A Computational Study of a Data Assimilation Algorithm for the Two-Dimensional Navier-Stokes Equations (Communications in Computational Physics, 2018)
We study the numerical performance of a continuous data assimilation(downscaling) algorithm, based on ideas from feedback control theory, in the contextof the two-dimensional incompressible Navier-Stokes equations. Our model problemis to recover an unknown reference solution, asymptotically in time, by usingcontinuous-in-time coarse-mesh nodal-point observational measurements of the velocityfield of this reference solution (subsampling), as might be measured by an arrayof weather vane anemometers. Our calculations show that the required nodal observationdensity is remarkably less than what is suggested by the analytical study; andis in fact comparable to the number of numerically determining Fourier modes, which wasreported in an earlier computational study by the authors. Thus, this method is computationallyefficient and performs far better than the analytical estimates suggest.