Q:

What is the exponential trick to include laplacian term in Rayleigh-Bernard simulation

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.

A:

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.

