Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods

  • Authors:

  • I. Aavatsmark;T. Barkve;O. Bøe

  • Affiliations:

  • -;-;-

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 1998

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Abstract

Discretization methods are proposed for control-volume formulations on polygonal and triangular grid cells in two space dimensions. The methods are applicable for any system of conservation laws where the flow density is defined by a gradient law, like Darcy's law for porous-media flow. A strong feature of the methods is the ability to handle media inhomogeneities in combination with full-tensor anisotropy. This paper gives a derivation of the methods, and the relation to previously published methods is also discussed. A further discussion of the methods, including numerical examples, is given in the companion paper, Part II [SIAM J. Sci. Comput., pp. 1717--1736].