TRIPLY RESONANT DOUBLE DIFFUSIVE CONVECTION IN A FLUID LAYER

We study the problem of double-diffusive convection in a horizontal plane fluid layer when there is a heat sink/source which is linear in the vertical coordinate which is in the opposite direction to gravity. The thresholds for linear instability are found and compared to those derived by a global nonlinear energy stability analysis. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.

Triply resonant penetrative convection

A thermal convection model is considered that consists of a layer of viscous incompressible fluid contained between two horizontal planes. Gravity is acting vertically downward, and the fluid has a density maximum in the active temperature range. A heat source/sink that varies with vertical height is imposed. It is shown that in this situation there are three possible (different) sub-layers that may induce convective overturning instability. The possibility of resonance between the motion in these layers is investigated. A region is discovered where a very sharp increase in Rayleigh number is observed. In addition to a linearized instability analysis, two global (unconditional) nonlinear stability thresholds are derived.

Global stability for thermal convection in a fluid overlying a 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

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.

On the Modeling of Shells in Multibody Dynamics

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems involving shell components. The proposed schemes are designed to meet four specific requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material non-linearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed approach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation.