scholarly journals Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

2021 ◽  
Author(s):  
Florinda Capone ◽  
Roberta De Luca ◽  
Giuliana Massa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Nonlinear Stability ◽  
Linear Instability ◽  
Combined Effects ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Linear And Nonlinear ◽  
The Stability

AbstractThermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the $$L^2$$ L 2 -norm is obtained.

scholarly journals Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

2021 ◽  
Author(s):  
Florinda Capone ◽  
Maurizio Gentile ◽  
Jacopo A. Gianfrani
Keyword(s):  
Porous Layer ◽  
Nonlinear Stability ◽  
Steady Motion ◽  
Vertical Axis ◽  
Linear Instability ◽  
List Type ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Anisotropic Porous Medium ◽  
Necessary And Sufficient

Abstract The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction.

A nonlinear stability analysis in a double-diffusive magnetized ferrofluid with magnetic-field-dependent viscosity saturating a porous medium

2009 ◽  
Vol 87 (6) ◽  
pp. 659-673 ◽  
Author(s):  
Sunil ◽  
Amit Mahajan
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nonlinear Stability ◽  
Stability Result ◽  
Darcy Number ◽  
Linear Instability ◽  
Nonlinear Stability Analysis ◽  
Field Dependent ◽  
Magnetized Ferrofluid ◽  
Mfd Viscosity

A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic-field-dependent (MFD) viscosity saturating a porous medium, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic-body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that, in case of a non-ferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of the magnetic parameter, M3; solute gradient, Sf; Darcy number, Da; and MFD viscosity parameter, δ; on the subcritical instability region has also been analyzed.

A Nonlinear Stability Analysis for Difference Equations Using Semi-Implicit Mobility

1977 ◽  
Vol 17 (01) ◽  
pp. 79-91 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Finite Difference ◽  
Nonlinear Stability ◽  
Difference Equations ◽  
Nonlinear Stability Analysis ◽  
Time Step ◽  
Two Phase ◽  
Linearized Stability ◽  
The Stability

Abstract The usual linearized stability analysis of the finite-difference solution for two-phase flow in porous media is not delicate enough to distinguish porous media is not delicate enough to distinguish between the stability of equations using semi-implicit mobility and those using completely implicit mobility. A nonlinear stability analysis is developed and applied to finite-difference equations using an upstream mobility that is explicit, completely implicit, or semi-implicit. The nonlinear analysis yields a sufficient (though not necessary) condition for stability. The results for explicit and completely implicit mobilities agree with those obtained by the standard linearized analysis; in particular, use of completely implicit mobility particular, use of completely implicit mobility results in unconditional stability. For semi-implicit mobility, the analysis shows a mild restriction that generally will not be violated in practical reservoir simulations. Some numerical results that support the theoretical conclusions are presented. Introduction Early finite-difference, Multiphase reservoir simulators using explicit mobility were found to require exceedingly small time steps to solve certain types of problems, particularly coning and gas percolation. Both these problems are characterized percolation. Both these problems are characterized by regions of high flow velocity. Coats developed an ad hoc technique for dealing with gas percolation, but a more general and highly successful approach for dealing with high-velocity problems has been the use of implicit mobility. Blair and Weinaug developed a simulator using completely implicit mobility that greatly relaxed the time-step restriction. Their simulator involved iterative solution of nonlinear difference equations, which considerably increased the computational work per time step. Three more recent papers introduced the use of semi-implicit mobility, which proved to be greatly superior to the fully implicit method with respect to computational effort, ease of use, and maximum permissible time-step size. As a result, semi-implicit mobility has achieved wide use throughout the industry. However, this success has been pragmatic, with little or no theoretical work to justify its use. In this paper, we attempt to place the use of semi-implicit mobility on a sounder theoretical foundation by examining the stability of semi-implicit difference equations. The usual linearized stability analysis is not delicate enough to distinguish between the semi-implicit and completely implicit difference equation. A nonlinear stability analysis is developed that permits the detection of some differences between the stability of difference equations using implicit mobility and those using semi-implicit mobility. DIFFERENTIAL EQUATIONS The ideas to be developed may be adequately presented using the following simplified system: presented using the following simplified system: horizontal, one-dimensional, two-phase, incompressible flow in homogeneous porous media, with zero capillary pressure. A variable cross-section is included so that a variable flow velocity may be considered. The basic differential equations are (1) (2) The total volumetric flow rate is given by (3) Addition of Eqs. 1 and 2 yields =O SPEJ P. 79

scholarly journals LINEAR AND NONLINEAR INSTABILITY OF FLOW IN CHANNEL OCCUPIED POROUS MEDIA

2017 ◽  
Vol 39 (3) ◽  
pp. 40-46
Author(s):  
A.A. Avramenko ◽  
N.P. Dmitrenko ◽  
Y.Y. Kovetskaya
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Kinematic Viscosity ◽  
Hydrodynamic Instability ◽  
Linear Instability ◽  
Nonlinear Instability ◽  
Linear Perturbations ◽  
Linear And Nonlinear

The paper investigates linear and nonlinear hydrodynamic instability of flow in channel ocuped porous medium. The effects of linear instability are considered using the method of linear perturbations. The nonlinear instability of the flow is considered using the renormalized expression for the coefficient of the kinematic viscosity.

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.

A nonlinear-stability analysis of second-order fluid in porous medium in presence of magnetic field

Analysis ◽  
2005 ◽  
Vol 25 (2) ◽  
Author(s):  
Lanxi Xu
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nonlinear Stability ◽  
Stability Boundary ◽  
Second Order ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Lyapunov’S Second Method ◽  
Chandrasekhar Number

AbstractNonlinear stability of the motionless state of the second-order fluid in porous medium in presence of magnetic field is studied by the Lyapunov’s second method. Through defining a Lyapunov function we will prove the inhibiting effect of the magnetic field on the onset of convection. If the Chandrasekhar number is below a computable constant depending on system parameters, we even prove the coincidence of linear and nonlinear stability boundary. Moreover, the medium permeability has a destabilizing effect.

scholarly journals Anisotropic bidispersive convection

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190206 ◽  
Author(s):  
B. Straughan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Rayleigh Number ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Linear Instability ◽  
Solid Skeleton ◽  
Nonlinear Stability Analysis ◽  
Cell Structures ◽  
Linear Instability Analysis

This paper investigates thermal convection in an anisotropic bidisperse porous medium. A bidisperse porous medium is one which possesses the usual pores, but in addition, there are cracks or fissures in the solid skeleton and these give rise to a second porosity known as micro porosity. The novelty of this paper is that the macro permeability and the micro permeability are each diagonal tensors but the three components in the vertical and in the horizontal directions may be distinct in both the macro and micro phases. Thus, there are six independent permeability coefficients. A linear instability analysis is presented and a fully nonlinear stability analysis is inferred. Several Rayleigh number and wavenumber calculations are presented and it is found that novel cell structures are predicted which are not present in the single porosity case.

Linear and nonlinear stability analysis of binary Maxwell fluid convection in a porous medium

2011 ◽  
Vol 48 (5) ◽  
pp. 863-874 ◽  
Author(s):  
Mahesha Narayana ◽  
P. Sibanda ◽  
S. S. Motsa ◽  
P. A. Lakshmi-Narayana
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Nonlinear Stability ◽  
Maxwell Fluid ◽  
Nonlinear Stability Analysis ◽  
Fluid Convection ◽  
Linear And Nonlinear

A Direct Comparison between the Negative and Positive Effects of Throughflow on the Thermal Convection in an Anisotropy and Symmetry Porous Medium

2015 ◽  
Vol 70 (5) ◽  
pp. 383-394 ◽  
Author(s):  
Akil J. Harfash ◽  
Ahmed K. Alshara
Keyword(s):  
Porous Medium ◽  
Three Dimensional ◽  
Convective Motion ◽  
Linear Instability ◽  
Nonlinear Stability Analysis ◽  
Positive Effects ◽  
Anisotropic Porous Medium ◽  
Regions Of Stability ◽  
Linear And Nonlinear ◽  
Dimensional Simulation

AbstractThe linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium are tested. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account. Then, the accuracy of the linear instability thresholds are tested using a three dimensional simulation. It is shown that the strong stabilising effect of gravity field. Moreover, the results support the assertion that the linear theory, in general, is accurate in predicting the onset of convective motion, and thus, regions of stability.

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