Related papers: Continuous data assimilation for two-phase flow: a…
In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation…
In this study, we analyzed a continuous data assimilation scheme applied on a double-diffusive natural convection model. The algorithm is introduced with a first order backward Euler time scheme along with a finite element discretization in…
We propose, analyze, and test a novel continuous data assimilation reduced order model (DA-ROM) for simulating incompressible flows. While ROMs have a long history of success on certain problems with recurring dominant structures, they tend…
We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations on the torus. We prove that, for any error threshold, if the…
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…
This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…
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…
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…
We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier--Stokes equations. Our model problem is…
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…
We introduce a continuous data assimilation (downscaling) algorithm for the two-dimensional Navier-Stokes equations employing coarse mesh measurements of only one component of the velocity field. This algorithm can be implemented with a…
This paper considers the ill-posed data assimilation problem associated with hyperbolic/parabolic systems describing 2D coupled sound and heat flow. Given hypothetical data at time T > 0, that may not correspond to an actual solution of the…
Understanding time-dependent blood flow dynamics in arteries is crucial for diagnosing and treating cardiovascular diseases. However, accurately predicting time-varying flow patterns requires integrating observational data with…
We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
Data-driven methods have demonstrated strong predictive capabilities in fluid mechanics, yet most current applications still focus on simplified configurations, often characterised by statistical stationarity or limited temporal…
We propose several continuous data assimilation (downscaling) algorithms based on feedback control for the 2D magnetohydrodynamic (MHD) equations. We show that for sufficiently large choices of the control parameter and resolution and…
An algorithm for continuous data assimilation for the two- dimensional B\'enard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm developed for the Navier-Stokes equations, which allows for the…
Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is…
Understanding and predicting people flow in urban areas is useful for decision-making in urban planning and marketing strategies. Traditional methods for understanding people flow can be divided into measurement-based approaches and…