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 …

A turbulence model for smoothed particle hydrodynamics

JJ Monaghan - European Journal of Mechanics-B/Fluids, 2011 - Elsevier
The aim of this paper is to describe a turbulence model for the particle method Smoothed
Particle Hydrodynamics (SPH). The model makes few assumptions, conserves linear and …

On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model

B Levant, F Ramos, ES Titi - 2010 - projecteuclid.org
Abstract The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid has been
recently proposed as a regularization of the 3D Navier-Stokes equations for the purpose of …

α regularization of the POD-Galerkin dynamical systems of the Kuramoto–Sivashinsky equation

F Sabetghadam, A Jafarpour - Applied Mathematics and Computation, 2012 - Elsevier
In order to improve the dynamics and stability of the POD-Galerkin models of strongly-stiff
systems, an α-like regularization is suggested and assessed in the present article. In this …

A data assimilation algorithm: The paradigm of the 3D Leray-α model of turbulence

A Farhat, E Lunasin, ES Titi - Partial differential equations arising …, 2019 - books.google.com
Data assimilation is a methodology to estimate weather or ocean variables by combining
(synchronizing) information from observational data with a numerical dynamical (forecast) …

Analysis of a general family of regularized Navier–Stokes and MHD models

M Holst, E Lunasin, G Tsogtgerel - Journal of Nonlinear Science, 2010 - Springer
We consider a general family of regularized Navier–Stokes and Magnetohydrodynamics
(MHD) models on n-dimensional smooth compact Riemannian manifolds with or without …

On the convergence rate of grad-div stabilized Taylor–Hood to Scott–Vogelius solutions for incompressible flow problems

A Linke, LG Rebholz, NE Wilson - Journal of Mathematical Analysis and …, 2011 - Elsevier
It was recently proven in Case et al.(2010)[2] that, under mild restrictions, grad-div stabilized
Taylor–Hood solutions of Navier–Stokes problems converge to the Scott–Vogelius solution …

The Navier–Stokes–Voight model for image inpainting

MA Ebrahimi, E Lunasin - The IMA Journal of Applied …, 2013 - academic.oup.com
In this paper, we investigate the advantages of the 2D Navier–Stokes–Voight (NSV)
turbulence model for use in algorithms and explore its limits in the context of image …

Toward consistent subgrid momentum closures in ocean models

S Danilov, S Juricke, A Kutsenko, M Oliver - Energy transfers in …, 2019 - Springer
State-of-the-art global ocean circulation models used in climate studies are only passing the
edge of becoming “eddy-permitting” or barely eddy-resolving. Such models commonly suffer …

On the rate of convergence of the two-dimensional α-models of turbulence to the Navier–Stokes equations

Y Cao, ES Titi - Numerical Functional Analysis and Optimization, 2009 - Taylor & Francis
Rates of convergence of solutions of various two-dimensional α-regularization models,
subject to periodic boundary conditions, toward solutions of the exact Navier–Stokes …