## THERMAL SCIENCE

International Scientific Journal

### A COMPARISON OF VARIOUS BASIS FUNCTIONS BASED ON MESHLESS LOCAL PETROV-GALERKIN METHOD FOR LINEAR STABILITY OF CIRCULAR JET

**ABSTRACT**

Various basis functions based on Fourier-Chebyshev Petrov-Galerkin spectral method are described for computation of temporal linear stability of a circular jet. Basis functions presented here are exponentially mapped Chebyshev functions. There is a linear dependence between the components of the perturbation vector field, and there are only two degrees of freedom for the perturbation continuum equation. According to the principle of permutation and combination, the basis function has three basic forms, i. e., the radial, azimuthal or axial component, respectively. The results show that three eigenvalues for various cases are consistent, but there is a preferable basis function for numerical computation.

**KEYWORDS**

PAPER SUBMITTED: 2013-01-18

PAPER REVISED: 2013-04-26

PAPER ACCEPTED: 2013-06-02

PUBLISHED ONLINE: 2013-12-28

**THERMAL SCIENCE** YEAR

**2013**, VOLUME

**17**, ISSUE

**Issue 5**, PAGES [1329 - 1335]

- Yu, M. Z., et al., Large Eddy Simulation of a Planar Jet Flow with Nanoparticle Coagulation, Acta Mech. Sinica, 22 (2006), 4, pp. 293-300
- Yu, M. Z., et al., Effect of Precursor Loading on Non-Spherical TiO2 Nanoparticle Synthesis in a Diffusion Flame Reactor, Chemical Engineering Science, 63 (2008), 9, pp. 2317-2329
- Yu, M. Z., et al., Numerical Simulation of Nanoparticle Synthesis in Diffusion Flame Reactor, Powder Technology, 181 (2008), 1, pp. 9-20
- Yu, M. Z., et al., Numerical Simulation for Nucleated Vehicle Exhaust Particulate Matters via the TEMOM/ LES Method, International Journal of Modern Physics C, 20 (2009), 3, pp. 399-421
- Lin, J. Z., et al., Effects of Operating Conditions on Droplet Deposition onto Surface of Atomization Impinging Spray, Surf. Coat. Technol., 203 (2009), 12, pp. 1733-1740
- Yin, Z. Q., et al., Numerical Simulation of the Formation of Pollutant Nanoparticles in the Exhaust Twin-Jet Plume of a Moving Car, Int. J. Nonlin. Sci. Num., 8 (2007), 4, pp. 535-543
- Lin, J. Z., et al., Effects of Coherent Structures on Nanoparticle Coagulation and Dispersion in a Round Jet, Int. J. Nonlin. Sci. Num., 8 (2007), 1, pp. 45-54
- Chan, T. L., et al., Temporal Stability of a Particle-Laden Jet, Int. J. Multiphas. Flow, 34 (2008), 2, pp. 176-187
- Drazin, P. G., Reid, W. H., Hydrodynamic Stability, 2nd ed., Cambridge University Press, Cambridge, 2000
- Priymak, V. G., Miyazakiy, T., Accurate Navier-Stokes Investigation of Transitional and Turbulent Flows in a Circular Pipe, J. Comput. Phys., 142 (1998), 2, pp. 370-411
- Meseguer, A., Trefethen, L. N., Linearized Pipe Flow to Reynolds Number 107, J. Comput. Phys., 186 (2003), 1, pp. 178-197
- Trefethen, L. N., et al., Hydrodynamic Stability without Eigenvalues, Science, 261 (1993), 5121, pp. 578-584
- Biau, D., Bottaro, A., An Optimal Path to Transition in a Duct, Philosophical Transactions of the Royal Society A, 367 (2009), 1888, pp. 529-544
- Grosch, C. E., Orszag, S. A., Numerical Solution of Problems in Unbounded Regions: Coordinate Transforms, J. Comput. Phys., 25 (1977), 3, pp. 273-296
- Boyd, J. P, Chebyshev and Fourier Spectral Methods, 2nd ed., Springer Verlag, Berlin, 1999
- Xie, M. L., Lin, J. Z., An Efficient Numerical Solution for Linear Stability of Circular Jet: a Combination of Petrov Galerkin Spectral Method and Exponential Coordinate Transformation Based on Fornberg's Treatment, Int. J. Numer. Methods Fluids, 61 (2009), 7, pp. 780-795