Ofertes treballs fi d'estudis

Títol: High-order methods for the resolution of the compressible Navier-Stokes and Shallow-Water equations

Director/a: Miro Jane, Arnau

Email del professor/a: arnau.miro@upc.edu

Departament del professor/a: 748-FIS

Codirector/a: Garcia Melendo, Enrique jose

Email del codirector/a: enrique.garcia.melendo@upc.edu

Departament del professor/a: 748-FIS

• 2010 - GRAU EN ENGINYERIA EN TECNOLOGIES AEROESPACIALS
• 2010 - GRAU EN ENGINYERIA EN VEHICLES AEROESPACIALS
• 2014 - MÀSTER UNIVERSITARI EN ENGINYERIA AERONÀUTICA

Identificador de l'oferta: 205-06428

Modalitat: Universitat

Possibilitat de beca/finançament: No

Paraules clau:

Descripció:

Hyperbolic PDEs such as the compressible Navier-Stokes or Shallow-Water equations are representative of atmospheric flows and internal aerodynamic flows among others. They present challenges in their numerical integration, in particular, the resolution of their characteristics leads to discontinuous solutions that must be taken into account when performing their numerical integration through a Riemann solver. Moreover, recent methods employ higher order polynomial reconstructions to achieve a more accurate solution. These methods coupled with a Riemann solver have been successfully used to provide solutions to these PDEs.

Objectius:

This study aims to develop and compare different numerical schemes (flux reconstruction, high order FVM through WENO schemes) with Riemann solvers (either exact or approximate), and assess their suitability towards the solution. Flows to be analyzed could be the SOD problem, atmospheric flows, nozzle flows (compressible) or dam break, drop or 2D vortex (Shallow-Water). A first analysis will be done in 1D and later, if time allows, a 2D analysis will

Tasques a realitzar / Característiques:

- Literature survey on high-order methods and Riemann solvers - Familiarization with FVM-WENO scheme in 1D - Familiarization with Flux Reconstruction scheme in 1D - Implementation of 2D compressible FVM-WENO - [optional] Implementation of 2D compressible/shallow water Flux Reconstruction - Study of test cases to be defined (by preference of the student)

Tema: ENGINYERIA AERONÀUTICA

Tipus: Estudi

Càrrega de treball:

300h GRETA i MUEA | 600h GREVA

Requisits:

Knowledge of programming languages is recommended (python in particular) Motivation and passion for fluid dynamics and numerical models

Temàtica ambiental: No

Confidencial (informatiu): No

Ambit de cooperació: No

Publicació: 11/12/2025

Caducitat: 01/06/2026