Solving the Navier–Stokes problem using large-scale optimization techniques
This thesis explores the application of large-scale optimization techniques to solve the Navier-Stokes equations for incompressible fluids in the steady-state regime. Due to the nonlinear and coupled nature of these equations, traditional solvers often face convergence difficulties and suffer from l...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/447014 |
| Acceso en línea: | https://hdl.handle.net/2117/447014 |
| Access Level: | acceso abierto |
| Palabra clave: | Navier-Stokes equations Mathematical optimization Computational fluid dynamics Navier-Stokes Stokes Large-scale Convex optimization Proximal gradient Dual ascent Augmented Lagrangian method Equacions de Navier-Stokes Optimització matemàtica Dinàmica de fluids computacional Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics Àrees temàtiques de la UPC::Enginyeria mecànica::Mecànica de fluids |
| Sumario: | This thesis explores the application of large-scale optimization techniques to solve the Navier-Stokes equations for incompressible fluids in the steady-state regime. Due to the nonlinear and coupled nature of these equations, traditional solvers often face convergence difficulties and suffer from low computational efficiency. As an alternative, this work investigates convex optimization techniques and algorithms, with a focus on the proximal gradient method, dual ascent, and the augmented Lagrangian method, with the aim of developing more scalable solvers. The finite element method was used to discretize the problem, and the implementations were made in MATLAB within the Swan framework. The methodology was first validated on simpler, structurally similar problems (linear elasticity and Stokes flow) before being applied to the Navier-Stokes equations. The developed methods were compared with monolithic formulations in terms of accuracy, computational cost, memory usage, and convergence behaviour. The results show that, although optimization-based solvers do not always outperform monolithic approaches in computational time, they require fewer memory resources, making them particularly well-suited for large-scale problems and a promising alternative for solving fluid dynamics systems. |
|---|