A stable explicit fractional step procedure for the solution of heat and fluid flow through interfaces between saturated porous media and free fluids in presence of high source terms

In this paper, porous medium-free fluid interface problems in the presence of high source terms are studied for the first time by using a stable, accurate and efficient Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm. The interest in the AC-CBS scheme has increased, as its matrix-inversion free procedure offers the possibility of an easy and efficient parallelization. The present algorithm, recently introduced for the solution of porous media flows, presented some difficulties in solving complex interface problems. In this paper, the AC-CBS scheme has been specifically developed to overcome such difficulties and produce an accurate, stable, and efficient solution for the generalized porous medium flow equations for forced, free, and mixed convection through interfaces. In order to obtain the present results, a stability analysis for the AC-CBS scheme for the solution of problems with high source terms is carried out for the first time. The efficiency and the accuracy of the AC-CBS algorithm are verified through comparison with analytical, numerical, and experimental data available in the literature. The authors consider three different types of interface benchmark problems: (i) forced convection in a horizontal channel; (ii) mixed convection in a vertical channel; and (iii) natural convection in a vertically divided cavity. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  M. Velarde,et al.  Momentum transport at a fluid–porous interface , 2003 .

[2]  E. Kim,et al.  A mixed galerkin method for computing the flow between eccentric rotating cylinders , 1998 .

[3]  Fotis Sotiropoulos,et al.  Assessment of artificial dissipation models for three- dimensional incompressible flow solutions , 1997 .

[4]  Benoît Goyeau,et al.  Double Diffusive Natural Convection in a Composite Fluid-Porous Layer , 1998 .

[5]  P. Nithiarasu.  An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows , 2003 .

[6]  Tamer M. Wasfy,et al.  Parallel finite element computation of unsteady incompressible flows , 1998 .

[7]  Arnaud G. Malan,et al.  An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part I. Theory and implementation , 2002 .

[8]  R. Viskanta,et al.  Natural convection in vertical enclosures containing simultaneously fluid and porous layers , 1988, Journal of Fluid Mechanics.

[9]  Andrey V. Kuznetsov,et al.  Influence of the stress jump condition at the porous-medium/clear-fluid interface on a flow at a porous wall , 1997 .

[10]  Wayne A. Smith,et al.  Preconditioning Applied to Variable and Constant Density Flows , 1995 .

[11]  Andrey V. Kuznetsov,et al.  Analytical Study of Fluid Flow and Heat Transfer during Forced Convection in a Composite Channel Partly Filled with a Brinkman–Forchheimer Porous Medium , 1998 .

[12]  Hamid Hadim,et al.  Handbook of Porous Media, Second Edition , 2000 .

[13]  D. Assanis,et al.  Comparison of Pressure-Based and Artificial Compressibility Methods for Solving 3D Steady Incompressible Viscous Flows , 1996 .

[14]  P. Cheng,et al.  Thermal dispersion in a porous medium , 1990 .

[15]  J. Caltagirone,et al.  Natural convection in a square cavity with thin porous layers on its vertical walls , 1991 .

[16]  Jean-François Mercier,et al.  Heat Transfer Associated to Natural Convection Flow in a Partly Porous Cavity , 2002 .

[17]  O. C. Zienkiewicz,et al.  On the stable finite element procedures for dynamic problems of saturated porous media , 2004 .

[18]  Peng Yu,et al.  A numerical method for forced convection in porous and homogeneous fluid domains coupled at interface by stress jump , 2008 .

[19]  Mehrdad T. Manzari,et al.  An explicit finite element algorithm for convection heat transfer problems , 1999 .

[20]  T. W. Tong,et al.  Natural convection in enclosures containing an insulation with a permeable fluid-porous interface , 1988 .

[21]  A. Carotenuto,et al.  Microscopic and macroscopic approach for natural convection in enclosures filled with fluid saturated porous medium , 2003 .

[22]  Arnaud G. Malan,et al.  An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part II. Application , 2002 .

[23]  Ann L Gaitonde,et al.  A dual-time method for two-dimensional unsteady incompressible flow calculations , 1998 .

[24]  S. Whitaker.  Diffusion and dispersion in porous media , 1967 .

[25]  Eli Turkel,et al.  Review of preconditioning methods for fluid dynamics , 1993 .

[26]  Yong Zhao,et al.  A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids , 2000 .

[27]  Wen-Jeng Chang,et al.  Mixed convection in a vertical parallel-plate channel partially filled with porous media of high permeability , 1996 .

[28]  C. Sung,et al.  Explicit Runge-Kutta method for three-dimensional internal incompressible flows , 1992 .

[29]  Kankanhalli N. Seetharamu,et al.  DOUBLE-DIFFUSIVE NATURAL CONVECTION IN AN ENCLOSURE FILLED WITH FLUID-SATURATED POROUS MEDIUM: A GENERALIZED NON-DARCY APPROACH , 1996 .

[30]  Kambiz Vafai,et al.  Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer , 2001 .

[31]  E. Turkel,et al.  Preconditioned methods for solving the incompressible low speed compressible equations , 1987 .

[32]  C. L. Merkle,et al.  The application of preconditioning in viscous flows , 1993 .

[33]  O. C. Zienkiewicz,et al.  Natural convection in porous medium‐fluid interface problems ‐ A finite element analysis by using the CBS procedure , 2001 .

[34]  K. N. Seetharamu,et al.  Fundamentals of the Finite Element Method for Heat and Fluid Flow , 2004 .

[35]  J. Peraire,et al.  Unstructured grid finite-element methods for fluid mechanics , 1998 .

[36]  Kambiz Vafai,et al.  between a porous medium and a fluid layer---an exact solution , 1990 .

[37]  C. L. Tien,et al.  Boundary and inertia effects on flow and heat transfer in porous media , 1981 .

[38]  Fausto Arpino,et al.  Artificial Compressibility-Based CBS Scheme for the Solution of the Generalized Porous Medium Model , 2009 .

[39]  Dimos Poulikakos,et al.  Forced convection in a duct partially filled with a porous material , 1987 .

[40]  C. Hickox,et al.  Simulation of Coupled Viscous and Porous Flow Problems , 1996 .

[41]  R. Viskanta,et al.  Natural Convection Flow and Heat Transfer Between a Fluid Layer and a Porous Layer Inside a Rectangular Enclosure , 1987 .