Enhancing nonlinear solvers for the Navier–Stokes equations with continuous (noisy) data assimilation
We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier–Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is incorporated/assimilated into the solution through a nudging term addition t...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::88aa1931b3d4f65476d119c08a743856 |
| Acceso en línea: | https://hdl.handle.net/11441/156142 https://doi.org/10.1016/j.cma.2024.116903 |
| Access Level: | acceso abierto |
| Palabra clave: | Navier Stokes equations Picard iteration Newton iteration Continuous data assimilation |
| Sumario: | We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier–Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is incorporated/assimilated into the solution through a nudging term addition to the Picard iteration that penalized the difference between the coarse mesh interpolants of the true solution and solver solution, analogous to how continuous data assimilation (CDA) is implemented for time dependent PDEs. This was considered in the paper (Li et al. 2023), and we extend the methodology by improving the analysis to be in the norm instead of a weighted norm where the weight depended on the coarse mesh width, and to the case of noisy measurement data. For noisy measurement data, we prove that the CDA-Picard method is stable and convergent, up to the size of the noise. Numerical tests illustrate the results, and show that a very good strategy when using noisy data is to use CDA-Picard to generate an initial guess for the classical Newton iteration. |
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