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ANALYSIS OF DISPERSION ERRORS IN ACOUSTIC WAVE SIMULATIONS

R. A. C. Germanos, L. F. de Souza

Abstract


The governing equations of the acoustic problem are the compressible Euler equations. The discretization of these equations has to ensure that the acoustic waves are transported with non-dispersive and non-dissipative characteristics. In the present study numerical simulations of a standing acoustic wave are performed. Four different space discretization schemes are tested, namely, a second order finite-differences, a fourth order finitedifferences, a fourth order finite-differences compact scheme and a sixth order finite-differences compact scheme. The time integration is done with a fourth order Runge-Kutta scheme. The results obtained are compared with linearized analytical solutions. The influence of the dispersion on the simulation of a standing wave is analyzed. The results confirm that high order accuracy schemes can be more efficient for simulation of acoustic waves, especially the waves with high frequency.

Keywords


acoustic wave, dispersion error, compressible flows, standing wave, finite-difference method, high order methods

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DOI: http://dx.doi.org/10.5380/reterm.v5i1.61663