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Sharp global nonlinear stability for a fluid overlying a highly porous material (2010)
Journal Article
Hill, A. A., & Carr, M. (2010). Sharp global nonlinear stability for a fluid overlying a highly porous material. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2113), 127-140. https://doi.org/10.1098/rspa.2009.0322

The stability of convection in a two-layer system in which a layer of fluid with a temperature-dependent viscosity overlies and saturates a highly porous material is studied. Owing to the difficulties associated with incorporating the nonlinear advec... Read More about Sharp global nonlinear stability for a fluid overlying a highly porous material.

Poiseuille flow in a fluid overlying a highly porous material (2009)
Journal Article
Straughan, B., Hill, A. A., Hill, A. A., & Straughan, B. (2009). Poiseuille flow in a fluid overlying a highly porous material. Advances in Water Resources, 32(11), 1609-1614. https://doi.org/10.1016/j.advwatres.2009.08.007

This paper investigates the instability of Poiseuille flow in a fluid overlying a highly porous material. A two layer approach is adopted, where the Darcy-Brinkman equation is employed to describe the fluid flow in the porous medium, with a tangentia... Read More about Poiseuille flow in a fluid overlying a highly porous material.

Instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer (2009)
Journal Article
Hill, A. A. (2009). Instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer. Acta Mechanica, 206(1-2), 95-103. https://doi.org/10.1007/s00707-008-0099-2

The instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer saturated with the same fluid is studied. A three layer configuration is adopted, where a variable effective viscosity is modelled between the outer fluid and po... Read More about Instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer.

A differential constraint approach to obtain global stability for radiation-induced double-diffusive convection in a porous medium (2009)
Journal Article
Hill, A. A. (2009). A differential constraint approach to obtain global stability for radiation-induced double-diffusive convection in a porous medium. Mathematical Methods in the Applied Sciences, 32(8), 914-921. https://doi.org/10.1002/mma.1073

The stability of double-diffusive porous convection with a concentration-based internal heat source is studied. Owing to the significant sensitivity of standard energy method, a highly desirable reduction in the number of required coupling parameters... Read More about A differential constraint approach to obtain global stability for radiation-induced double-diffusive convection in a porous medium.

Anisotropy and symmetry in porous media convection (2009)
Journal Article
Hill, A. A., Capone, F., Gentile, M., & Hill, A. A. (2009). Anisotropy and symmetry in porous media convection. Acta Mechanica, 208(3-4), 205-214. https://doi.org/10.1007/s00707-008-0135-2

The linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium is performed. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic th... Read More about Anisotropy and symmetry in porous media convection.

Global stability for thermal convection in a fluid overlying a highly porous material (2009)
Journal Article
Hill, A. A., & Straughan, B. (2009). Global stability for thermal convection in a fluid overlying a highly porous material. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 465(2101), 207-217. https://doi.org/10.1098/rspa.2008.0303

This paper investigates the instability thresholds and global nonlinear stability bounds for thermal convection in a fluid overlying a highly porous material. A two-layer approach is adopted, where the Darcy-Brinkman equation is employed to describe... Read More about Global stability for thermal convection in a fluid overlying a highly porous material.

Penetrative convection in a fluid layer with throughflow (2008)
Journal Article
Capone, F., Gentile, M., & Hill, A. A. (2008). Penetrative convection in a fluid layer with throughflow. Ricerche di matematica, 57(2), 251-260. https://doi.org/10.1007/s11587-008-0035-8

Linear and nonlinear stability analyses of vertical throughflow in a fluid layer, where the density is quadratic in temperature, are studied. To avoid the loss of key terms a weighted functional is used in the energy analysis. Both conditional and un... Read More about Penetrative convection in a fluid layer with throughflow.

Global stability for penetrative double-diffusive convection in a porous medium (2008)
Journal Article
Hill, A. A., & Hill, A. A. (2008). Global stability for penetrative double-diffusive convection in a porous medium. Acta Mechanica, 200(1-2), 1-10. https://doi.org/10.1007/s00707-007-0575-0

Linear and nonlinear stability analyses of penetrative double-diffusive convection in a porous medium are performed. Adopting a standard energy method approach yields a nonlinear threshold which is independent of the salt field. An adaptation of a ne... Read More about Global stability for penetrative double-diffusive convection in a porous medium.

Poiseuille flow in a fluid overlying a porous medium (2008)
Journal Article
Hill, A. A., & Straughan, B. (2008). Poiseuille flow in a fluid overlying a porous medium. Journal of Fluid Mechanics, 603, 137-149. https://doi.org/10.1017/S0022112008000852

This paper numerically investigates the instability of Poiseuille flow in a fluid overlying a porous medium saturated with the same fluid. A three-layer configuration is adopted. Namely, a Newtonian fluid overlying a Brinkman porous transition layer,... Read More about Poiseuille flow in a fluid overlying a porous medium.

Global stability for penetrative convection with throughflow in a porous material (2007)
Journal Article
Hill, A. A., Hill, A. A., Rionero, S., & Straughan, B. (2007). Global stability for penetrative convection with throughflow in a porous material. IMA Journal of Applied Mathematics, 72(5), 635-643. https://doi.org/10.1093/imamat/hxm036

This paper investigates penetrative convection in a layer of porous material saturated with water when there is throughflow present. The density is quadratic in temperature. A linearized instability analysis is derived and compared with a weighted no... Read More about Global stability for penetrative convection with throughflow in a porous material.

Unconditional nonlinear stability for convection in a porous medium with vertical throughflow (2007)
Journal Article
Hill, A. A., & Hill, A. A. (2007). Unconditional nonlinear stability for convection in a porous medium with vertical throughflow. Acta Mechanica, 193(3-4), 197-206. https://doi.org/10.1007/s00707-007-0473-5

Linear and nonlinear stability analyses of vertical throughflow in a fluid saturated porous layer, which is modelled using a cubic Forchheimer model, are studied. To ensure unconditional nonlinear results are obtainable, and to avoid the loss of key... Read More about Unconditional nonlinear stability for convection in a porous medium with vertical throughflow.

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.

Double-diffusive convection in a porous medium with a concentration based internal heat source (2005)
Journal Article
Hill, A. A. (2005). Double-diffusive convection in a porous medium with a concentration based internal heat source. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461(2054), 561-574. https://doi.org/10.1098/rspa.2004.1328

Linear and nonlinear stability analyses of double-diffusive convection in a fluid-saturated porous layer with a concentration based internal heat source are studied. Darcy's law and the Boussinesq approximation are employed, with the equation of stat... Read More about Double-diffusive convection in a porous medium with a concentration based internal heat source.

Penetrative convection induced by the absorption of radiation with a nonlinear internal heat source (2004)
Journal Article
Hill, A. A. (2004). Penetrative convection induced by the absorption of radiation with a nonlinear internal heat source. Dynamics of Atmospheres and Oceans, 38(1), 57-67. https://doi.org/10.1016/j.dynatmoce.2004.03.002

A model for convection induced by the selective absorption of radiation in a fluid layer is investigated. The concentration based internal heat source is modelled quadratically. A linear analysis and conditional nonlinear analysis are performed. Due... Read More about Penetrative convection induced by the absorption of radiation with a nonlinear internal heat source.

Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium (2004)
Journal Article
Hill, A. A., & Hill, A. A. (2004). Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium. Continuum Mechanics and Thermodynamics, 16(4), 305-318. https://doi.org/10.1007/s00161-003-0151-3

Convection induced by the selective absorption of radiation is investigated, for the case of an internal heat source that is modelled quadratically with respect to concentration. The growth rate for the linearised system is shown to be real, and a li... Read More about Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium.

Convection induced by the selective absorption of radiation for the Brinkman model (2004)
Journal Article
Hill, A. A., & Hill, A. A. (2004). Convection induced by the selective absorption of radiation for the Brinkman model. Continuum Mechanics and Thermodynamics, 16(1-2), 43-52. https://doi.org/10.1007/s00161-003-0140-6

Convection induced by the selective absorption of radiation in a porous medium is studied analytically and numerically using the Brinkman model. Both linear instability analysis and nonlinear stability analysis are employed. The thresholds show excel... Read More about Convection induced by the selective absorption of radiation for the Brinkman model.