Immersed boundary methods for fixed and moving bodies using high-order solvers

• Autores: Jiaqing Kou
• Directores de la Tesis: Esteban Ferrer Vaccarezza (dir. tes.), Soledad Le Clainche Martínez (codir. tes.)
• Lectura: En la Universidad Politécnica de Madrid ( España ) en 2022
• Idioma: español
• Programa de doctorado: Programa de Doctorado en Ingeniería Aeroespacial por la Universidad Politécnica de Madrid
• Materias:
  • Matemáticas
    • Análisis numérico
      • Ecuaciones diferenciales en derivadas parciales
  • Física
    • Física de fluidos
      • Mecánica de fluidos
  • Ciencias tecnológicas
    • Ingeniería y tecnología aeronáuticas
• Enlaces
  • Tesis en acceso abierto en: Archivo Digital UPM
• Resumen

  • This thesis by compendium proposed immersed boundary method for fixed and moving bodies based on high-order solvers. It mainly included methods based on volume penalization, flux reconstruction, and eigensolution analysis. The proposed solutions have contributed to the development of high-order solvers that simulate flow past obstacles based on non-conforming grids, which have been validated by test cases with increasing complexity. Moreover, the doctoral work presented applications that go beyond the state of art, by transferring the knowledge and implementation to the NUMECA's OMNIS software platform that allows industry-level simulation based on the proposed method. Main contributions are summarized as follows:

    Firstly, a data-driven method to perform eigensolution analyses and quantify numerical errors in a non-intrusive manner is proposed, where only solution snapshots from numerical simulations are required to quantify the numerical errors (dispersion and diffusion) in time and/or space.

    Secondly, immersed boundary method for high-order flux reconstruction based on volume penalization is proposed. This work combines the numerical advantages of the high-order flux reconstruction method and the simplicity of the mesh generation (or lack thereof) of the immersed boundary method for steady and unsteady problems over moving geometries.

    Thirdly, eigensolution and non-modal analyses for immersed boundary method based on volume penalization for the high-order methods are presented. Through a semi-discrete analysis, we find that the inclusion of immersed boundary adds additional dissipation without changing significantly the dispersion of the original numerical discretization. From a stability point view, the variation of penalty parameter can be analyzed based on a fully-discrete analysis, which leads to practical guidelines on the selection of penalization parameter. As an alternative, we propose to include a second-order term in the solid for the no-slip wall boundary condition.

    Finally, the industrial applications of the proposed method are shown, through simulating flow past fixed geometries based on the OMNIS software platform.