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I have come across a Rayleigh-Bernard simulation code which doesn't have the laplacian term but an integrating factor (in the exponential form) containing viscosity and diffusivity. I found out that it is an exponential trick. I couldn't find any literature on it except that. I would like to know more. Can someone point me to a reference.

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I found what I was looking for, so I will share:

Check out: "Time integration and treatment of viscous/diffusive terms" on page 5.

K. B. Winters, J. McKinnon, and B. Mills. A spectral model for process studies of density stratified flows. J. of Atmos. Ocean. Techn. (submitted), 2003.

https://journals.ametsoc.org/doi/pdf/10.1175/1520-0426%282004%29021%3C0069%3AASMFPS%3E2.0.CO%3B2

The above article uses an exponential integrating factor while integrating and the laplacian term of the N-S equation and other scalar equations is treated through the integrating factor.

Similar was the case in the R-B simulation code, which I didn't understood at the time.

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  • $\begingroup$ Can you provide details to your answer? $\endgroup$ – nicoguaro Aug 30 at 11:49
  • $\begingroup$ @nicoguaro I hope the answer is clearer now. The question I asked was pretty specific to my case. I just did not understood the implementation at the time. $\endgroup$ – user162281 Aug 30 at 13:27

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