Project Grant 2207207

This three-year National Science Foundation Project Grant of $900,000 will support the development of robust uncertainty quantification techniques and structure-preserving numerical methods for stochastic shallow water equations and related hyperbolic balance laws. Funded through the Mathematical and Physical Sciences program (CFDA 47.049), this award to the University of Utah will make significant advances in computational tools used across science and engineering disciplines that involve wave propagation and fluid flow modeling. Key outcomes include new intrusive and non-intrusive uncertainty quantification approaches to generate physically relevant stochastic shallow water models. The project will also design and analyze adaptive high-order accurate deterministic and stochastic solvers. Efforts will focus on the shallow water equations but tools will apply more broadly. This work addresses outstanding challenges in numerical methods for nonlinear conservation laws and uncertainty quantification for transport problems. Results from this NSF-funded research have the potential to improve predictive capabilities for applications involving coastal engineering, atmospheric and oceanographic phenomena modeling.