Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
17
6
2019
A FICTITIOUS SOURCE METHOD FOR A MULTIFREQUENCY ACOUSTIC SOURCE OVER GROUND WITH VARIABLE IMPEDANCE
563-582
10.1615/IntJMultCompEng.2019030576
Y.
Kamoun
Department of Aerospace Engineering, TechnionāIsrael Institute of Technology Haifa 32000,
Israel
Dan
Givoli
Department of Aerospace Engineering, TechnionāIsrael Institute of Technology, Haifa 32000, Israel; Faculty of Civil Engineering & Geosciences, Technical University of Delft, 2600 GA Delft, The Netherlands
multifrequency
multiscale
SPL
Helmholtz equation
equivalent sources
fictitious sources
acoustic waves
ground impedance
Green's function
aircraft noise
Finding the sound pressure level (SPL) distribution near the ground due to aircraft noise is an important problem in environmental engineering. Since the human hearing range is very wide, ranging from 20 Hz to 20 kHz, the determination of the SPL distribution for a given source spectrum is a difficult multiscale problem, and requires the repeated solution, for many different wave numbers, of the Helmholtz equation in the upper half space, while imposing a given impedance boundary condition on the ground. Previously, a simple computational scheme, based on the use of fictitious sources, was proposed for the efficient solution of such problems, for aflat ground with a given constant impedance. In the present study, this scheme is improved and extended in several ways. First, the ground impedance is allowed to vary with location, representing a varying type of ground (soil, water, asphalt, etc.). Second, a mechanism for verification of the method and for error estimation is developed, whereas previously only the boundary condition residual was evaluated. Third, the use of the appropriate Green's function, associated with a ringlike source, is made precise. Two simplifying assumptions which are maintained are that the ground is flat and that its impedance function is axially symmetric. Numerical experiments are used to demonstrate the performance of the scheme.