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General-Domain Compressible Navier-Stokes Solvers Exhibiting Quasi-Unconditional Stability and High Order Accuracy in Space and Time


Cubillos-Moraga, Max Anton (2015) General-Domain Compressible Navier-Stokes Solvers Exhibiting Quasi-Unconditional Stability and High Order Accuracy in Space and Time. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9WW7FKW.


This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Navier-Stokes equations; quasi-unconditional stability; high-order accuracy; alternating direction implicit
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Awards:The W. P. Carey & Co., Inc., Prize In Applied Mathematics, 2015
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bruno, Oscar P.
Thesis Committee:
  • Bruno, Oscar P. (chair)
  • Blanquart, Guillaume
  • Colonius, Tim
  • Owhadi, Houman
Defense Date:22 May 2015
Record Number:CaltechTHESIS:05082015-184801592
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8851
Deposited By: Max Cubillos-Moraga
Deposited On:05 Jun 2015 18:23
Last Modified:25 Oct 2023 21:10

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