A Certified Reduced-Order Framework Based on Legendre Collocation for a Rayleigh-Bénard Problem
This paper presents a reduced-order framework for computing bifurcations in a Rayleigh-Bénard problem using a Legendre collocation spectral method as high-fidelity discretization. The framework combines a certified reduced basis method specialized in approximating isolated solution branches, with a...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Castilla-La Mancha |
| Repositorio: | RUIdeRA. Repositorio Institucional de la UCLM |
| OAI Identifier: | oai:ruidera.uclm.es:10578/46123 |
| Acceso en línea: | https://doi.org/10.1007/s10915-025-03037-2 https://link.springer.com/article/10.1007/s10915-025-03037-2 https://hdl.handle.net/10578/46123 |
| Access Level: | acceso abierto |
| Palabra clave: | A posteriori error estimation Bifurcation problems Legendre collocation Proper Orthogonal Decomposition Rayleigh-Bénard instability Reduced-order methods |
| Sumario: | This paper presents a reduced-order framework for computing bifurcations in a Rayleigh-Bénard problem using a Legendre collocation spectral method as high-fidelity discretization. The framework combines a certified reduced basis method specialized in approximating isolated solution branches, with a reduced-order procedure designed to calculate bifurcation points. The certified method produces, for each branch of solutions, a reduced-order model formulated as a least-squares problem that minimizes the restriction of the high-fidelity residual to a reduced basis. To ensure certification, the reduced bases are built iteratively through a POD-greedy algorithm guided by rigorous a posteriori error estimates. These estimates are defined as the quotient between the high-fidelity residual and a stability factor, which, notably, is approximated using a second reduced basis approach. The reduced-order procedure designed to approximate the bifurcation points accomplishes its purpose by performing an efficient analysis of the regularity of the high-fidelity Jacobian. Numerical results demonstrate that the proposed framework enables accurate, efficient, and reliable computation of the target bifurcation diagram without assuming any a priori knowledge of the bifurcation phenomenon. |
|---|