12 research outputs found
Inferring flow parameters and turbulent configuration with physics-informed data assimilation and spectral nudging
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A Computational Study of a Data Assimilation Algorithm for the Two-dimensional Navier-Stokes Equations
We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier-Stokes equations. Our model problem is to recover an unknown reference solution, asymptotically in time, by using continuous-in-time coarse-mesh nodal-point observational measurements of the velocity field of this reference solution (subsampling), as might be measured by an array of weather vane anemometers. Our calculations show that the required nodal observation density is remarkably less than what is suggested by the analytical study; and is in fact comparable to the number of numerically determining Fourier modes, which was reported in an earlier computational study by the authors. Thus, this method is computationally efficient and performs far better than the analytical estimates suggest
Leaching of colloidal matter and dissolved organic carbon from surface soil columns during multiple irrigation periods
A Discrete Data Assimilation Scheme for the Solutions of the Two-Dimensional Navier--Stokes Equations and Their Statistics
Uniform-in-Time Error Estimates for the Postprocessing Galerkin Method Applied to a Data Assimilation Algorithm
Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model
Continuous Data Assimilation for a 2D BĂ©nard Convection System Through Horizontal Velocity Measurements Alone
Downscaling the 2D BĂ©nard convection equations using continuous data assimilation
We consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D BĂ©nard convection equations into a finer grid. In this CDA, a nudging term, estimated as the misfit between some interpolants of the assimilated coarse-grid measurements and the fine-grid model solution, is added to the model equations to constrain the model. The main contribution of this study is a performance analysis of CDA for downscaling measurements of temperature and velocity. These measurements are assimilated either separately or simultaneously, and the results are compared against those resulting from the standard point-to-point nudging approach (NA). Our numerical results suggest that the CDA solution outperforms that of NA, always converging to the true solution when the velocity is assimilated as has been theoretically proven. Assimilation of temperature measurements only may not always recover the true state as demonstrated in the case study. Various runs are conducted to evaluate the sensitivity of CDA to noise in the measurements, the size, and the time frequency of the measured grid, suggesting a more robust behavior of CDA compared to that of NA