Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm

E Carlson, A Larios, ES Titi - Journal of Nonlinear Science, 2024 - Springer
We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
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 …

Data assimilation with model error: Analytical and computational study for Sabra shell model

N Chen, A Farhat, E Lunasin - Physica D: Nonlinear Phenomena, 2023 - Elsevier
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 …

The bleeps, the sweeps, and the creeps: convergence rates for dynamic observer patterns via data assimilation for the 2D Navier–Stokes equations

T Franz, A Larios, C Victor - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
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 …

Concurrent MultiParameter Learning Demonstrated on the Kuramoto--Sivashinsky Equation

B Pachev, JP Whitehead, SA McQuarrie - SIAM Journal on Scientific …, 2022 - SIAM
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 …

Determining modes, synchronization, and intertwinement

E Carlson, A Farhat, VR Martinez, C Victor - arXiv preprint arXiv …, 2024 - arxiv.org
This article studies the interrelation between the determining modes property in the two-
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 …

Accelerating and enabling convergence of nonlinear solvers for Navier–Stokes equations by continuous data assimilation

X Li, EV Hawkins, LG Rebholz, D Vargun - Computer Methods in Applied …, 2023 - Elsevier
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 …

[HTML][HTML] Adaptive parameter selection in nudging based data assimilation

A Çıbık, R Fang, W Layton, F Siddiqua - Computer Methods in Applied …, 2025 - Elsevier
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 …

Identifying the body force from partial observations of a two-dimensional incompressible velocity field

A Farhat, A Larios, VR Martinez, JP Whitehead - Physical Review Fluids, 2024 - APS
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 …