Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul. 1 (2003) 260-303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on the velocity field.
Mots-clés : numerical homogenization, well-driven flow, heterogeneous porous medium, multiscale finite element
@article{M2AN_2007__41_5_945_0, author = {Jiang, Meiqun and Yue, Xingye}, title = {Numerical homogenization of well singularities in the flow transport through heterogeneous porous media : fully discrete scheme}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {945--957}, publisher = {EDP-Sciences}, volume = {41}, number = {5}, year = {2007}, doi = {10.1051/m2an:2007044}, mrnumber = {2363890}, zbl = {1140.76437}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2007044/} }
TY - JOUR AU - Jiang, Meiqun AU - Yue, Xingye TI - Numerical homogenization of well singularities in the flow transport through heterogeneous porous media : fully discrete scheme JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 945 EP - 957 VL - 41 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2007044/ DO - 10.1051/m2an:2007044 LA - en ID - M2AN_2007__41_5_945_0 ER -
%0 Journal Article %A Jiang, Meiqun %A Yue, Xingye %T Numerical homogenization of well singularities in the flow transport through heterogeneous porous media : fully discrete scheme %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 945-957 %V 41 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2007044/ %R 10.1051/m2an:2007044 %G en %F M2AN_2007__41_5_945_0
Jiang, Meiqun; Yue, Xingye. Numerical homogenization of well singularities in the flow transport through heterogeneous porous media : fully discrete scheme. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 5, pp. 945-957. doi : 10.1051/m2an:2007044. http://www.numdam.org/articles/10.1051/m2an:2007044/
[1] Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal. 31 (1994) 945-981. | Zbl
, and ,[2] A mixed multiscale finite element method for elliptic problem with oscillating coefficients. Math. Comp. 72 (2003) 541-576. | Zbl
and ,[3] Numerical homogenization of well singularities in the flow transport through heterogeneous porous media. Multiscale Model. Simul. 1 (2003) 260-303. | Zbl
and ,[4] Numerical-calculation of equivalent grid block permeability tensors for heterogeous porous media. Water Resour. Res. 27 (1991) 699-708.
,[5] Scale up in the Near-Well Region, SPE 51940, in Proceedings of the 15th SPE Symposium on Reservoir Simulation, Houston, February (1999) 14-17.
, and ,[6] W. E and B. Engquist, The heterogeneous multiscale methods. Commun. Math. Sci. 1 (2003) 87-132. | Zbl
[7] The convergence of non-conforming multiscale finite element methods. SIAM J. Numer. Anal. 37 (2000) 888-910. | Zbl
, and ,[8] A direct approach to numerical homogenization in finite elasticity. Netw. Heterog. Media 1 (2006) 109-141.
,[9] A analytical framework for the numerical homogenization of monotone elliptic operators and quasiconvex energies. Multiscale Model. Simul. 5 (2006) 996-1043. | Zbl
,[10] A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169-189. | Zbl
and ,[11] Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients. Math. Comp. 68 (1999) 913-943. | Zbl
, and ,[12] Homogenization of Differential Operators and Integral Functionals. Springer, Berlin (1994). | MR | Zbl
, and ,[13] Scale up in the vicinity of horizontal wells, in Proceedings of the 20th Annual International Energy Agency Workshop and Symposium, Paris, September (1999) 22-24.
and ,[14] Generalized -FEM in homogenization. Numer. Math. 86 (2000) 319-375. | Zbl
, and ,[15] Interpretation of well-block pressures in numerical reservoir simulations. Soc. Pet. Eng. J. 18 (1978) 183-194.
,[16] Upscaling hydraulic conductivities in heterogeneous media: an overview. J. Hydrol. 183 (1996) ix-xxxii.
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