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A family of multi-point flux approximation schemes for general element types in two and three dimensions with convergence performance.(English)Zbl 1253.76125

Summary: A family of flux-continuous, locally conservative, control-volume-distributed multi-point flux approximation (CVD-MPFA) schemes has been developed for solving the general geometry-permeability tensor pressure equation on structured and unstructured grids. These schemes are applicable to the full-tensor pressure equation with generally discontinuous coefficients and remove the \(O(1)\) errors introduced by standard reservoir simulation schemes when applied to full-tensor flow approximation. The family of flux-continuous schemes is characterized by a quadrature parameterization. Improved numerical convergence for the family of CVD-MPFA schemes using the quadrature parameterization has been observed for structured and unstructured grids in two dimensions.
The CVD-MPFA family cell-vertex formulation is extended to classical general element types in 3-D including prisms, pyramids, hexahedra and tetrahedra. A numerical convergence study of the CVD-MPFA schemes on general unstructured grids comprising of triangular elements in 2-D and prismatic, pyramidal, hexahedral and tetrahedral shape elements in 3-D is presented.

MSC:

76S05 Flows in porous media; filtration; seepage

Cite

References:

[1]Edwards, Finite volume discretization with imposed flux continuity for the general tensor pressure equation, Computational Geosciences 2 pp 259– (1998) ·Zbl 0945.76049 ·doi:10.1023/A:1011510505406
[2]Edwards, Unstructured, control-volume distributed, full-tensor finite volume schemes with flow based grids, Computational Geosciences 6 pp 433– (2002) ·Zbl 1036.76034 ·doi:10.1023/A:1021243231313
[3]Pal, Convergence study of a family of flux-continuous, finite-volume schemes for the general tensor pressure equation, International Journal of Numerical Methods in Fluids 51 pp 1177– (2006) ·Zbl 1108.76046 ·doi:10.1002/fld.1211
[4]Pal M Families of control-volume distributed multi-point flux approximation finite volume schemes for the porous media pressure equation on structured and unstructured grids 2007
[5]Pal M Edwards MG Quasi-monotonic Darcy-flux approximation for general 3-D grids of any element type paper SPE 106486 proc: SPE Reservoir Simulation Symposium 2007
[6]Eigestad, On the convergence of the multi-point flux approximation O-method: numerical experiments for the discontinuous permeability, Numerical Methods in Partial Differential Equations 21 (6) pp 1079– (2005) ·Zbl 1089.76037 ·doi:10.1002/num.20079
[7]Aavatsmark, IMA Volume Series, in: Compatible Spatial Discretization pp 1– (2006) ·doi:10.1007/0-387-38034-5_1
[8]Lee, A finite-volume method with hexahedral multiblock grid for modeling flow in porous media, Computational Geosciences 6 (3-4) pp 353– (2002) ·Zbl 1094.76541 ·doi:10.1023/A:1021287013566
[9]Pal, Non-linear flux-splitting schemes with imposed discrete maximum principle for elliptic equations with highly anisotropic coefficients, International Journal for Numerical Methods in Fluids 66 pp 299– (2011) ·Zbl 1301.86002 ·doi:10.1002/fld.2258
[10]Pal M Edwards MG Family of flux-continuous finite-volume schemes with improved monotonicity Proceedings of the 10th European Conference on the Mathematics of Oil Recovery 4 7 2006
[11]Edwards, Double-families of quasi-positive Darcy-flux approximations with highly anisotropic tensors on structured and unstructured grids, Journal of Computational Physics 229 pp 594– (2010) ·Zbl 1253.76091 ·doi:10.1016/j.jcp.2009.09.037
[12]Edwards, A quasi-positive family of continuous Darcy-flux finite volume schemes with full pressure support, Journal of Computational Physics 227 pp 9333– (2008) ·Zbl 1231.76178 ·doi:10.1016/j.jcp.2008.05.028
[13]Mlacnik, Unstructured grid optimization for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients, Journal of Computational Physics 216 (1) pp 337– (2006) ·Zbl 1173.76413 ·doi:10.1016/j.jcp.2005.12.007
[14]Mallison, A compact multipoint flux approximation method with improved robustness, Numerical Methods for Partial Differential Equations 24 pp 1329– (2008) ·Zbl 1230.65114 ·doi:10.1002/num.20320
[15]LePotier, Schema volume finis pour des operator operateurs de diffusion fortement anisotropes sur des maillages de triangle nonstructures, Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 340 (12) pp 921– (2005) ·Zbl 1076.76049 ·doi:10.1016/j.crma.2005.05.011
[16]Edwards, Quasi M-matrix multi-family continuous Darcy-flux approximations with full pressure support on structured and unstructured grids in 3-D, SIAM Journal on Scientific Computing 33 (2) pp 455– (2011) ·Zbl 1368.74070 ·doi:10.1137/080745390
[17]Lipnikov, Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes, Journal of Computational Physics 227 pp 492– (2008) ·Zbl 1130.65113 ·doi:10.1016/j.jcp.2007.08.008
[18]Friis, A family of MPFA finite volume schemes with full pressure support for the general tensor pressure equation on cell-centred triangular grids, Journal of Computational Physics 230 (1) pp 205– (2011) ·Zbl 1427.76161 ·doi:10.1016/j.jcp.2010.09.012
[19]Edwards MG Split full tensor discretization operators for structured and unstructured grids in three dimensions SPE 66358 Proc: SPE Reservoir Simulation Symposium 11 14 2001
[20]Verma S Flexible grids for reservoir simulation 1996
[21]Edwards, Higher-resolution hyperbolic-coupled-elliptic flux-continuous CVD schemes on structured and unstructured grids in 3-D, International Journal for Numerical Methods in Fluids 51 (9-10) pp 1079– (2006) ·Zbl 1158.76364 ·doi:10.1002/fld.1289
[22]Edwards, Higher-resolution hyperbolic-coupled-elliptic flux-continuous CVD schemes on structured and unstructured grids in 2-D, International Journal of Numerical Methods in Fluids 51 pp 1059– (2006) ·Zbl 1158.76363 ·doi:10.1002/fld.1245
[23]Aavatsmark, Numerical convergence of MPFA-O and U methods on general quadrilateral grids, International Journal of Numerical Methods in Fluids 51 pp 939– (2006) ·Zbl 1158.65331 ·doi:10.1002/fld.1096
[24]Friis, Symmetric positive definite flux-continuous full-tensor finite-volume schemes on unstructured cell centered triangular grids, SIAM Journal on Scientific Computing 31 pp 1192– (2008) ·Zbl 1190.65163 ·doi:10.1137/070692182
[25]Aavatsmark, Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: derivation of the methods, SIAM Journal on Scientific Computing 19 pp 1700– (1998) ·Zbl 0951.65080 ·doi:10.1137/S1064827595293582
[26]Edwards, Positive definite q-families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element method, International Journal for Numerical Methods in Fluids 57 pp 355– (2008) ·Zbl 1236.76035 ·doi:10.1002/fld.1586
[27]Edwards, M-matrix flux splitting for general full tensor discretization operator on structured and unstructured grids, Journal of Computational Physics 160 pp 1– (2000) ·Zbl 0983.76055 ·doi:10.1006/jcph.2000.6418
[28]Wheeler, A multipoint flux mixed finite element method, SIAM 44 pp 2082– (2006) ·Zbl 1121.76040
[29]Klausen, Convergence of multipoint flux approximation on quadrilateral grids, Numerical Methods for Partial Differential Equations 22 pp 1438– (2006) ·Zbl 1106.76043 ·doi:10.1002/num.20158
[30]Abrogast T Keenan PT Wheeler MF Yotov I Logically rectangular mixed methods for Darcy flow on general geometry Proceedings of the 13th SPE RSS 1995 51 59
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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