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Finite volume (FV) methods are still the most popular methods in practical reservoir simulation. They have good accuracy when used properly and are computationally very cheap. FV can be used on unstructured grids, but grid generation becomes a very difficult task. More advanced methods, discontinuous Galerkin (DG) for example, work on more general meshes, but are computationally more expensive and are still not accepted by the practitioners. We propose coupling of FV and DG methods that can improve the accuracy of the FV with reasonable increase of the computational cost. We developed the algorithms for coupling DG and FV for model diffusion and convection diffusion problems on Voronoi /PEBI grids. We demonstrate with examples how DG can be used to alleviate the problems with grids in 2-D, gridding around pinch-outs and patch local refinement for areas with tensor coefficients.
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