Evaluation of Local Preconditioners for Multigrid Solutions of the Compressible Euler Equations.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 18, 1997
- Accession Number
- ADA323965
Entities
People
- Barrett T. Mccann
Organizations
- Air Force Institute of Technology