Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Mechanical Engineering

Committee Director

Ayodeji O. Demuren

Committee Member

Arthur C. Taylor, III

Committee Member

Thomas L. Jackson

Committee Member

Surendra N. Tiwari


Recent progress in Computational Fluid Dynamics is encouraging scientists to look at fine details of flow physics of problems in which natural unsteady phenomena have hitherto been neglected. The acceleration methods that have proven very successful in steady state computations can be explored for time dependent computations. In this work, an efficient multigrid methods is developed to solve the time-dependent Euler and Navier-Stokes equations. The Beam-Warming ADI method is used as the base algorithm for time stepping calculations. Application of the developed algorithm proved very efficient in selected steady and unsteady test problems. For instance, the inherent unsteadiness present in the supersonic mixed compression inlet flow is identified and studied with a saving in CPU time of more than two orders of magnitude less than corresponding single grid computations. To achieve this success, detailed local mode analysis is performed to compute the smoothing factor and the bi-grid amplification factor. Multigrid performance is predicted using these two factors. The results obtained for various implicit schemes for solving the Euler and Navier-Stokes equations are presented and discussed. The bi-grid analysis was found to possess more accurate predictive capability.