Accession Number : ADA323965
Title : Evaluation of Local Preconditioners for Multigrid Solutions of the Compressible Euler Equations.
Descriptive Note : Master's thesis,
Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
Personal Author(s) : McCann, Barrett T.
PDF Url : ADA323965
Report Date : 18 APR 1997
Pagination or Media Count : 63
Abstract : The goal of this study is to examine and compare the effectiveness of two local preconditioners, when used in a multigrid algorithm, in accelerating the rate of convergence to an accurate steady solution of the two-dimensional compressible Euler equations. In this study, both the matrix preconditioner developed by Turkel and the block-Jacobi preconditioner are tested. While both preconditioners exhibit similar damping properties for error modes which are high-frequency in both coordinate directions (i.e., high-high modes), it is known that the Turkel preconditioner provides significantly better low-frequency propagation. In this thesis, this improved low-frequency propagation is shown to also improve (albeit nominally) the damping for modes which are high-frequency in only one direction (high-low and low-high modes). Thus, an important aspect of this work is assessing how improved low-frequency propagation can enhance multigrid convergence rates for preconditioned iterative techniques with similar damping properties. The results of first- and second-order numerical studies in a full-coarsening multigrid algorithm over several low freestream Mach numbers and with different boundary conditions indicate that the superior low-frequency propagation characteristics of Turkel's preconditioner result in better convergence rates than the block-Jacobi preconditioner. In addition, conclusions are drawn about the usefulness of multigrid with and without preconditioning, as well as the relative accuracy of the different solution methods used.
Descriptors : *COMPRESSIBLE FLOW, *EULER EQUATIONS, ALGORITHMS, MATRICES(MATHEMATICS), ACCURACY, THESES, FLOW VISUALIZATION, GRIDS(COORDINATES), FLOW FIELDS, CONVERGENCE, MACH NUMBER, INVISCID FLOW, FREE STREAM, ITERATIONS, HYPERBOLIC DIFFERENTIAL EQUATIONS.
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE