Data assimilation in 2D viscous Burgers equation using a stabilized explicit finite difference scheme run backward in time

DOI10.1080/17415977.2021.2009476OpenAlexW4200362350MaRDI QIDQ5861356

Alfred S. Carasso

Publication date: 4 March 2022

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17415977.2021.2009476

zbMATH Keywords

numerical experimentsdata assimilationhigh Reynolds numbersstabilized explicit scheme2D time-reversed Burgers equation

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30) Quasilinear parabolic equations (35K59)

Cites Work

• Unnamed Item
• Some remarks on ill-posed problems for viscous fluids
• Computing small solutions of Burgers' equation backwards in time
• Stability estimates for Burgers-type equations backward in time
• On the stability of solutions of Navier-Stokes equations backward in time
• Uniqueness and continuous dependence criteriafor the Navier-Stokes equations
• Numerical aspects of large-time optimal control of Burgers equation
• An evolution of the back and forth nudging for geophysical data assimilation: application to Burgers equation and comparisons
• The Back and Forth Nudging algorithm for data assimilation problems : theoretical results on transport equations
• Reconstructing the past from imprecise knowledge of the present: Effective non‐uniqueness in solving parabolic equations backward in time
• Stable explicit stepwise marching scheme in ill-posed time-reversed 2D Burgers' equation
• Computing ill-posed time-reversed 2D Navier–Stokes equations, using a stabilized explicit finite difference scheme marching backward in time
• Filtered Gradient Algorithms for Inverse Design Problems of One-Dimensional Burgers Equation
• Iterative methods for data assimilation for Burgers' equation
• On a quasi-linear parabolic equation occurring in aerodynamics
• Stabilized leapfrog scheme run backward in time, and the explicit O(Δ t)² stepwise computation of ill-posed time-reversed 2D Navier–Stokes equations

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