English
Related papers

Related papers: Data assimilation for slightly compressible flow

200 papers

Sparse sensor networks in weather and ocean modeling observe only a small fraction of the system state, which destabilizes standard nudging-based data assimilation. We introduce Interpolated Discrepancy Data Assimilation (IDDA), which…

Numerical Analysis · Mathematics 2025-11-03 Tong Wu , Humberto Godinez , Vitaliy Gyrya , James M. Hyman

We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is…

Numerical Analysis · Mathematics 2024-01-15 Bosco Garcia-Archilla , Xuejian Li , Julia Novo , Leo Rebholz

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…

Fluid Dynamics · Physics 2025-02-25 Amirmoez Jamaat , Yalan Song , Farshid Rahmani , Jiangtao Liu , Kathryn Lawson , Chaopeng Shen

Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system…

Dynamical Systems · Mathematics 2015-05-20 Kevin Hayden , Eric Olson , Edriss S. Titi

We introduce a continuous (downscaling) data assimilation algorithm for the 2D B\'enard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to…

Analysis of PDEs · Mathematics 2017-09-11 Aseel Farhat , Hans Johnston , Michael S. Jolly , Edriss S. Titi

This paper shows how continuous data assimilation (CDA) can be used to provably enable and accelerate convergence of a (efficient at each iteration due to a physics-splitting, but generally slowly converging and not robust) nonlinear solver…

Numerical Analysis · Mathematics 2026-03-25 Victoria Luongo Fisher , Jessica C. Franklin , Leo G. Rebholz

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…

Analysis of PDEs · Mathematics 2015-06-19 Hakima Bessaih , Eric Olson , E. S. Titi

We present a novel reduced-order pressure stabilization strategy based on continuous data assimilation(CDA) for two-dimensional incompressible Navier-Stokes equations. A feedback control term is incorporated into pressure-correction…

Numerical Analysis · Mathematics 2023-04-04 Xi Li , Youcai Xu , Minfu Feng

Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling and astrophysics. Up to now, spectral nudging was applied for empirical…

Fluid Dynamics · Physics 2018-10-29 P. Clark Di Leoni , A. Mazzino , L. Biferale

Motivated by the presence of a finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, we present a continuous data assimilation algorithm for the…

Analysis of PDEs · Mathematics 2014-08-26 Débora A. F. Albanez , Helena J. Nussenzveig Lopes , Edriss S. Titi

Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…

Optimization and Control · Mathematics 2023-03-08 Tarek Diaa-Eldeen , Marcus Krogh Nielsen , Carl Fredrik Berg , Morten Hovd , John Bagterp Jørgensen

Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on…

Image and Video Processing · Electrical Eng. & Systems 2026-05-15 Yixuan Jia , Siyi Chen , Yida Pan , Xiao Li , Lianghe Shi , Chanyong Jung , Haijie Yuan , Ismail Alkhouri , Yue Cynthia Wu , Saiprasad Ravishankar , Jeffrey A Fessler , Qing Qu

Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past…

Systems and Control · Electrical Eng. & Systems 2026-01-21 Marios Andreou , Nan Chen , Yingda Li

In this paper we propose a continuous data assimilation (downscaling) algorithm for a two-dimensional B\'enard convection problem. Specifically we consider the two-dimensional Boussinesq system of a layer of incompressible fluid between two…

Analysis of PDEs · Mathematics 2017-02-01 Aseel Farhat , Evelyn Lunasin , Edriss S. Titi

The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…

Numerical Analysis · Mathematics 2020-04-21 Bosco García Archilla , Julia Novo , Samuele Rubino

Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses continuous data assimilation for a model arising as a…

Analysis of PDEs · Mathematics 2026-02-03 Eduard Feireisl , Piotr Gwiazda , Agnieszka Świerczewska-Gwiazda

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…

Analysis of PDEs · Mathematics 2015-06-15 Abderrahim Azouani , Eric Olson , Edriss S. Titi

We propose, analyze, and test a novel continuous data assimilation two-phase flow algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed using coarse mesh observations, converge at an exponential rate…

Numerical Analysis · Mathematics 2022-06-22 Yat Tin Chow , Wing Tat Leung , Ali Pakzad

We introduce, analyze and test a new interpolation operator for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an…

Analysis of PDEs · Mathematics 2018-10-09 Leo G. Rebholz , Camille Zerfas

We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due…

Numerical Analysis · Mathematics 2023-02-14 Elizabeth Hawkins , Leo G. Rebholz , Duygu Vargun