UNCONDITIONAL NONLINEAR STABILITY VIA THE ENERGY METHOD

2002 ◽  
Author(s):  
B. STRAUGHAN
Keyword(s):  
Nonlinear Stability ◽  
Energy Method ◽  
Unconditional Nonlinear Stability

POROUS PENETRATIVE CONVECTION WITH A SALT FIELD AND INTERNAL HEAT SOURCE

1992 ◽  
Vol 02 (04) ◽  
pp. 407-421
Author(s):  
LORNA RICHARDSON
Keyword(s):  
Porous Medium ◽  
Temperature Gradient ◽  
Heat Source ◽  
Nonlinear Stability ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Penetrative Convection ◽  
Weighted Energy ◽  
The Stability ◽  
Unconditional Nonlinear Stability

We investigate the stability of convection in a porous medium containing a heat source in which a destabilizing salt field and stabilizing temperature gradient are present. Both conditional and unconditional nonlinear stability thresholds are calculated and we note that RaE(conditional)>RaE(unconditional). The unconditional nonlinear analysis requires the use of a “weighted” energy.

Global stability for thermal convection in a fluid overlying a highly porous material

2008 ◽  
Vol 465 (2101) ◽  
pp. 207-217 ◽  
Author(s):  
Antony A Hill ◽  
Brian Straughan
Keyword(s):  
Porous Medium ◽  
Porous Material ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Linear Instability ◽  
Brinkman Equation ◽  
Onset Of Convection ◽  
Unconditional Nonlinear Stability ◽  
Highly Porous ◽  
Highly Porous Material

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 the fluid flow in the porous medium. An excellent agreement is found between the linear instability and unconditional nonlinear stability thresholds, demonstrating that the linear theory accurately emulates the physics of the onset of convection.

UNCONDITIONAL NONLINEAR STABILITY FOR TEMPERATURE-DEPENDENT DENSITY FLOW IN A POROUS MEDIUM

2003 ◽  
Vol 13 (02) ◽  
pp. 207-220 ◽  
Author(s):  
MAGDA CARR
Keyword(s):  
Porous Medium ◽  
Nonlinear Stability ◽  
Saturated Porous Medium ◽  
Unconditional Stability ◽  
Nonlinear Stability Analysis ◽  
Temperature Dependent ◽  
Density Flow ◽  
Unconditional Nonlinear Stability ◽  
Dependent Density ◽  
Drag Term

A nonlinear stability analysis of thermal convection in a saturated porous medium is presented. Density is assumed to have a cubic temperature dependence and the equations of flow in the porous medium are described via Darcy's law with a Forchheimer drag term. Unconditional stability is established using L3 and L4 norms and it is shown that L2 theory is insufficient to obtain similar results. Previous authors have established conditional nonlinear stability but we believe this is the first analysis that addresses the important problem of unconditional stability for the system in hand.

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