Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional
aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large
number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the
early stages of the design process, a fast and robust flow solution algorithm is necessary.
This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional
Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model.
The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous
approximation terms (SATs) to enforce block interface coupling and boundary conditions.
The discrete equations are solved iteratively with an inexact-Newton method, while the linear
system at each Newton iteration is solved using the flexible Krylov
subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the
correspondence of the current algorithm with several established flow solvers.
The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results.
Using 128 processors, deep convergence is obtained in under 90 minutes.
The solution of transonic flow over the Common Research Model wing-body geometry with
grids with up to 150 million nodes exhibits the expected grid
convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop,
with the algorithm producing solutions that compare favourably with several widely used flow solvers.
The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT
spatial discretization, which can be readily extended to high order, in combination with
the Newton-Krylov-Schur iterative method to produce a powerful parallel algorithm for the numerical solution of
the Reynolds-averaged Navier-Stokes equations.
The algorithm can efficiently solve the flow over a range of clean geometries, making it suitable for
use at the core of an optimization algorithm.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/43684 |
| Date | 13 January 2014 |
| Creators | Osusky, Michal |
| Contributors | Zingg, David W. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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