Spectral Differentiation Operators and Hydrodynamic Models for Stability of Swirling Fluid Systems

TL;DR

This paper introduces spectral differential operators in hydrodynamic models to analyze the spatial stability of swirling fluid systems, incorporating viscosity effects and employing spectral methods for accurate stability analysis.

Contribution

It develops novel spectral differential operator-based hydrodynamic models for viscous and inviscid swirling fluids, enabling precise stability analysis using polynomial eigenvalue problems.

Findings

Models successfully applied to Q-vortex structures

Spectral methods provide accurate stability predictions

Viscous and inviscid models show consistent results

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.