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Journal of Applied Mathematics
Volume 2012, Article ID 545120, 9 pages
Review Article

Numerical Simulation of Unsteady Compressible Flow in Convergent Channel: Pressure Spectral Analysis

1Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University in Prague, Karlovo Nám. 13, 121 35 Praha 2, Czech Republic
2Institute of Thermomechanics AS CR, Dolejškova 5, 18200 Prague 8, Czech Republic

Received 16 January 2012; Accepted 8 March 2012

Academic Editor: Fu-Yun Zhao

Copyright © 2012 Petra Pořízková et al. 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.


This study deals with the numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The flow is described by the system of Navier-Stokes equations for laminar flows. The numerical solution is implemented using the finite volume method (FVM) and the predictor-corrector Mac-Cormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. Due to the motion of the grid, the basic system of conservation laws is considered in the arbitrary Lagrangian-Eulerian (ALE) form. The numerical results of unsteady flows in the channel are presented for inlet Mach number 𝑀=0.012, Reynolds number Re=4481, and the wall motion frequency 100 Hz.