Error analysis of a residual-based stabilization-motivated POD-ROM for incompressible flows
This article presents error bounds for a velocity–pressure segregated POD reduced order model discretization of the Navier–Stokes equations. The stability is proven in L∞(L2) and energy norms for velocity, with bounds that do not depend on the viscosity, while for pressure it is proven in a semi-nor...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/154021 |
| Acceso en línea: | https://hdl.handle.net/11441/154021 https://doi.org/10.1016/j.cma.2022.115627 |
| Access Level: | acceso abierto |
| Palabra clave: | Navier–Stokes equations Residual-based stabilization Proper orthogonal decomposition Reduced order models Incompressible flows Numerical analysis |
| Sumario: | This article presents error bounds for a velocity–pressure segregated POD reduced order model discretization of the Navier–Stokes equations. The stability is proven in L∞(L2) and energy norms for velocity, with bounds that do not depend on the viscosity, while for pressure it is proven in a semi-norm of the same asymptotic order as the L2 norm with respect to the mesh size. The proposed estimates are calculated for the two flow problems, the flow past a cylinder and the lid-driven cavity flow. Their quality is then assessed in terms of the predicted logarithmic slope with respect to the velocity POD contribution ratio. We show that the proposed error estimates allow a good approximation of the real errors slopes and thus a good prediction of their rate of convergence. |
|---|