##
**On the convergence of the multi-point flux approximation O-method: numerical experiments for discontinuous permeability.**
*(English)*
Zbl 1089.76037

Summary: This article presents numerical convergence results for the multi-point flux approximation O-method applied to the pressure equation in two dimensions. The discretization is made directly in physical space, and the investigated cases are simulated on structured, but generally skew grids. Skew grids need to be used to correctly represent the physics of the underlying flow problems. Special emphasis is made on cases which impose singularities in the velocity field. Such cases frequently arise in the description of subsurface flow. Analytical tools may not be applicable to fully answer the question of convergence for such cases; in particular not for the physical space discretization.

### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

76T30 | Three or more component flows |

PDF
BibTeX
XML
Cite

\textit{G. T. Eigestad} and \textit{R. A. Klausen}, Numer. Methods Partial Differ. Equations 21, No. 6, 1079--1098 (2005; Zbl 1089.76037)

Full Text:
DOI

### References:

[1] | and , Convergence of multi-point flux approximations on quadrilateral grids. Submitted. |

[2] | Aavatsmark, J Comput Phys 127 pp 2– (1996) |

[3] | , and , Control-volume discretization methods for 3D quadrilateral grids in inhomogeneous, anisotropic reservoirs, SPE 38000, 1997. |

[4] | Aavatsmark, SIAM J Sci Comput 19 pp 1700– (1998) |

[5] | Aavatsmark, SIAM J Sci Comput 19 pp 1717– (1998) |

[6] | Aavatsmark, Computat Geosci 5 pp 1– (2001) |

[7] | Aavatsmark, Comput Geosci 6 pp 405– (2002) |

[8] | Edwards, Comput Geosci 2 pp 259– (1998) |

[9] | Edwards, J Comput Phys 160 pp 1– (2000) |

[10] | Edwards, Comput Geosci 6 pp 433– (2002) |

[11] | and , A control volume scheme for flexible grids in reservoir simulation, SPE 37999, 1997. |

[12] | , and , Discretization on non-orthogonal curvilinear grids for multi-phase flow, Proc ECMOR IV, Røros, Norway, 1994. |

[13] | and , A flux continuous scheme for the full tensor pressure equation, Proc ECMOR IV, Røros, Norway, 1994. |

[14] | Lee, Comput Geosci 6 pp 353– (2002) |

[15] | , and , Implementation of a flux-continuous finite difference method for stratigraphic, Hexahedron Grids, SPE 51901, 1999. |

[16] | Klausen, Comput Geosci. |

[17] | Arbogast, SIAM J Numer Anal 34 pp 828– (1997) |

[18] | Jeannin, Oil Gas Sci Technol Rev IFP 55 (2000) |

[19] | Cai, Computat Geosci 1 pp 289– (1997) |

[20] | Naff, Comput Geosci 6 pp 285– (2002) |

[21] | Shashkov, J Comput Phys 129 pp 383– (1996) |

[22] | Riviere, Comput Geosci 4 pp 337– (2000) |

[23] | Weiser, SIAM J Numer Anal 25 pp 351– (1988) |

[24] | and , An analysis of the finite element method, Wiley, New York, 1973. |

[25] | and , Mixed and hybrid finite element methods, Springer Series in Computational Mathematics 15, Springer-Verlag, 1991. · Zbl 0788.73002 |

[26] | LeVeque, Cambridge Texts in Applied Mathematics (2002) |

[27] | Nordbotten, Comput Geosci |

[28] | and , Monotonicity conditions for control volume methods on general quadrilateral grids; Application to MPFA, Proc 16th Nordic Seminar on Computational Mechanics, 2003. |

[29] | Hyman, J Comput Phys 132 pp 130– (1997) |

[30] | , , , and , Recent advances for MPFA methods, Proc ECMOR IX, Cannes, France, 2004. |

[31] | Marini, SIAM J Numer Anal 22 (1985) |

[32] | and , Multi point flux approximations and finite element methods: Practical aspects of discontinuous media, Proc ECMOR IX, Cannes, France, 2004. |

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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.