Data assimilation for the Navier-Stokes equations using local observables
| Autor: | Animikh Biswas, Zachary Bradshaw, Michael S. Jolly |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
010102 general mathematics
Mathematics::Analysis of PDEs Observable Torus 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics Data assimilation Mathematics - Analysis of PDEs Modeling and Simulation Primary 35Q30 76B75 34D06 Secondary 35Q35 35Q93 0103 physical sciences FOS: Mathematics Applied mathematics Navier stokes Synchronization algorithm 0101 mathematics Navier–Stokes equations Analysis Mathematics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2008.06949 |
| Popis: | 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 reference flow is analytic with sufficiently large analyticity radius, then it can be recovered within that threshold. Numerical computations are included to demonstrate the effectiveness of this approach, as well as variants with data on moving subdomains. In particular, we demonstrate numerically that machine precision synchronization is achieved for mobile data collected from a small fraction of the domain. Comment: 11 figures, 27 pages |
| Databáze: | OpenAIRE |
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