Project R-11778

A novel high-order time integration procedure for singularly perturbed bio-inspired flows (Research)

The potential risks and threats of climate change are omnipresent in everyday's life. In a controlled environment ("ecotron"), biologists and researchers from other disciplines experiment on the impacts of climate change on crop growth. These experiments are evidently very time-consuming and need hence to be equipped by suitable forecasting, typically obtained from some sort of mathematical modelling and numerical discretization. Even with today's supercomputing possibilities, there is still a need for efficient numerical methods to use resources as economically as possible. In this project, we suggest to explore a novel discretization paradigm that will lead to an efficient treatment of equations modelling water and vapor flow in ecotrons. These so-called partial differential equations couple spatial behavior to temporal evolution. It is for the temporal part that we suggest a new treatment based on the addition of more temporal derivatives. This is then combined with a smart treatment of the spatial part. The resulting method is analyzed mathematically, with a special focus on the stability if a small parameter - inherent to the equations - goes to zero. Subsequently, it is implemented and the results are compared first to more established methods, and second to experimental data from the ecotron.

01 October 2021 - 30 September 2025