Subgrid scale stabilized finite elements for low speed flows.

• Autores: Príncipe Rubio Ricardo Javier
• Directores de la Tesis: Ramón Codina Rovira (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2008
• Idioma: español
• Tribunal Calificador de la Tesis: Sergio Rodolfo Idelson Barg (presid.), Guillaume Houzeaux (secret.), Bernard A. Schrefler (voc.), Guillermo Hauke Bernardos (voc.), Volker Gravemeier (voc.)
• Materias:
  • Matemáticas
    • Análisis numérico
  • Física
    • Mecánica
      • Mecánica de fluidos
  • Ciencias tecnológicas
    • Tecnología de la construcción
      • Presas
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• Resumen

  • A general description of a fluid flow involves the solution of the compressible Navier-Stokes equations, a very complex problem whose mathematical structure is not well understood, Therefore, simplified models can be derived by asymptotic analysis under some assumptions on the problem, made in terms of dimensionless parameters that measure the relative importance of different physical processes. Low speed flows can be described by several models including the incompressible Navier Stokes equations whose mathematical structure is much better understood. However many important flows cannot be considered as incompressible, even at low speed, due to the presence of thermal effects. In such kind of problems another class of simplified equations can be derived: the Boussinesq equations and the Low Mach number equations.

    The complexity of these mathematical problems makes their numerical solution very difficult. For these problems the standard finite element method is unstable, what in practice means that node to node oscillations of non physical nature may appear in the numerical solution. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective terms. Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modelling of the subgrid scale and its influence leads to a modified coarse scale problem that now can be shown to be stable.

    Although stabilization techniques are nowadays widely used, important problems remain open. Contributing to their understanding, several aspects of the subgrid scale modelling are analyzed in this work. For second order scalar problems, the dependence of the subgrid scale on the mesh size, in the general anisotropic case, is clarified. These ideas are extended to systems of equations to consider the Os