Continuous Data Assimilation for the 2D Bénard Convection through Velocity Measurements Alone

Abstract

An algorithm for continuous data assimilation for the two- dimensional Bénard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm developed for the Navier-Stokes equations, which allows for the implementation of variety of observables: low Fourier modes, nodal values, finite volume averages, and finite elements. The novelty here is that the observed data is obtained for the velocity field alone; i.e. no temperature measurements are needed for this algorithm. We provide conditions on the spatial resolution of the observed data, under the assumption that the observed data is free of noise, which are sufficient to show that the solution of the algorithm approaches, at an exponential rate, the unique exact unknown solution of the Bénard convection problem associated with the observed (finite dimensional projection of) velocity.

References in corpus (5)

• Continuous Data Assimilation Using General Interpolant Observables
• Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations
• Accuracy and Stability of The Continuous-Time 3DVAR Filter for The Navier-Stokes Equation
• A unified approach to determining forms for the 2D Navier-Stokes equations - the general interpolants case
• Global Well-posedness for The 2D Boussinesq System Without Heat Diffusion and With Either Anisotropic Viscosity or Inviscid Voigt-$\alpha$ Regularization

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