Internal wave reflections and transmissions arising from a nonuniform mesh. III  The occurrence of evanescent waves in the CrankNicolson linear finite element scheme
Abstract
The numerical scheme upon which this paper is based is the 1D CrankNicolson linear finite element scheme. In Part I of this series it was shown that for a certain range of incident wavelengths impinging on the interface of an expansion in nodal spacing, an evanescent (or spatially damped) wave results in the downstream region. Here in Part III an analysis is carried out to predict the wavelength and the spatial rate of damping for this wave. The results of the analysis are verified quantitatively with seven 'hotstart' numerical experiments and qualitatively with seven 'coldstart' experiments. Weare has shown that evanescent waves occur whenever the frequency of a disturbance at a boundary exceeds the maximum frequency given by the dispersion relation. In these circumstances the 'extended dispersion' relation can be used to determine the rate of spatial decay. In the context of a domain consisting of two regions with different nodal spacings, the use of the group velocity concept shows that evanescent waves have no energy flux associated with them when energy is conserved.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 July 1989
 DOI:
 10.1002/fld.1650090706
 Bibcode:
 1989IJNMF...9..833C
 Keywords:

 Computational Fluid Dynamics;
 Computational Grids;
 CrankNicholson Method;
 Finite Element Method;
 Internal Waves;
 Wave Reflection;
 Damping;
 Fourier Analysis;
 Incidence;
 Nodes (Standing Waves);
 Wave Equations;
 Fluid Mechanics and Heat Transfer