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Linear and non-linear stability thresholds for thermal convection in a box (2006)
Journal Article
Hill, A. A., Hill, A. A., & Straughan, B. (2006). Linear and non-linear stability thresholds for thermal convection in a box. Mathematical Methods in the Applied Sciences, 29(17), 2123-2132. https://doi.org/10.1002/mma.770

We analyse the problem of finding instability thresholds and global non-linear stability bounds for thermal convection in a linearly viscous fluid in a finite box. The vertical walls are maintained at different temperatures which gives rise to a non-... Read More about Linear and non-linear stability thresholds for thermal convection in a box.

A Legendre spectral element method for eigenvalues in hydrodynamic stability (2006)
Journal Article
Hill, A. A., Hill, A. A., & Straughan, B. (2006). A Legendre spectral element method for eigenvalues in hydrodynamic stability. Journal of Computational and Applied Mathematics, 193(1), 363-381. https://doi.org/10.1016/j.cam.2005.06.011

A Legendre polynomial-based spectral technique is developed to be applicable to solving eigenvalue problems which arise in linear and nonlinear stability questions in porous media, and other areas of Continuum Mechanics. The matrices produced in the... Read More about A Legendre spectral element method for eigenvalues in hydrodynamic stability.