Multiscale space-time algorithms and data structures for the simulation of porous media flow.

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Codes to simulate oil and gas flow in porous media (Darcy) are mature today. Codes to simulate gas flow in free space (hyperbolic systems) are mature today, too. In this project, we are interested in setups of porous media (rocks) that are fissured/fractured. Networks and submanifold are embedded into the rock. Along the fractures, the fluid is best described as a hyperbolic equation system. Within the rocks, it exhibits diffusive nature. The most popular codes simulating the diffusion rely on (block-) structured data structures such as adaptive Cartesian grids, while the flow along the submanifold can be simulated more efficiently with network-like data structures. Each domain alone can be simulated efficiently. The picture changes as soon as the creeping flow `hits` fractures that run through the computational domain. Slow, creeping flow starts to rush through the domain, while the flow along the factures in turn induces slow flow motion in the adjacent porous medium. This is a multiscale problem both in terms of spatial dimensions as well as temporal and spatial scale. Furthermore, fast codes simulating such a setup have to bring together Cartesian or structured adaptive meshes with low-dimensional data structures.