Abstract
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.
Cain, Michael D (1999). A robust locally preconditioned semi-coarsening multigrid algorithm for the 2-D Navier-Stokes equations. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1999 -THESIS -C34.