A spectrally-accurate algorithm for analysis of the stability of spatially modulated convection. (30th April 2019) - Moradi, H.V.; Floryan, J.M.
Highlights: A spectrally-accurate algorithm for analysis of the stability of spatially modulated convection has been developed. Modulations can be generated using either geometric, or heating, or both types of irregularities. The algorithm uses a combination of Fourier expansions in the horizontal directions, Chebyshev expansions in the vertical direction. The Immersed Boundary Conditions (IBC) method to capture geometric irregularities. Various tests confirm that the algorithm delivers spectral accuracy for the eigenvalues and the eigenfunctions. Abstract: A spectrally-accurate algorithm for analysis of the stability of spatially modulated convection has been developed. Modulations can be generated using either geometric, or heating, or both types of irregularities. The algorithm uses a combination of Fourier expansions in the horizontal directions, Chebyshev expansions in the vertical direction and the Immersed Boundary Conditions (IBC) method to capture geometric irregularities. The resulting gridless discretization provides means for an efficient handling of multiple geometries as well as for geometry optimization. Various tests confirm that the algorithm delivers spectral accuracy for the eigenvalues and the eigenfunctions. Examples of applications are provided.