Spectral Differentiation Operators and Hydrodynamic Models for Stability of Swirling Fluid Systems
Spectral Theory
2012-04-02 v1 Numerical Analysis
Dynamical Systems
Numerical Analysis
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 Lagrangian 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.
Keywords
Cite
@article{arxiv.1203.6758,
title = {Spectral Differentiation Operators and Hydrodynamic Models for Stability of Swirling Fluid Systems},
author = {Diana Alina Bistrian and Florica Ioana Dragomirescu and George Savii},
journal= {arXiv preprint arXiv:1203.6758},
year = {2012}
}