Variational multiscale stabilization and local preconditioning for compressible flow

• Autores: Margarida Moragues Ginard
• Directores de la Tesis: Mariano Vázquez (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2016
• Idioma: inglés
• Tribunal Calificador de la Tesis: Alvaro Coutinho (presid.), Sonia Fernández Méndez (secret.), Johan Hoffman (voc.)
• Materias:
  • Matemáticas
    • Análisis y análisis funcional
      • Ecuaciones diferenciales en derivadas parciales
    • Análisis numérico
  • Física
    • Mecánica
      • Mecánica de fluidos
  • Ciencias de la tierra y del espacio
    • Ciencias de la atmósfera
      • Simulación numérica
• Enlaces
  • Tesis en acceso abierto en: TDX
• Resumen

  • This thesis is about the stabilization of the numerical solution of the Euler and Navier- Stokes equations of compressible flow. When simulating numerically the flow equations, if no stabilization is added, the solution presents non-physical (but numerical) oscillations. For this reason the stabilization of partial differential equations and of the fluid dynamics equations is of great importance. In the framework of the so-called variational multiscale stabilization, we present here a stabilization method for compressible flow. The method assessment is done first of all on a batch of academical examples for different Mach numbers, for viscous and inviscid, steady and transient flow. Afterwards the method is applied to atmospheric flow simulations. To this end we solve the Euler equations for dry and moist atmospheric flow. In the presence of moisture a set of transport equations for water species should be solved as well. This domain of application is a real challenge from the stabilization point of view because the correct amount of stabilization must be added in order to preserve the physical properties of the atmospheric flow. At this point, in order to even improve our method, we turn towards local preconditioning. Local preconditiong permits to reduce the stiffness problems that present the flow equations and cause a bad and slow convergence to the solution. With this purpose in mind we combine our stabilization method with local preconditioning and present a stabilization method for the preconditioned Navier-Stokes equations of compressible flow, that we call P-VMS. This method is tested over several examples at different Mach numbers and proves a significant improvement not only in the convergence to the solution but also in the accuracy and robustness of the method. Finally, the benefits of P-VMS are theoretically assessed using Fourier stability analysis. As a result of this analysis a modification on the computation of the time step is done even improving the convergence of the method.