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In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…
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…
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…
The paper presents a new state estimation algorithm for a bilinear equation representing the Fourier- Galerkin (FG) approximation of the Navier-Stokes (NS) equations on a torus in R2. This state equation is subject to uncertain but bounded…
Data assimilation is a vital component in modern global medium-range weather forecasting systems to obtain the best estimation of the atmospheric state by combining the short-term forecast and observations. Recently, AI-based 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…
Lagrangian data assimilation of complex nonlinear turbulent flows is an important but computationally challenging topic. In this article, an efficient data-driven statistically accurate reduced-order modeling algorithm is developed that…
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…
This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…
Motivated by the challenge of moment recovery in hydrodynamic approximation in kinetic theory, we propose a data-driven approach for the hydrodynamic models. Inspired by continuous data assimilation, our method introduces a relaxation-based…
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…
The present study proposes a sensor selection method based on the proximal splitting algorithm and the A-optimal design of experiment using the alternating direction method of multipliers (ADMM) algorithm. The performance of the proposed…
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…
In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…
Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…
We demonstrate a formulation of the Azouani-Olson-Titi (AOT) algorithm in the MPAS-Ocean implementation of the primitive equations of the ocean, presenting global ocean simulations with realistic coastlines and bathymetry. We observe an…
Previous works have shown that the small-scale information of incompressible homogeneous isotropic turbulence (HIT) is fully recoverable as long as sufficient large-scale structures are continuously enforced through temporally continuous…
Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
Based on a previously introduced downscaling data assimilation algorithm, which employs a nudging term to synchronize the coarse mesh spatial scales, we construct a determining map for recovering the full trajectories from their…