The Multiscale Mixed Finite-Element Method (MsMFEM)

Basic idea: Use a mixed finite-element method on a coarse scale with special basis that satisfy local flow problems and thereby account for subgrid variations. This way, an approximate fine-scale solution is constructed at the cost of solving a coarse-scale problem.

MsMFEM is formulated using two grids, a fine underlying grid on which the media properties are given, and a coarse simulation grid where each block can consists of an arbitrary connected collection of cells from the fine grid. In this sense, the method is very flexible and can be applied to almost any grid, structured or unstructured, and can easily be built on-top-of existing pressure solvers.

MsMFEM offers fast, accurate, and robust pressure solvers for highly heterogeneous porous media to be used for

• direct simulation on high-resolution grid models with multimillion cells,
• fast simulation of multiple (stochastic) realisations of reservoir heterogeneity.

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Fast Flow Simulations by Optimal Reordering and Discontinuous Galerkin Discretisations

Fast, accurate, and robust solution of advection dominated transport equations

• time-of-flight and single-phase tracer flow
• multiphase and multicomponent flow

A grid-based alternative to streamline simulation that is mass-conservative and avoids problems with mapping and choice of representative streamline distribution.

Basic idea: Combine a localized high-order discretization with an optimal reordering that allows a fast block-wise solution of the resulting (non)linear discrete system.

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