## Applied Mathematics Colloquium: Dr. Joshua Hudson

#### Johns Hopkins Applied Physics Laboratory

Friday, December 4, 2020 · 2 PM - 3 PM

Title: Data assimilation via nudging for fluid dynamics with parameter recovery.

Abstract: We will discuss a data assimilation algorithm known as nudging, focussing on fluid dynamics applications. The idea of nudging is to add a damping term to the system based on coarse observations, which results in convergence of the data assimilation approximation to the true solution. In 2014, a rigorous mathematical proof was given by Azouani Olson and Titi giving conditions for the success of nudging for the 2D Navier-Stokes equations. Subsequently similar results were obtained for several related equations.

We will present some theoretical and computational results of nudging applied to the Magnetohydrodynamic equations, considering various possibilities for the availability of measurements from a subset of the evolutionary variables, as well as some adaptive extensions of nudging and the inclusion of noise in the measurements. We will then consider the Navier-Stokes equations with the viscosity as an unknown parameter, giving rigorous bounds for convergence and discussing an algorithm designed to recover the true solution and the unknown viscosity using only velocity measurements.

We will present some theoretical and computational results of nudging applied to the Magnetohydrodynamic equations, considering various possibilities for the availability of measurements from a subset of the evolutionary variables, as well as some adaptive extensions of nudging and the inclusion of noise in the measurements. We will then consider the Navier-Stokes equations with the viscosity as an unknown parameter, giving rigorous bounds for convergence and discussing an algorithm designed to recover the true solution and the unknown viscosity using only velocity measurements.