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The lowest spatial resolution for a given system 

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January 15, 2023, 17:18 
The lowest spatial resolution for a given system

#1 
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Mingming Zhang
Join Date: Dec 2019
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Dear all,
What is the lowest spatial resolution required for a given system (i.e., Ra and Pr)? Of course, time marching is correspondingly adapted. I have developed a spectral method code for modeling naiverstokes flow in an annulus. For low Ra (<=10^6), a low spatial resolution like 384(azimuthal)*128(radial)*128(mode) is fine enough and the convection would start quickly. For high Ra (>=10^9), I don't know how many grids is required. If it is too coarse, the model would crash immediately, while the grid is too fine, it will absolutely resolve much finer eddies but that would take prohibitively long time, even for the onset of the convection. I don't want to waste too much time and computation resources, so I need to know for a given Ra and Pr, the lowest spatial resolution to resolve this system. Any ideas? Thanks! Mingming 

January 16, 2023, 03:24 

#2  
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
The answer depends on the goal of your simulation. If you don't want to resolve all flow structures, you have to decide what formulation between either LES or RANS want to adopt. Furthermore, you have to decide if you want a wall resolved resolution or you add a wall modelled BCs. Clearly, if you want to perform an LES the grid resolution must be able to capture the inertial range and is finer than the grid in RANS. On the other hand, depending on your flow problem, using RANS (statistically steady flow) you can also use a 2D assumption. 

January 28, 2023, 19:05 

#3  
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Mingming Zhang
Join Date: Dec 2019
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Quote:
Thanks for continuously answering questions on this forum! I'm not using LES or RANS, it looks more like a direct numerical simulation. I know how to quantify the minimum grid for the onset of 'stable' convection (stable means not crash) for a given Ra and P in a Cartesian coordinate system, but annulus is not that straightforward. But thanks anyway MM. 

January 29, 2023, 05:31 

#4  
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Filippo Maria Denaro
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Quote:
I assume you are talking of an unresolved DNS (or, equivalently, LES nomodel), therefore depending on your scheme, you could have instability due to the energy pileup at the grid cutoff. This effect is quite typical of some schemes. A solution could be in the suitable choice of a scheme that produces an ILES formulation. That will help you in getting a stable solution without resolving all characteristic scales. On the other hand, if you are not interested in computing wall stresses, you can reduce the grid resolution near the walls. Annulus is not so different from a channel flow. 

January 31, 2023, 03:39 

#5 
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EM
Join Date: Sep 2019
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a priory estimates are very poor predictors of required
resolution and some are downright inappropriate like the kolmogorov scale applied to wallbounded flows. you have to make continuous runtime tests and use the endtime stats as well. for all numerical methods of incompressible bounded flows, the instantaneous nearwall asymptotic behaviour of uvw away from geometric singularities should be: u~y, v~y**2 and w~y (y is the local normal.) you can also test for the pointwise residual of the averaged momentum, energy, dissipation, intensities, enstrophy, ad infinitum and when appropriate, the continuity equation itself (when using weak formulations.) full spectral methods are best in this respect. if there is at least one fourier direction, then, you should be aiming for at least 4 orders drop in velocities and even in derived quantities eg dissipation. another good monitoring approach is plotting the instantaneous dissipation rate which must remain smooth virtually always and everywhere  jagged distributions are a good indicator of inadequate resolution. spectral methods should always use low Re at the start and increase it gradually.  Last edited by gnwt4a; February 2, 2023 at 00:11. Reason: +s 

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