A robust locally preconditioned semi-coarsening multigrid algorithm for the 2-D Navier-Stokes equations

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to digital@library.tamu.edu, referencing the URI of the item.Includes bibliographical references (leaves 58-60).Issued also on microfiche from Lange Micrographics.The goal of this thesis is to develop an efficient and robust locally preconditioned semi-coarsening multigrid algorithm for the two-dimensional Navier-stokes equations. This thesis examines the performance of the multigrid algorithm with local preconditioning for an upwind discrimination of the Navier-stokes equations. A block Jacobi iterative scheme is used because of its high frequency error mode damping ability. At low Mach numbers, the performance of a flux preconditioned is investigated. The flux preconditioned utilizes a new limiting technique based on local information that was developed by Siu. Full-coarsening and semi-coarsening are examined as well as the multigrid V-cycle and full multigrid. The numerical tests were performed on a NACA 0012 airfoil at a range of Mach numbers. The tests show that semi-coarsening with flux preconditioning is the most efficient and robust combination of coarsening strategy and iterative scheme - especially at low Mach numbers