A novel, high-order, parallel-in-time integration procedure for complex fluid flows

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In this project, the class of implicit multiderivative (MD) schemes for numerical treatment of ordinary differential equations is analyzed, extended and used as a parallel-in-time integrator for complex partial differential equations. Yielding high-order of accuracy with relatively low storage requirements, MD schemes offer a highly attractive option for being combined with a spatial discretization by discontinuous Galerkin spectral elements (DGSEM). A subset of the class of MD schemes, written in predictor/corrector form, provides a natural possibility of time parallelization, being of course attractive for high performance computing.The first step in this project is the analysis and development of novel MD schemes with a special focus on memory requirements, discretization error and temporal adaptivity. Having those schemes in place, they are combined with the DGSEM. Here, focus is on a consistent discretization of the multiderivative terms being essential for a stable method as well as on the exploitation of the nodal structure of the DGSEM. Finally, the time-parallel capabilities of MD schemes are investigated. As the implementation is done within a spatially parallelized code framework suitable for high performance computing, not only analytical investigations are carried out but also practical questions on real-world examples can be tackled.