Parameter Recovery for the 2 Dimensional Navier--Stokes Equations via Continuous Data Assimilation
Elizabeth Carlson, Joshua Hudson, Adam Larios
Abstract
We study a continuous data assimilation algorithm proposed by Azouani, Olson, and Titi (AOT) in the context of an unknown viscosity. We determine the large-time error between the true solution of the 2 dimensional Navier--Stokes equations and the assimilated solution due to discrepancy between an approximate viscosity and the physical viscosity. Additionally, we develop an algorithm that can be run in tandem with the AOT algorithm to recover both the true solution and the true viscosity using only spatially discrete velocity measurements.
Topics & Concepts
Data assimilationViscosityMathematicsNavier–Stokes equationsContext (archaeology)Assimilation (phonology)Applied mathematicsViscosity solutionMathematical analysisMechanicsMeteorologyPhysicsThermodynamicsLinguisticsPhilosophyBiologyPaleontologyCompressibilityMeteorological Phenomena and SimulationsFluid Dynamics and Turbulent FlowsModel Reduction and Neural Networks