메뉴 건너뛰기




Volumn 66, Issue 1, 2006, Pages 122-152

Convergence of the generalized volume averaging method on a convection-diffusion problem: A spectral perspective

Author keywords

Convection; Diffusion; Homogenization; Picard's successive approximation method; Spectral methods; Spectral theory; Sturm Liouville; Volume averaging

Indexed keywords

APPROXIMATION THEORY; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; HEAT CONVECTION; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

EID: 33644583620     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040610015     Document Type: Article
Times cited : (3)

References (41)
  • 1
    • 0002864183 scopus 로고
    • On the dispersion of a solute in a fluid flowing through a tube
    • R. ARTS, On the dispersion of a solute in a fluid flowing through a tube, Proc. Roy. Soc. Ser. A, 235 (1956), pp. 65-77.
    • (1956) Proc. Roy. Soc. Ser. A , vol.235 , pp. 65-77
    • Arts, R.1
  • 2
    • 0028332615 scopus 로고
    • Recent developments in modeling heat transfer in blood perfused tissues
    • H. ARKIN, L. X. Xu, AND K. R. HOLMES, Recent developments in modeling heat transfer in blood perfused tissues, IEEE Trans. Biomed. Engrg., 41 (1994), pp. 97-107.
    • (1994) IEEE Trans. Biomed. Engrg. , vol.41 , pp. 97-107
    • Arkin, H.1    Xu, L.X.2    Holmes, K.R.3
  • 3
    • 0022820567 scopus 로고
    • Heat transport mechanisms in vascular tissues: A model comparison
    • J. W. BAISH, P. S. AYYASWAMY, AND K. R. FOSTER, Heat transport mechanisms in vascular tissues: A model comparison, J. Biomech. Engrg., 108 (1986), pp. 324-331.
    • (1986) J. Biomech. Engrg. , vol.108 , pp. 324-331
    • Baish, J.W.1    Ayyaswamy, P.S.2    Foster, K.R.3
  • 4
    • 0029104166 scopus 로고
    • Dispersion of chemical solutes in chromatographs and reactors
    • V. BALAKOTAIAH AND H. C. CHANG, Dispersion of chemical solutes in chromatographs and reactors, Proc. Trans. Roy. Soc. Lond. Ser. A, 351 (1995), pp. 39-75.
    • (1995) Proc. Trans. Roy. Soc. Lond. Ser. A , vol.351 , pp. 39-75
    • Balakotaiah, V.1    Chang, H.C.2
  • 5
    • 0012247573 scopus 로고    scopus 로고
    • Hyperbolic homogenized models for thermal and solutal dispersion
    • V. BALAKOTAIAH AND H. C. CHANG, Hyperbolic homogenized models for thermal and solutal dispersion, SIAM J. Appl. Math., 63 (2003), pp. 1231-1258.
    • (2003) SIAM J. Appl. Math. , vol.63 , pp. 1231-1258
    • Balakotaiah, V.1    Chang, H.C.2
  • 7
    • 36849122625 scopus 로고
    • Laminar flow in channels with porous walls
    • A. BERMAN, Laminar flow in channels with porous walls, J. Appl. Phys., 24 (1953), pp. 1232-1235.
    • (1953) J. Appl. Phys. , vol.24 , pp. 1232-1235
    • Berman, A.1
  • 9
    • 0001781873 scopus 로고
    • Dispersion resulting from flow through spatially periodic porous media
    • H. BRENNER, Dispersion resulting from flow through spatially periodic porous media, Philos. Trans. Roy. Soc. London Ser. A, 297 (1980), pp. 81-133.
    • (1980) Philos. Trans. Roy. Soc. London Ser. A , vol.297 , pp. 81-133
    • Brenner, H.1
  • 10
    • 0030088180 scopus 로고    scopus 로고
    • Multiple-timescale analysis of taylor dispersion in converging and diverging flows
    • M. D. BRYDEN AND H. BRENNER, Multiple-timescale analysis of taylor dispersion in converging and diverging flows, J. Fluid Mech., 311 (1996), pp. 343-359.
    • (1996) J. Fluid Mech. , vol.311 , pp. 343-359
    • Bryden, M.D.1    Brenner, H.2
  • 11
    • 0037135384 scopus 로고    scopus 로고
    • Low-dimensional models for describing mixing effects in laminar flow turbulent reactors
    • S. CHAKRABORTY AND V. BALAKOTAIAH, Low-dimensional models for describing mixing effects in laminar flow turbulent reactors, Chem. Engrg. Sci., 57 (2002), pp. 2545-2564.
    • (2002) Chem. Engrg. Sci. , vol.57 , pp. 2545-2564
    • Chakraborty, S.1    Balakotaiah, V.2
  • 12
    • 0021641594 scopus 로고
    • On unifying the concepts of scale, instrumentation and stochastics in the development of multiple phase transport theory
    • J. H. CUSHMAN, On unifying the concepts of scale, instrumentation and stochastics in the development of multiple phase transport theory, Water Res. Resour., 20 (1984), pp. 1668-1676.
    • (1984) Water Res. Resour. , vol.20 , pp. 1668-1676
    • Cushman, J.H.1
  • 16
    • 27844567232 scopus 로고    scopus 로고
    • Heat and mass transfer in tubes: An analysis using the method of volume averaging
    • F. GOLFIER, M. QUINTARD, AND S. WHITAKER, Heat and mass transfer in tubes: An analysis using the method of volume averaging, J. Por. Media, 5 (2002), pp. 169-185.
    • (2002) J. Por. Media , vol.5 , pp. 169-185
    • Golfier, F.1    Quintard, M.2    Whitaker, S.3
  • 17
    • 0002640843 scopus 로고
    • On the thermal conductivity of liquids
    • L. GRAETZ, On the thermal conductivity of liquids, Ann. Phys. Chem., 18 (1883), pp. 79-94.
    • (1883) Ann. Phys. Chem. , vol.18 , pp. 79-94
    • Graetz, L.1
  • 18
    • 37249006592 scopus 로고
    • General conservation equations for multi-phase systems 1 averaging procedure
    • S. HASSANIZADEH AND W. GRAY, General conservation equations for multi-phase systems 1 averaging procedure, Adv. Water Resour., 2 (1979), pp. 131-144.
    • (1979) Adv. Water Resour. , vol.2 , pp. 131-144
    • Hassanizadeh, S.1    Gray, W.2
  • 20
    • 0000178441 scopus 로고
    • Les lois de transmission de la chaleur par convection
    • M. A. LÉVÉQUE, Les lois de transmission de la chaleur par convection, Annales des Mines, Paris, 13 (1928), pp. 201-409.
    • (1928) Annales des Mines, Paris , vol.13 , pp. 201-409
    • Lévéque, M.A.1
  • 21
    • 0019371056 scopus 로고
    • The effect of wall conductance on heat diffusion in duct flow
    • E. M. LUNGU AND H. K. MOFFAT, The effect of wall conductance on heat diffusion in duct flow, J. Engrg. Math., 16 (1982), pp. 121-136.
    • (1982) J. Engrg. Math. , vol.16 , pp. 121-136
    • Lungu, E.M.1    Moffat, H.K.2
  • 22
    • 0019929594 scopus 로고
    • On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media
    • C. M. MARLE, On macroscopic equations governing multiphase flow with diffusion and chemical reactions in porous media, Internat. J. Engrg. Sci., 20 (1982), pp. 643-662.
    • (1982) Internat. J. Engrg. Sci. , vol.20 , pp. 643-662
    • Marle, C.M.1
  • 23
    • 77956697899 scopus 로고    scopus 로고
    • Some applications of the homogenization theory
    • C. MEI, J. L. AURIAULT, AND C. NG, Some applications of the homogenization theory, Adv. Appl. Mech., 32 (1996), pp. 278-348.
    • (1996) Adv. Appl. Mech. , vol.32 , pp. 278-348
    • Mei, C.1    Auriault, J.L.2    Ng, C.3
  • 24
    • 0025567096 scopus 로고
    • A center manifold description of contaminant dispersion in channels with varying flow properties
    • G. N. MERCER AND A. J. ROBERTS, A center manifold description of contaminant dispersion in channels with varying flow properties, SIAM J. Appl. Math., 50 (1990), pp. 1547-1565.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1547-1565
    • Mercer, G.N.1    Roberts, A.J.2
  • 25
    • 0027628337 scopus 로고
    • Transport in ordered and disordered porous media: Volume-averaged equations, closure problems and comparison with experiment
    • M. QUINTARD AND S. WHITAKER, Transport in ordered and disordered porous media: Volume-averaged equations, closure problems and comparison with experiment, Chem. Engrg. Sci., 48 (1993), pp. 2537-2564.
    • (1993) Chem. Engrg. Sci. , vol.48 , pp. 2537-2564
    • Quintard, M.1    Whitaker, S.2
  • 26
    • 1242297110 scopus 로고    scopus 로고
    • A volume averaging theory and its sub-control-volume model for analyzing heat and fluid flow within complex heat transfer equipment
    • J. Taine, ed., Grenoble, Elsevier, Paris
    • A. NAKAYAMA, F. KUWAHARA, A. NAOKI, AND G. Xu, A volume averaging theory and its sub-control-volume model for analyzing heat and fluid flow within complex heat transfer equipment, in Proceedings of the 12th International Heat Transfer Conference, Vol. 2, J. Taine, ed., Grenoble, Elsevier, Paris, 2002, pp. 851-856.
    • (2002) Proceedings of the 12th International Heat Transfer Conference , vol.2 , pp. 851-856
    • Nakayama, A.1    Kuwahara, F.2    Naoki, A.3    Xu, G.4
  • 27
    • 0035909045 scopus 로고    scopus 로고
    • A two-energy equation model for conduction and convection in porous media
    • A. NAKAYAMA, F. KUWAHARA, M. SUGIYAMA, AND G. Xu, A two-energy equation model for conduction and convection in porous media, Int. J. Heat Mass Transfer, 44 (2001), pp. 4375-4379.
    • (2001) Int. J. Heat Mass Transfer , vol.44 , pp. 4375-4379
    • Nakayama, A.1    Kuwahara, F.2    Sugiyama, M.3    Xu, G.4
  • 28
    • 0031854729 scopus 로고    scopus 로고
    • Invited editorial on "Pennes' 1948 paper revisited
    • D. A. NELSON, Invited editorial on "Pennes' 1948 paper revisited, " J. Appl. Physiol., 85 (1998), pp. 2-3.
    • (1998) J. Appl. Physiol. , vol.85 , pp. 2-3
    • Nelson, D.A.1
  • 29
    • 0035067632 scopus 로고    scopus 로고
    • Macroscopic turbulence modeling for incompressible flow through undeformable porous media
    • M. PEDRAS AND M. D. LEMOS, Macroscopic turbulence modeling for incompressible flow through undeformable porous media, Int. J. Heat Mass Transfer, 44 (2001), pp. 1081-1093.
    • (2001) Int. J. Heat Mass Transfer , vol.44 , pp. 1081-1093
    • Pedras, M.1    Lemos, M.D.2
  • 30
    • 84888360034 scopus 로고
    • Analysis of tissue and arterial blood temperatures in the resting human forearm
    • H. H. PENNES, Analysis of tissue and arterial blood temperatures in the resting human forearm, J. Appl. Physiol., 1 (1948), pp. 93-122.
    • (1948) J. Appl. Physiol. , vol.1 , pp. 93-122
    • Pennes, H.H.1
  • 31
    • 0029415601 scopus 로고
    • Time-dependent transport by convection and diffusion with exchange between two phases
    • C. G. PHILLIPS, S. R. KAYE, AND C. D. ROBINSON, Time-dependent transport by convection and diffusion with exchange between two phases, J. Fluid Mech., 297 (1995), pp. 373-401.
    • (1995) J. Fluid Mech. , vol.297 , pp. 373-401
    • Phillips, C.G.1    Kaye, S.R.2    Robinson, C.D.3
  • 32
    • 0028669433 scopus 로고
    • Convection, dispersion, and interfacial transport of contaminants: Homogeneous porous media
    • M. QUINTARD AND S. WHITAKER, Convection, dispersion, and interfacial transport of contaminants: Homogeneous porous media, Adv. Water Resour., 17 (1994), pp. 221-239.
    • (1994) Adv. Water Resour. , vol.17 , pp. 221-239
    • Quintard, M.1    Whitaker, S.2
  • 33
    • 0000144318 scopus 로고
    • The utility of an invariant manifold description of the evolution of a dynamical system
    • A. J. ROBERTS, The utility of an invariant manifold description of the evolution of a dynamical system, SIAM J. Appl. Math., 20 (1989), pp. 1447-1458.
    • (1989) SIAM J. Appl. Math. , vol.20 , pp. 1447-1458
    • Roberts, A.J.1
  • 34
    • 0031257015 scopus 로고    scopus 로고
    • Taylor dispersion in curved channels
    • S. ROSENCRANS, Taylor dispersion in curved channels, SIAM J. Appl. Math., 57 (1997), pp. 1216-1241.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1216-1241
    • Rosencrans, S.1
  • 36
    • 0002197945 scopus 로고
    • Nonhomogeneous media and vibration theory
    • Springer, New York
    • E. SANCHEZ-PALENCIA, Nonhomogeneous Media and Vibration Theory, Lecture Notes in Phys. 127, Springer, New York, 1980.
    • (1980) Lecture Notes in Phys. , vol.127
    • Sanchez-Palencia, E.1
  • 37
    • 0000795099 scopus 로고
    • Laminar flow forced convection in ducts
    • R. K. SHAH AND A. L. LONDON, Laminar flow forced convection in ducts, Adv. Heat Trans., Suppl. 1 (1978).
    • (1978) Adv. Heat Trans. , Issue.1 SUPPL.
    • Shah, R.K.1    London, A.L.2
  • 38
    • 0003381083 scopus 로고
    • Dispersion of solute matter in solvent flowing slowly through a tube
    • G. I. TAYLOR, Dispersion of solute matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Ser. A., 219 (1953), pp. 186-203.
    • (1953) Proc. Roy. Soc. Ser. A. , vol.219 , pp. 186-203
    • Taylor, G.I.1
  • 40
    • 36449005018 scopus 로고
    • Shear dispersion
    • W. R. YOUNG AND S. JONES, Shear dispersion, Phys. Fluid, 3 (1991), pp. 1087-1101.
    • (1991) Phys. Fluid , vol.3 , pp. 1087-1101
    • Young, W.R.1    Jones, S.2
  • 41
    • 0026255482 scopus 로고
    • Thermal dispersion in thick-walled tubes as a model of porous media
    • Z.-G. YUAN, W. H. SOMERTON, AND K. S. UDELL, Thermal dispersion in thick-walled tubes as a model of porous media, Int. J. Heat Mass Transfer, 34 (1991), pp. 2715-2726.
    • (1991) Int. J. Heat Mass Transfer , vol.34 , pp. 2715-2726
    • Yuan, Z.-G.1    Somerton, W.H.2    Udell, K.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.