Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study

Farhat, Aseel; Johnston, Hans; Jolly, Michael S.; Titi, Edriss S.

doi:10.1007/s10915-018-0686-x

Cited by 43 publications

(27 citation statements)

References 42 publications

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“…All of the above works on abridged algorithms provide rigorous estimates for lower bounds on µ and upper bounds on the spatial resolution h. It is likely that the algorithms perform better, i.e., convergence is achieved with data that is much more coarse than the estimates require. This is in fact demonstrated in numerical tests carried out for the 2D NSE [20,22], and 2D RB convection model [2,14].…”

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confidence: 69%

Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations

Hudson¹,

Jolly²

2019

Journal of Computational Dynamics

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We study the computational efficiency of several nudging data assimilation algorithms for the 2D magnetohydrodynamic equations, using varying amounts and types of data. We find that the algorithms work with much less resolution in the data than required by the rigorous estimates in [7]. We also test other abridged nudging algorithms to which the analytic techniques in [7] do not seem to apply. These latter tests indicate, in particular, that velocity data alone is sufficient for synchronization with a chaotic reference solution, while magnetic data alone is not. We demonstrate that a new nonlinear nudging algorithm, which is adaptive in both time and space, synchronizes at a super exponential rate.2010 Mathematics Subject Classification. Primary: 34D06, 76W05.

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confidence: 69%

Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations

Hudson¹,

Jolly²

2019

Journal of Computational Dynamics

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“…(see also references therein). Continuous data assimilation has also been used in numerical studies, for example, with the Chafee-Infante reaction-diffusion equation the Kuramoto-Sivashinsky equation (in the context of feedback control) [36], Rayleigh-Bénard convection equations [3], [18], and the Navier-Stokes equations [25], [28]. However, there is much less numerical analysis of this technique.…”

Section: Introductionmentioning

confidence: 99%

Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations

García-Archilla¹,

Novo²,

Titi³

2020

SIAM J. Numer. Anal.

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In this paper we analyze a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two and three dimensional Navier-Stokes equations corresponding to given measurements on a coarse spatial scale. For representing the coarse mesh measurements we consider different types of interpolation operators including a Lagrange interpolant. We obtain uniform-in-time estimates for the error between a finite element approximation and the reference solution corresponding to the coarse mesh measurements. We consider both the case of a plain Galerkin method and a Galerkin method with grad-div stabilization. For the stabilized method we prove error bounds in which the constants do not depend on inverse powers of the viscosity. Some numerical experiments illustrate the theoretical results.

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“…In the context of NWP, different formulations of nudging have been used to study the state estimation problem using finite-dimensional dynamical systems and weather models [25,[29][30][31], and for boundary condition matching [32][33][34]. In the context of turbulence, for the cases of a two-dimensional Navier-Stokes equation (NSE) [35][36][37][38], the three-dimensional Navier-Stokes α model [39], and Rayleigh-Bénard convection [40,41], it has been rigorously proven that given a sufficient amount of input data, a nudged field will eventually synchronize with its nudging field. Indeed, both DA [42] and nudging can be framed as a synchronization problem; see Ref.…”

Section: Introductionmentioning

confidence: 99%

Synchronization to Big Data: Nudging the Navier-Stokes Equations for Data Assimilation of Turbulent Flows

Leoni

Mazzino²,

Biferale

2020

Phys. Rev. X

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Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it to the canonical problem of fluid dynamics: three-dimensional homogeneous and isotropic turbulence. By doing numerical experiments we perform a systematic assessment of how well the technique reconstructs large-and small-scale features of the flow with respect to the quantity and the quality or type of data supplied to it. The types of data used are (i) field values on a fixed number of spatial locations (Eulerian nudging), (ii) Fourier coefficients of the fields on a fixed range of wave numbers (Fourier nudging), or (iii) field values along a set of moving probes inside the flow (Lagrangian nudging). We present state-of-the-art quantitative measurements of the scale-by-scale transition to synchronization and a detailed discussion of the probability distribution function of the reconstruction error, by comparing the nudged field and the truth point by point. Furthermore, we show that for more complex flow configurations, like the case of anisotropic rotating turbulence, the presence of cyclonic and anticyclonic structures leads to unexpectedly better performances of the algorithm. We discuss potential further applications of nudging to a series of applied flow configurations, including the problem of field reconstruction in thermal Rayleigh-Bénard convection and in magnetohydrodynamics, and to the determination of optimal parametrization for small-scale turbulent modeling. Our study fixes the standard requirements for future applications of nudging to complex turbulent flows.

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Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study

Cited by 43 publications

References 42 publications

Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations

Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations

Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations

Synchronization to Big Data: Nudging the Navier-Stokes Equations for Data Assimilation of Turbulent Flows

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