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Stability of 3D thermal LBM model

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    I am working on thermal LBM and during the solution of the benchmark problem of natural convection in a differentially heated cavity I found out that the 3D model is not as stable as the 2D model. I use the D3Q19 scheme with the two-relaxation rate approximation for flow whereas the advection/diffusion equation is solved by the conventional finite difference technique. As expected, the instabilities are observed with the Rayleigh number higher than 10^9. However, the 2D model with the D2Q9 scheme works relatively fine with Ra=10^9 and Ra=10^10 whereas the 3D model is unstable with the same values of relaxation rates and grid size along two coordinates. My first thought was to extend the number of speeds to D3Q27. Unfortunately, it did not work. Did someone meet this problem? Or can someone suggest to me the direction of this problem solution?


    Hi Alex,

    3D simulations being easier to be instable sounds resonable. You have more degrees of freedom, more calculations that could potentially intodruce numerical errors. Also, do not forget that turbulence in 2D is a completely different phenomenon than in 3D!

    Above Ra>=1e7 these simulations transition to turbulent natural convection and eddies will arise. Are you using a turbulence model for your simulations or are you wanting to resolve all structures? If no turbulence model is applied, check your resolution. It should be high enough to resolve the boundary layer that develops close to the heated and cooled walls. You can find some more info in e.g.



    Dear Dr. Gaedtke,

    Thank you for your response. I strongly agree that turbulence is a 3D process. However, in the case of the differentially heated cavity 2D model is also fine as the first approximation which gives similar patterns to 3D.
    I am trying to perform a pseudo-direct numerical simulation to make the model free from empirical constants. What concerns LES, Smagorinsky model works fine in 3D. But Cs significantly affects both the results and numerical stability. BTW, when I did the literature review I read the paper you mentioned

    kind regards,

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