Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations

DOI10.3934/era.2020113zbMath1468.65141arXiv2006.07295OpenAlexW3094051949MaRDI QIDQ2030407

Camille Zerfas, Adam Larios, Leo G. Rebholz, Duygu Vargun, Matthew Gardner

Publication date: 7 June 2021

Published in: Electronic Research Archive (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.07295

zbMATH Keywords

Navier-Stokes equationsdata assimilationvelocity-vorticity scheme

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (10)

Continuous data assimilation algorithm for the two dimensional Cahn-Hilliard-Navier-Stokes system ⋮ The bleeps, the sweeps, and the creeps: convergence rates for dynamic observer patterns via data assimilation for the 2D Navier-Stokes equations ⋮ Dynamically learning the parameters of a chaotic system using partial observations ⋮ High Order Efficient Algorithm for Computation of MHD Flow Ensembles ⋮ Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes ⋮ Deferred correction method for the continuous data assimilation model ⋮ Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: the 2D Navier-Stokes equation paradigm ⋮ Finite time synchronization of the continuous/discrete data assimilation algorithms for Lorenz 63 system based on the back and forth nudging techniques ⋮ Sensitivity analysis for the 2D Navier-Stokes equations with applications to continuous data assimilation ⋮ Regularity and convergence results of the velocity-vorticity-Voigt model of the 3D Boussinesq equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations
• Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations
• On the accuracy of the rotation form in simulations of the Navier-Stokes equations
• Continuous data assimilation for the 3D primitive equations of the ocean
• On well-posedness of a velocity-vorticity formulation of the stationary Navier-Stokes equations with no-slip boundary conditions
• Downscaling data assimilation algorithm with applications to statistical solutions of the Navier-Stokes equations
• Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations
• Theory and practice of finite elements.
• Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier-Stokes equations
• Continuous data assimilation reduced order models of fluid flow
• Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier-Stokes equations
• Continuous data assimilation for the 2D Bénard convection through velocity measurements alone
• On conservation laws of Navier-Stokes Galerkin discretizations
• Continuous data assimilation using general interpolant observables
• Natural vorticity boundary conditions on solid walls
• Continuous data assimilation for the three-dimensional Navier–Stokes-α model
• A second-order ensemble method based on a blended backward differentiation formula timestepping scheme for time-dependent Navier-Stokes equations
• On Error Analysis for the 3D Navier–Stokes Equations in Velocity-Vorticity-Helicity Form
• The Scott-Vogelius finite elements revisited
• Uniform-in-Time Error Estimates for the Postprocessing Galerkin Method Applied to a Data Assimilation Algorithm
• Grad-div stablilization for Stokes equations
• Data Assimilation in Large Prandtl Rayleigh--Bénard Convection from Thermal Measurements
• Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study
• Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations
• Parameter Recovery for the 2 Dimensional Navier--Stokes Equations via Continuous Data Assimilation
• A Data Assimilation Algorithm: the Paradigm of the 3D Leray-α Model of Turbulence
• Spectral Filtering of Interpolant Observables for a Discrete-in-Time Downscaling Data Assimilation Algorithm
• Continuous data assimilation with stochastically noisy data
• Data Assimilation
• On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
• A Computational Study of a Data Assimilation Algorithm for the Two-dimensional Navier-Stokes Equations
• The Mathematical Theory of Finite Element Methods
• A Discrete Data Assimilation Scheme for the Solutions of the Two-Dimensional Navier--Stokes Equations and Their Statistics
• Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates

This page was built for publication: Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations