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Modelling and Simulation in Engineering
Volume 2011, Article ID 537464, 17 pages
Research Article

A Preconditioned Method for Rotating Flows at Arbitrary Mach Number

Mechanical, Industrial, and Manufacturing Engineering Department, The University of Toledo, 2801 W. Bancroft Street, MS 312, Toledo, OH 43606, USA

Received 17 April 2011; Accepted 25 July 2011

Academic Editor: Antonio Munjiza

Copyright © 2011 Chunhua Sheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An improved preconditioning is proposed for viscous flow computations in rotating and nonrotating frames at arbitrary Mach numbers. The key to the current method is the use of both free stream Mach number and rotating Mach number to construct a preconditioning matrix, which is applied to the compressible governing equations written in terms of primitive variables. A Fourier analysis is conducted that reveals the efficacy of the modified preconditioning. Numerical approximations for the convective and diffusive fluxes are detailed based on the preconditioned system of equations. A set of boundary conditions using characteristic variables are described for internal and external flow computations. Numerical validations are performed on four realistic viscous flows in both fixed and rotating frames. The results indicated that the modified preconditioning has a superior performance compared to the original method to predict flows from extremely low to supersonic Mach numbers.