Solution Acceleration and Accuracy Improvements for Navier-Stokes Solvers
Hager, James Onslow
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https://hdl.handle.net/2142/72372
Description
Title
Solution Acceleration and Accuracy Improvements for Navier-Stokes Solvers
Author(s)
Hager, James Onslow
Issue Date
1994
Doctoral Committee Chair(s)
Lee, Ki D.
Department of Study
Aeronautical and Astronautical Engineering
Discipline
Aeronautical and Astronautical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Aerospace
Engineering, Mechanical
Abstract
There are two competing goals in computational fluid dynamics: high solution accuracy, and low computational cost. In the present research, three major tasks were performed to improve the solution accuracy and increase the convergence of steady-state solutions: (1) investigate the sources of inaccuracies and the causes of slow convergence, (2) develop new algorithms that eliminate these problems, and (3) combine different solution acceleration techniques to produce a robust and efficient flow solver.
Two modeling techniques were found to contribute to the power behavior of current high-resolution upwind schemes. The grid alignment problem, where the Euler flow on each side of a discontinuity becomes decoupled when the grid is aligned with the flow, can degrade the solution quality and slow the convergence of Euler, and high-Reynold's number Navier-Stokes, calculations. The problem can be alleviated by adding artificial viscosity to Roe's scheme using an entropy-fix-like correction.
The second modeling technique that was found to contribute to poor accuracy is the current method of imposing boundary conditions using ghost cells: they do not take into account the limiters that are used during the extrapolation. Because solid-wall boundary conditions introduce a discontinuity, the values that are extrapolated to the wall boundary may not satisfy the boundary conditions. A new technique was developed, where the extrapolated values are corrected to satisfy the boundary conditions. Improved solution accuracy was obtained while not affecting the convergence.
Finally, multigrid (MG), generalized minimum residual (GMRES), and Jacobian freezing were shown to be effective solution acceleration techniques when applied in combination: the time to obtain a solution can be reduced by a factor of seven, and the scheme is more robust. However, MG and GMRES did not remove the extremely slow final convergence-rates encountered with viscous solutions. This suggests that there is an additional mismatch between the interior flow field calculation and the Navier-Stokes wall boundary conditions. Therefore, additional research must be performed to determine the cause of the poor convergence and to develop appropriate solution techniques.
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