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IMA Journal of Applied Mathematics Advance Access originally published online on September 22, 2007
IMA Journal of Applied Mathematics 2007 72(5):635-643; doi:10.1093/imamat/hxm036
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Global stability for penetrative convection with throughflow in a porous material

A. A. Hill{dagger}

Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK

S. Rionero

Department of Mathematics and Applications ‘R. Caccioppoli’, University of Naples Federico II, Via Cinzia, 80126 Naples, Italy

B. Straughan

Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK

{dagger} Email: a.a.hill{at}durham.ac.uk

Received on September 1, 2006; Accepted on February 22, 2007

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 non-linear energy stability analysis. A weighted analysis is necessary to achieve a global non-linear stability threshold. Parameter ranges are found where the linear instability boundary is close to the non-linear stability one.

Keywords: energy method; throughflow; penetrative convection.


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