Spectral vanishing viscosity method combined with spectral element method for convectiondiffusion equation

Abstract

Abstract:

The Chebyshev spectral element method combined with spectral vanishing viscosity method is used to solve the onedimensional convectiondiffusion equation, aiming at the instability phenomenon of spectral element method for convectiondiffusion equation with high Reynolds number. The stability of the method is deduced with character analysis, and the feasibility of the proposed scheme is verified by a numerical example. The influence of spectral vanishing viscosity parameters on stability and accuracy is discussed. It is demonstrated that the stability and accuracy at high Reynolds number of spectral vanishing viscosity method are obviously improved compared with that of spectal element method. Larger spectal vanishing viscosity term is beneficial for extending the stable region and smaller viscosity term is beneficial for improving the accuracy at the condition of stable computation. The size of the viscosity term could be appropriately set to guarantee the stability and obtain numerical solution with high accuracy.

Key words:

">">convection">">diffusion equation；spectral element method；spectral vanishing viscosity method；stability；high Reynolds number">

SHI Yongxing.

Spectral vanishing viscosity method combined with spectral element method for convectiondiffusion equation

[J]. Huadian Technology, 2017, 39(10): 25-29.

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Spectral vanishing viscosity method combined with spectral element method for convectiondiffusion equation

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