Application of Multi-Fidelity Methods to Uncertainty Quantification of Gravity Currents

Density variations due to sources such as heat or solute concentration are often observed in physical systems, including deposition of saline solutions into fresh water and smoke generation from wildfires. These belong to a class of flows known as gravity currents, where differences in density may induce flow due to buoyancy effects. In this study, we consider a simplified model of a lock-exchange problem, where a heavy fluid is placed in a lighter ambient with an impermeable barrier that is then removed. A nonlinearly varying ambient density profile is assumed, leading to a three-dimensional parameter space for the strength, shape, and height of the ambient profile. A system of shallow water equations (SWEs) has been derived to model the front location, area, and concentration of the current. Comparisons with two- and three-dimensional direct numerical simulations (DNSs) shows the SWEs are able to capture trends with variations in ambient stratification within the slumping phase. Finally, we discuss the applicability of using a bi-fidelity method to correct these quantities with a limited amount of DNS, which will enable for efficient exploration of the parameter space.