A Coupled Finite Element Framework for Multi-Physics Environmental Flows

A Coupled Finite Element Framework for Multi-Physics Environmental Flows

HYDROCOUPLE proposes to develop (1) a new coupled finite element (FE) method for environmental flows, (2) goal-oriented adaptive mesh refinement strategies, and (3) to apply the new techniques to physical watersheds for verification of its capabilities as well as to demonstrate these. The project is a collaboration between three researchers, the applicant Eirik Valseth (currently at The University of Texas at Austin), Prof. Kent-Andre Mardal (The University of Oslo) and Prof. Ethan Kubatko (The Ohio State University). Many current approximation techniques for multiphysics phenomena, where two or more models (partial differential equations) govern the physics, focuses on the approximation of these as separate phenomena and prescribe appropriate interface conditions to exchange information between the models. Recent attention has been given to monolithically coupled methods (Kuchta et al. 2021), where all models are approximated simultaneously thanks to careful algorithm design and numerical analysis. HYDROCOUPLE will extend the theory of these monolithic coupling schemes to environmental flow problems and develop a FE framework for their corresponding numerical approximation. This developed framework can subsequently be applied in flood prediction and hydropower production planning as the models in environmental flows govern both overland and riverine flows which are critical in both applications. HYDROCOUPLE will also develop mesh-adaptive refinement techniques based on goal-oriented error estimation to ensure the high fidelity of its numerical approximations. Finally, the proposed framework will be verified against available data for existing watersheds to demonstrate its efficiency and accuracy to end users in industry and government. Working in the Section of Mechanics at the Department of Mathematics with a world renowned scientist will provide a perfect setting to integrate my knowledge and start my research career in Europe.