Unstructured, control-volume distributed, full-tensor finite-volume schemes with flow based grids

Locally conservative flux-continuous, full-tensor, discretization schemes are presented for general unstructured grids. The schemes are control-volume distributed, where flow variables and rock properties are assigned to the polygonal control-volumes derived from the primal grid. A relationship between these finite volume schemes and the mixed finite element method is established. An extension for unstructured grids is described that leads to a general symmetric positive definite discretization matrix for both quadrilateral and triangular grids. A novel flow based gridding approach for unstructured mesh generation is also proposed for heterogeneous reservoir domains. Results computed with the flux continuous schemes on unstructured flow-based grids demonstrate the advantages of the methods.