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**Unstructured, control-volume distributed, full-tensor finite volume schemes with flow based grids.**
*(English)*
Zbl 1036.76034

Summary: 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 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.

### MSC:

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

76S05 | Flows in porous media; filtration; seepage |