Stabilized reduced order models for low speed flows

• Autores: Ricardo Reyes Sotomayor
• Directores de la Tesis: Ramón Codina Rovira (dir. tes.), Sergio Rodolfo Idelson Barg (codir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2020
• Idioma: español
• Materias:
  • Matemáticas
    • Análisis numérico
      • Ecuaciones diferenciales en derivadas parciales
    • Estadística
      • Análisis multivariante
  • Física
    • Física de fluidos
      • Flujos de fluidos
      • Mecánica de fluidos
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• Resumen

  • This thesis presents the a stabilized projection-based Reduced Order Model (ROM) formulation in low speed fluid flows using a Variational Multi-Scale (VMS) approach. To develop this formulation we use a Finite Element (FE) method for the Full Order Model (FOM) and a Proper Orthogonal Decomposition (POD) to construct the basis.

    Additional to the ROM formulation, we introduce two techniques that became possible using this approach: a mesh-based hyper-reduction that uses an Adaptive Mesh Refinement (AMR) approach, and a domain decomposition scheme for ROMs.

    To illustrate and test the proposed formulation we use five different models: a convection–diffusion–reaction, the incompressible Navier–Stokes, a Boussinesq approximation, a low Mach number model, and a three-field incompressible Navier–Stokes.