A classical finite volume scheme well known in computational aerodynamics [1] for solving the Transonic full potential equation is imported into reservoir simulation and applied to the full tensor pressure equation. Cell vertex discretisation is shown to be a natural framework for approximation. With permeability placed at the cell centres and potential at the vertices (cell corner points), of the grid the scheme is flux continuous and locally conservative. Analysis is presented which proves that the resulting discrete matrix is symmetric positive definite provided the full permeability tensor is symmetric elliptic. The discrete matrix is also diagonally dominant subject to a sufficient ellipticity condition. For a diagonal anisotropic tensor the discrete matrix is always symmetric positive definite and the scheme is upto 4th order accurate. A cell centred version of the scheme is indicated.

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