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Splitting schemes for compressible Navier-Stokes equations

  • Author / Creator
    Roman Frolov
  • The main goal of this work is the development of all-speed numerical methods
    for the compressible Navier-Stokes equations, i.e. methods that remain
    efficient in incompressible, weakly compressible, and compressible regimes. To
    achieve this goal we propose algorithms based on the direction splitting approach
    in Cartesian and spherical coordinates. First, we consider the case
    of the Cartesian coordinates and develop a Linearized-Block-Implicit (LBI)
    scheme suitable for computations of low- and high-Mach number flows. Next,
    we introduce a second-order direction splitting method for solving the incompressible
    Navier-Stokes-Boussinesq system in spherical geometries coupled
    with the artificial compressibility regularization of the incompressible Navier-
    Stokes system. Finally, we develop a numerical method for nearly incompressible
    and weakly compressible flows in spherical shells. Numerical experiments
    confirm that the scheme retains stability and convergence for extremely low
    values of the Mach number, preserves the incompressibility of the initial data,
    and has excellent parallel performance. Thus, we hope that it may serve as a
    foundation for the next generation of dynamical cores for weather and climate
    models, as well as be useful in other applications.

  • Subjects / Keywords
  • Graduation date
    Fall 2020
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/r3-7evw-n905
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.