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Complex geometric and geological features of realistic reservoirs motivate the need for flexible and robust flux discretization for forecasting of fluid flow in porous media. Advanced seismic modelling in combination with history matching reveal that faults and fractures frequently occur in North Sea reservoirs, and may significantly affect the flow patterns. In this work we present a flexible grid structure which can incorporate grid configurations due to complex faults and fractures in a consistent manner. On these grids we have implemented general control volume discretizations. This allows a consistent treatment of the resulting skewed and non-matching grid cells, heterogeneities and general anisotropies. The general flux-discretisation techniques may be combined with streamline simulation on general grids. Such approaches utilize tools for multiple realizations of general porous media flows and ranking of models. Numerical examples will here be given which illuminate the performance on some representative large-scale problems.