Title page for ETD etd-10132005-152548


Type of Document Dissertation
Author Ajmani, Kumud
URN etd-10132005-152548
Title Preconditioned conjugate gradient methods for the Navier-Stokes equations
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Ng, Fai Committee Chair
Moses, Hal L. Committee Member
Nelson, Douglas J. Committee Member
Ribbens, Calvin J. Committee Member
Vick, Brian L. Committee Member
Keywords
  • Conjugate gradient methods.
  • Navier-Stokes equations.
Date of Defense 1991-11-03
Availability restricted
Abstract

A generalized Conjugate Gradient like method is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. Preconditioning techniques are employed with the Conjugate Gradient like method to enhance the stability and convergence rate of the overall iterative method. The superiority of the new solver is established by comparisons with a conventional Line GaussSeidel Relaxation (LGSR) solver. Comparisons are based on 'number of iterations required to converge to a steady-state solution' and 'total CPU time required for convergence'. Three test cases representing widely varying flow physics are chosen to investigate the performance of the solvers. Computational test results for very low speed (incompressible flow over a backward facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (shockon- shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the 1vfach 0.1 case, speed-up factors of 30 (in terms of iterations) and 20 (in terms of CPU time) are found in favor of the new solver when compared with the LGSR solver. The corresponding speed-up factors for the transonic flow case are 20 and 18, respectively. The hypersonic case shows relatively lower speed-up factors of 5 and 4, respectively. This study reveals that preconditioning can greatly enhance the range of applicability and improve the performance of Conjugate Gradient like methods.

Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
[BTD] LD5655.V856_1991.A452.pdf 5.88 Mb 00:27:11 00:13:59 00:12:14 00:06:07 00:00:31
[BTD] next to an author's name indicates that all files or directories associated with their ETD are accessible from the Virginia Tech campus network only.

Browse All Available ETDs by ( Author | Department )

dla home
etds imagebase journals news ereserve special collections
virgnia tech home contact dla university libraries

If you have questions or technical problems, please Contact DLA.