Direct numerical simulation and regularization modelling of turbulent flows on loosely coupled parallel computers using symmnetry-preserving discretizations

• Autores: Francesc Xavier Trias Miquel
• Directores de la Tesis: Asensio Oliva Llena (dir. tes.), Manel Soria Guerrero (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2006
• Idioma: español
• Tribunal Calificador de la Tesis: Antonio Lecuona Neumann (presid.), Carlos David Pérez Segarra (secret.), Cristóbal Cortés Gracia (voc.), Roel Verstappen (voc.), Eduard Egusquiza (voc.)
• Materias:
  • Matemáticas
    • Álgebra
      • Álgebra lineal
  • Física
    • Física de fluidos
      • Mecánica de fluidos
  • Ciencias tecnológicas
    • Procesos tecnológicos
      • Transferencia de calor
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• Resumen

  • The main purpose of this thesis has been to contribute to the development of numerical algorithms for the Direct Numerical Simulation (DNS) and regularization modelling of turbulent flows on loosely coupled parallel computers, In the last decades, DNS has become a very important area of contemporary fluid dynamics, because it is an essential tool to give new insights into the physics of turbulence and to provide indispensable data for future progresses on turbulence modelling. In the first chapter, a general symmetry-preserving discretization method is presented. The formulation presented intends to lead to a generalisation of the work of Verstappen and Veldman (J.Comput.Physics 187 (2003) 343) for general unstructured meshes. The operator formulation used here is based on the 'shift' transformation idea recently proposed by Kicken et al. (J.Comput.Physics 208 (2005) 704). It allows matrix operators for collocated variables to be easily transformed into matrix operators for staggered variables while preserving symmetries. The basic idea behind remains the same: mimicking the crucial symmetry properties of the underlying differential operators, i.e., the convective operator is approximated by a skew-symmetric matrix and the diffusive operator by a symmetric, positive-definite matrix. In chapter 2, a parallel Direct Schur-Fourier Decomposition (DSFD) algorithm for the direct solution of arbitrary order discrete Poisson equations on parallel computers is presented. It is based on a combination of a Direct Schur method and a Fourier Decomposition and allows to solve each Poisson equation to machine accuracy using only one global communication episode. Thus, it is perfectly well suited for loosely coupled parallel computers, that have a high network latency compared with the CPU performance. Several numerical examples illustrating its robustness and scalability on a PC cluster with a conventional 100 Mbits/s network are presented. Numerical methods presented in the first