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Computes the linear stability in the Rayleigh-Bénard problem.
The curve of critical Rayleigh number as function of wavenumber is computed and plotted and the minimum value of the Rayleigh number is obtained along with the corresponding value of the wavenumber. The first unstable mode can also be plotted, both as profiles of the z dependence and as temperature-velocity maps.
Any type of the classical boundary conditions can be computed at either boundary for each variable, horizontal velocity (u), vertical velocity (w), and temperature (t). Example calculations are provided and cna be turned on or off by setting the options at the beginning of the file:
- COMPUTE_FREESLIP for free slip BCs at both boundaries
- COMPUTE_NOSLIP for rigid BCs at both boundaries
- COMPUTE_FREERIGID for free slip top BC and rigid bottom Resulting figures are also provided. Results for other BCs can be obtained following this last example.
Other options can be changed at the beginning of the file:
- NCHEB is the number of Chebyshev points to use in the computation
- FTSZ is the fontsize for the annotation on the plots
Example of figures obtained for the most classical cases of boundary conditions (combinations of free-slip and rigid on either sides) are provided in pdf format.
The calculation uses an implementation of DMSuite in Python available on github as part of the pyddx package (https://github.com/labrosse/dmsuite). DMSuite was originally developed for matlab by Weidemann and Reddy and explained in ACM Transactions of Mathematical Software, 4, 465-519 (2000). The present code is based on an octave code originally developed by T. Alboussière and uses the Chebyshev differentiation matrices.