IMA Journal of Applied Mathematics · 2007 · 68 citations · 0 references
EngineeringHydrologyPetroleum EngineeringFluid DynamicsHeat TransferSubsurface Fluid FlowBoundary Layer FlowFluid-flow In Porous MediaPorous MaterialsPorous Media FlowSaturated FlowTransport In Porous MediaConvectionGlobal StabilityGlobal Stability AnalysisLinear StabilityLinear Stability AnalysisPenetrative ConvectionPorous MediaPorous Media Boundary Layers
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. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.