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

  • Spherical coordinates
  • Navier-Stokes equations
  • Numerical methods
  • Direction splitting
  • Mach number

• Graduation date

  Fall 2020

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-7evw-n905

• License

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