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.
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.
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.