zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Numerical methods for multiscale transport equations and application to two-phase porous media flow. (English) Zbl 1089.76049
Summary: We discuss numerical methods for linear and nonlinear transport equations with multiscale velocity fields. These methods are themselves multiscaled in nature in the sense that they use macro and micro grids and multiscale test functions. We demonstrate the efficiency of these methods and apply them to two-phase flows in heterogeneous porous media.

MSC:
76M50Homogenization (fluid mechanics)
76S05Flows in porous media; filtration; seepage
76T10Liquid-gas two-phase flows, bubbly flows
WorldCat.org
Full Text: DOI
References:
[1] Allaire, G.: Homogenization and two-scale convergence. SIAM J. Math. anal. 23, 1482-1518 (1992) · Zbl 0770.35005
[2] Chorin, A. J.: Numerical solution of the Navier-Stokes equations. Math. comput. 22, 745-762 (1968) · Zbl 0198.50103
[3] Christie, M. A.: Upscaling for reservoir simulation. J. petrol. Technol. 48, 1004-1010 (1996)
[4] E, W.: Homogenization of linear and nonlinear transport equations. Commun. pure appl. Math. 45, 301-326 (1992) · Zbl 0794.35014
[5] E., W.; Engquist, B.: The heterogeneous multi-scale methods. Commun. math. Sci. 1, 87-120 (2003)
[6] W. E, B. Engquist, The heterogeneous multi-scale method for homogenization problems, Multiscale Model. Simulat., submitted. Available at <http://www.math.princeton.edu/multiscale/>.
[7] E., W.; Ming, P. B.; Zhang, P. W.: Analysis of the heterogeneous multiscale method for elliptic homogenization problems. J. AMS 18, 121-156 (2005) · Zbl 1060.65118
[8] Efendiev, Y.; Durlofsky, L. J.: Numerical modeling of subgrid heterogeneity in two phase flow simulations. Water resour. Res. 38, 1128-1138 (2002)
[9] Efendiev, Y.; Durlofsky, L. J.: A generalized convection-diffusion model for subgrid transport in porous media. Multiscale model. Simulat. 1, 504-526 (2003) · Zbl 1191.76098
[10] Engquist, B.: Computation of oscillatory solutions to hyperbolic differential equations. Springer lect. Notes math. 1270, 10-22 (1987)
[11] Evans, L. C.: The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. roy. Soc. Edinburgh 111A, 359-375 (1989) · Zbl 0679.35001
[12] Langlo, P.; Espedal, M. S.: Macrodispersion for two-phase, immisible flow in porous media. Adv. water resour. 17, 297-316 (1994)
[13] Matache, A. -M.; Schwab, C.: Two-scale FEM for homogenization problems. Math. model. Numer. anal. 36, 537-572 (2002) · Zbl 1070.65572
[14] P.B. Ming, X. Yue, Numerical methods for multiscale elliptic problems. Preprint 2003. Available at <http://www.math.princeton.edu/multiscale/>. · Zbl 1092.65102
[15] Nguetseng, G.: A general convergence result for a functional related to the theory of homogenization. SIAM J. Math. anal. 20, 608-623 (1989) · Zbl 0688.35007
[16] Oden, J. T.; Vemaganti, K. S.: Estimation of local modelling error and global-oriented adaptive modeling of heterogeneous materials: error estimates and adaptive algorithms. J. comput. Phys. 164, 22-47 (2000) · Zbl 0992.74072
[17] Schwab, C.; Matache, A. -M.: Generalized FEM for homogenization problems. Lecture notes in computational science and engineering (2002)
[18] L. Tartar, Solutions oscillantes des quations de Carleman, Goulaouic-Meyer-Schwartz Seminar, 1980-1981, Exp. No. XII, 15 pp., cole Polytech., Palaiseau, 1981.
[19] Wallstrom, T. C.; Hou, S.; Christie, M. A.; Durlofsky, L. J.; Sharp, D. H.: Accurate scale up of two phase flow using renormalization and nonuniform coarsening. Comput. geosci. 3, 69-87 (1999) · Zbl 0963.76558
[20] Zhang, D.; Li, L.; Tchelepi, H. A.: Stochastic formulation for uncertainty analysis of two-phase flow in heterogeneous reservoirs. Spe j. 5, 60-70 (2000)