Multirate Variational Time Stepping with Error Control for Reactive Flows in Deformable Porous Media (MATEROC)

Numerical modeling of reactive flow in deformable porous media as a multi-physics system continues to remain a challenging task. Beyond the coupling of fluid-structure interaction, which is currently a research topic of strong scientific interest by itself, multicomponent reactive transport is further involved. Typically, the time scales of the three coupled physical systems differ by orders of magnitude which is a considerable problem for numerical simulations and the indispensable resolution of all relevant time scales. Standard single-rate time discretization methods for multi-physics systems work with time steps that are allowed to vary in time but are constant over the involved subproblems. To exploit local time scale variations and ensure reliable simulations, one needs multirate (multiscale in time) methods that use different local time steps over the system's subproblems. The objective of this research project is to develop multirate schemes for reactive flow in deformable porous media with self-adaptive local time stepping based on a posteriori error control such that large-scale simulations become feasible. The developed schemes will work for a large range of discretization methods, including higher-order space-time methods.