1,437 research outputs found
Efficient dynamical downscaling of general circulation models using continuous data assimilation
Continuous data assimilation (CDA) is successfully implemented for the first
time for efficient dynamical downscaling of a global atmospheric reanalysis. A
comparison of the performance of CDA with the standard grid and spectral
nudging techniques for representing long- and short-scale features in the
downscaled fields using the Weather Research and Forecast (WRF) model is
further presented and analyzed. The WRF model is configured at 25km horizontal
resolution and is driven by 250km initial and boundary conditions from
NCEP/NCAR reanalysis fields. Downscaling experiments are performed over a
one-month period in January, 2016. The similarity metric is used to evaluate
the performance of the downscaling methods for large and small scales.
Similarity results are compared for the outputs of the WRF model with different
downscaling techniques, NCEP reanalysis, and Final Analysis. Both spectral
nudging and CDA describe better the small-scale features compared to grid
nudging. The choice of the wave number is critical in spectral nudging;
increasing the number of retained frequencies generally produced better
small-scale features, but only up to a certain threshold after which its
solution gradually became closer to grid nudging. CDA maintains the balance of
the large- and small-scale features similar to that of the best simulation
achieved by the best spectral nudging configuration, without the need of a
spectral decomposition. The different downscaled atmospheric variables,
including rainfall distribution, with CDA is most consistent with the
observations. The Brier skill score values further indicate that the added
value of CDA is distributed over the entire model domain. The overall results
clearly suggest that CDA provides an efficient new approach for dynamical
downscaling by maintaining better balance between the global model and the
downscaled fields
Convergence Analysis of a Viscosity Parameter Recovery Algorithm for the 2D Navier-Stokes Equations
In this paper, the convergence of an algorithm for recovering the unknown
kinematic viscosity of a two-dimensional incompressible, viscous fluid is
studied. The algorithm of interest is a recursive feedback control-based
algorithm that leverages observations that are received continuously-in-time,
then dynamically provides updated values of the viscosity at judicious moments.
It is shown that in an idealized setup, convergence to the true value of the
viscosity can indeed be achieved under a natural and practically verifiable
non-degeneracy condition. This appears to be first such result of its kind for
parameter estimation of nonlinear partial differential equations. Analysis for
two parameter update rules is carried out: one which involves instantaneous
evaluation in time and the other, averaging in time. The proofs of convergence
for either rule exploits sensitivity-type bounds in higher-order Sobolev
topologies, while the instantaneous version particularly requires delicate
energy estimates involving the time-derivative of the sensitivity-type
variable. Indeed, a crucial component in the analysis of the first update rule
is the identification of a dissipative structure for the time-derivative of the
sensitivity-type variable, which ultimately ensures a favorable dependence on
the tuning parameter of the algorithm.Comment: 35 pages, results expanded to include alternative update formula,
exposition adjusted accordingly, additional remarks included, to appear in
Nonlinearit
Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows
We propose a variational approach to identification of an optimal nonlinear
eddy viscosity as a subscale turbulence representation for POD models. The
ansatz for the eddy viscosity is given in terms of an arbitrary function of the
resolved fluctuation energy. This function is found as a minimizer of a cost
functional measuring the difference between the target data coming from a
resolved direct or large-eddy simulation of the flow and its reconstruction
based on the POD model. The optimization is performed with a data-assimilation
approach generalizing the 4D-VAR method. POD models with optimal eddy
viscosities are presented for a 2D incompressible mixing layer at
(based on the initial vorticity thickness and the velocity of the high-speed
stream) and a 3D Ahmed body wake at (based on the body height and
the free-stream velocity). The variational optimization formulation elucidates
a number of interesting physical insights concerning the eddy-viscosity ansatz
used. The 20-dimensional model of the mixing-layer reveals a negative
eddy-viscosity regime at low fluctuation levels which improves the transient
times towards the attractor. The 100-dimensional wake model yields more
accurate energy distributions as compared to the nonlinear modal eddy-viscosity
benchmark {proposed recently} by \"Osth et al. (2014). Our methodology can be
applied to construct quite arbitrary closure relations and, more generally,
constitutive relations optimizing statistical properties of a broad class of
reduced-order models.Comment: 41 pages, 16 figures; accepted for publication in Journal of Fluid
Mechanic
Accelerating and enabling convergence of nonlinear solvers for Navier-Stokes equations by continuous data assimilation
This paper considers improving the Picard and Newton iterative solvers for
the Navier-Stokes equations in the setting where data measurements or solution
observations are available. We construct adapted iterations that use continuous
data assimilation (CDA) style nudging to incorporate the known solution data
into the solvers. For CDA-Picard, we prove the method has an improved
convergence rate compared to usual Picard, and the rate improves as more
measurement data is incorporated. We also prove that CDA-Picard is contractive
for larger Reynolds numbers than usual Picard, and the more measurement data
that is incorporated the larger the Reynolds number can be with CDA-Picard
still being contractive. For CDA-Newton, we prove that the domain of
convergence, with respect to both the initial guess and the Reynolds number,
increases as as the amount of measurement data is increased. Additionally, for
both methods we show that CDA can be implemented as direct enforcement of
measurement data into the solution. Numerical results for common benchmark
Navier-Stokes tests illustrate the theory
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