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The permeability of the Earth's crust commonly varies over many orders of magnitude. Flow velocity can range over several orders of magnitude in structures of interest that vary in scale from centimeters to kilometers. To accurately and efficiently model multiphase flow in geologic media, we introduce a fully conservative node-centered finite volume method coupled with a Galerkin finite element method on an unstructured triangular grid with a complementary finite volume subgrid. The effectiveness of this approach is demonstrated by comparison with traditional solution methods and by multiphase flow simulations for heterogeneous permeability fields including complex geometries that produce transport parameters and lengths scales varying over four orders of magnitude.

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Water supply authorities usually operate and maintain a few large reservoirs and a larger number of smaller water supply reservoirs as part of a city's water reticulation system. These water authorities are required to assess the risk of failure and develop a flood warning plan for all of their large reservoirs. Risk assessment of the water supply reservoirs is not required despite the fact that these reservoirs are generally located in elevated positions in residential areas. In recognition of the potential risks, a computer model has been developed to predict the progress of the flood ensuing from the collapse of a water supply reservoir. The computer model is based on the finite volume method and uses a first-order approximate Riemann solver to solve the shallow water wave equations on an unstructured triangular grid. The model is capable of resolving shocks, handling complex geometries, including the influence of steep bed slopes and obstructions, such as buildings and simulating flow over a dry bed. These features of the model are demonstrated using a case study.

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