Related papers: Data assimilation for slightly compressible flow

Various types of measurement techniques, such as Light Detection and Ranging (LiDAR) devices, anemometers, and wind vanes, are extensively utilized in wind energy to characterize the inflow. However, these methods typically gather data at…

Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact…

For the 2D incompressible Navier-Stokes equations, with given hypothetical non smooth data at time $T > 0 $that may not correspond to an actual solution at time $T$, a previously developed stabilized backward marching explicit leapfrog…

Anomalous dissipation, the persistence of a finite mean kinetic energy dissipation as the Reynolds number tends to infinity, occurs in flows with sufficiently spatially rough velocity fields. Compressible turbulence adds further anomalous…

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…

In this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity…

Smoothed particle hydrodynamics is a particle-based, fully Lagrangian, method for fluid-flow simulations. In this work, fundamental concepts of the method are first briefly recalled. Then, we present a thorough comparison of three different…

This paper improves the spectrally-filtered direct-insertion downscaling method for discrete-in-time data assimilation by introducing a relaxation parameter that overcomes a constraint on the observation frequency. Numerical simulations…

A challenge arising from the local Bayesian assimilation of data in an atmospheric flow simulation is the imbalances it may introduce. Acoustic fast-mode imbalances of the order of the slower dynamics can be negated by employing a blended…

This paper applies variational data assimilation to inundation problems governed by the shallow water equations with wetting and drying. The objective of the assimilation is to recover an unknown time-varying wave profile at an open ocean…

Particle methods play an important role in computational fluid dynamics, but they are among the most difficult to implement and solve. The most common method is smoothed particle hydrodynamics, which is suitable for problem settings that…

Purpose: This study aims to assess the accuracy of degree adaptive strategies in the context of incompressible Navier-Stokes flows using the high order hybridisable discontinuous Galerkin (HDG) method. Design/methodology/approach: The work…

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

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…

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…

Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…

Interpretable representation learning is a central challenge in modern machine learning, particularly in high-dimensional settings such as neuroimaging, genomics, and text analysis. Current methods often struggle to balance the competing…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

We review an algorithm developed for parameter estimation within the Continuous Data Assimilation (CDA) approach. We present an alternative derivation for the algorithm presented in a paper by Carlson, Hudson, and Larios (CHL, 2021). This…