Spectral differentiation operators and hydrodynamic models for stability of swirling fluid systems

Authors:
Diana Alina Bistrian;Florica Ioana Dragomirescu;George Savii
Affiliations:
Department of Electrical Engineering and Industrial Informatics Engineering Faculty of Hunedoara, "Politehnica" University of Timisoara, Hunedoara, Romania;Department of Mathematics, "Politehnica" University of Timisoara, Timisoara, Romania;Department of Mechatronics, Mechanical Engineering Faculty, "Politehnica" University of Timisoara, Timisoara, Romania
Venue:
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Year:
2009

Citing 4
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Abstract

In this paper we develop hydrodynamic models using spectral differential operators to investigate the spatial stability of swirling fluid systems. Including viscosity as a valid parameter of the fluid, the hydrodynamic model is derived using a nodal Lagrangean basis and the polynomial eigenvalue problem describing the viscous spatial stability is reduced to a generalized eigenvalue problem using the companion vector method. For inviscid study the hydrodynamic model is obtained by means of a class of shifted orthogonal expansion functions and the spectral differentiation matrix is derived to approximate the discrete derivatives. The models were applied to a Q-vortex structure, both schemes providing good results.