Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm
We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …
Convergence analysis of a viscosity parameter recovery algorithm for the 2D Navier–Stokes equations
VR Martinez - Nonlinearity, 2022 - iopscience.iop.org
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 …
viscosity of a two-dimensional incompressible, viscous fluid is studied. The algorithm of …
Data assimilation with model error: Analytical and computational study for Sabra shell model
Understanding the impact of model error on data assimilation is an important practical topic.
Model error in the subgrid scale is commonly seen in various applications as a natural …
Model error in the subgrid scale is commonly seen in various applications as a natural …
The bleeps, the sweeps, and the creeps: convergence rates for dynamic observer patterns via data assimilation for the 2D Navier–Stokes equations
We adapt a continuous data assimilation scheme, known as the Azouani–Olson–Titi (AOT)
algorithm, to the case of moving observers for the 2D incompressible Navier–Stokes …
algorithm, to the case of moving observers for the 2D incompressible Navier–Stokes …
Concurrent MultiParameter Learning Demonstrated on the Kuramoto--Sivashinsky Equation
We develop an algorithm based on the nudging data assimilation scheme for the concurrent
(on-the-fly) estimation of scalar parameters for a system of evolutionary dissipative partial …
(on-the-fly) estimation of scalar parameters for a system of evolutionary dissipative partial …
Determining modes, synchronization, and intertwinement
This article studies the interrelation between the determining modes property in the two-
dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the …
dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the …
Employing quantum fruit fly optimization algorithm for solving three-dimensional chaotic equations
QM Zainel, SM Darwish, MB Khorsheed - Mathematics, 2022 - mdpi.com
In a chaotic system, deterministic, nonlinear, irregular, and initial-condition-sensitive features
are desired. Due to its chaotic nature, it is difficult to quantify a chaotic system's parameters …
are desired. Due to its chaotic nature, it is difficult to quantify a chaotic system's parameters …
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 …
Stokes equations in the setting where data measurements or solution observations are …
[HTML][HTML] Adaptive parameter selection in nudging based data assimilation
Data assimilation combines (imperfect) knowledge of a flow's physical laws with (noisy, time-
lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow …
lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow …
Identifying the body force from partial observations of a two-dimensional incompressible velocity field
Using limited observations of the velocity field of the two-dimensional Navier-Stokes
equations, we successfully reconstruct the steady body force that drives the flow. The …
equations, we successfully reconstruct the steady body force that drives the flow. The …