POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution
In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods. Our set of snapshots includes the velocity approximation at t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/714220 |
| Acceso en línea: | http://hdl.handle.net/10486/714220 https://dx.doi.org/10.1137/22M1503853 |
| Access Level: | acceso abierto |
| Palabra clave: | grad-div stabilization incompressible Navier-Stokes equations proper orthogonal decomposition reduced order models robust pointwise in time estimates snapshots of the temporal derivative Matemáticas |
| Sumario: | In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods. Our set of snapshots includes the velocity approximation at the initial time from a full order mixed finite element method (FOM) together with approximations to the time derivative at different times. The approximation at the initial velocity can be replaced by the mean value of the velocities at the different times so that when implementing the method to the fluctuations, as done mostly in practice, only approximations to the time derivatives are included in the set of snapshots. For the POD method we study the differences between projecting onto L2 and H1. In both cases pointwise in time error bounds can be proved. Including grad-div stabilization in both the FOM and the POD methods, error bounds with constants independent of inverse powers of the viscosity can be obtained |
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