Contributions to the numerical solution of heterogeneous fluid mechanics models

• Autores: Saray Busto Ulloa
• Directores de la Tesis: María Elena Vázquez Cendón (dir. tes.) , José Luis Ferrín González (codir. tes.)
• Lectura: En la Universidade de Santiago de Compostela ( España ) en 2018
• Idioma: inglés
• Tribunal Calificador de la Tesis: Alfredo Bermúdez de Castro y López-Varela (presid.) , Macarena Gómez Mármol (secret.) , Michael Dumbser (voc.)
• Programa de doctorado: Programa de Doctorado en Métodos Matemáticos y Simulación Numérica en Ingeniería y Ciencias Aplicadas por la Universidad de A Coruña; la Universidad de Santiago de Compostela y la Universidad de Vigo
• Menciones:
  • Internacional
• Calificación: Sobresaliente Cum Laude
• Enlaces
  • Tesis en acceso abierto en: MINERVA
• Resumen

  • A high order projection hybrid finite volume – finite element method is developed to solve incompressible and compressible low Mach number flows. Furthermore, turbulent regimes are also considered thanks to the k–ε model. The unidimensional advection-diffusion-reaction equation is used to construct, analyze and assess high order finite volume schemes. Two families of methods are studied: Kolgan-type schemes and ADER methodology. A modification of the last one is proposed providing a new numerical method called Local ADER. The designed methods are extended to solve the transport-diffusion stage of the three-dimensional projection method. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the schemes and to assess the performance of the method on several realistic test problems.