so its solution is in terms of the fluctuation around the mean pressure (that decays along the streamwise direction).

[sjwon1991]

Thanks for your kind reply FMDenaro.

Your message meanss that I just solve only pressure fluctuations in pressure equation. (In fractional step method, the poisson eq.)

1. Then, how can I obtain or estimate mean pressure gradient of present simulation?

2. Driving force of my simulation is pressure gradient? (I didn't add mean pressure gradient term)

3. If I want to directly estimate the mean pressure gradient, can I just convert -1 by multiply (u_c/u_tau)^2 ? Does it make sense? (I didn't add mean pressure gradient term)

[FMDenaro]

If you use the fixed pressure gradient (I usually did this way), just sum to -1 the pressure gradient computed from the Poisson equation and multiply by rho*u_tau^2/L.
And yes, the driving force is the pressure gradient.

[sjwon1991]

Oh, I set fixed mass flow rate. Do you know how to estimate total pressure or gradient in this case?


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[FMDenaro]

Originally Posted by sjwon1991

Oh, I set fixed mass flow rate. Do you know how to estimate total pressure or gradient in this case?


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It a consequence of the balance with the wall stress... You can find several posts with similar discussion