An enhanced particle finite element method with special emphasis on landslides and debris flows

• Autores: Pablo Becker
• Directores de la Tesis: Eugenio Oñate Ibáñez de Navarra (dir. tes.), Sergio Rodolfo Idelson Barg (codir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2015
• Idioma: español
• Tribunal Calificador de la Tesis: Ramón Codina Rovira (presid.), Rainald Löhner (secret.), Mario Storti (voc.)
• Materias:
  • Matemáticas
    • Análisis numérico
  • Física
    • Mecánica
      • Mecánica de medios continuos
  • Ciencias de la tierra y del espacio
    • Ciencias de la atmósfera
      • Simulación numérica
  • Ciencias tecnológicas
    • Tecnología de la construcción
      • Mecánica del suelo (construcción)
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• Resumen

  • This thesis presents the implementation of a solution strategy to solve multi-material problems. Thealgorithm is based on the Particle Finite Element Method, second generation (PFEM-2). It consists on using a set of Lagrangian particles to convect properties, together with a fixed Finite Element (FE) mesh to solve the Lagrangian equations. One of the main goals in this research is to create an algorithm that is as general as possible, in order to be capable of solving a wide variety of problems. The resulting method is flexible enough as to solve both multi-fluid flows and Fluid-Structure Interaction (FSI) problems with minimum changes.

    The work developed in this thesis takes the single fluid PFEM-2 method as the starting point. This strategy uses concepts of both Lagrangian and Eulerian strategies. In order to tackle the large deformation problems, a set of Lagrangian particles with no connectivities are used to convect the properties. Having convected the particles, information is projected to a fixed FE mesh, where the Lagrangian equations are solved. Finally the corrections are sent back to the particles.

    In order to generalize the PFEM-2 to tackle multi-phase problems, sharp interfaces are defined, at which the material properties are considered discontinuous. Since this leads to discontinuities in the unknowns, the Finite Element space is enriched at those interfaces, later using a condensation procedure to maintain the number of unknowns in the system of equations. On the other hand, the convection strategy for the particles is also modified to take into account the change in the material properties, leading to a better approximation. The numerical examples show the accuracy on both multi-fluid and FSI problems.

    The final chapter of this thesis covers the implementation of a strategy to solve landslides and debris flows. All the tools developed in this thesis, together with special customizations for this particular problem are used. The numerical experiments show that the physics of the problem is correctly captured, with good correlation against experimental results.