Finite Difference Time Domain (FDTD) and time domain Finite Element Based methods for modelling Room Acoustics, Musical Acoustics and Environmental Acoustics
Dr Ian Drumm
I have developed in house software (dubbed WaveTank) that employs 3D Finite Difference Time Domain (FDTD) and a time domain Finite Element Based method to predict sound propagation within rooms and musical instruments. The FDTD based approach has many advantages over Ray, Beam, Image, Statistical and Empirical approaches as it can inherently describe broadband wave phenomena such as diffraction, interference and diffusion as well as frequency dependant interaction with surfaces.
The Finite Difference Time Domain method (FDTD) uses centre-difference representations of continuous partial differential equations to create iterative numerical models of wave propagation. The method can be applied to static and moving media.
I've been modelling surfaces within halls and rooms using a least-pth based filter design approach which can give a frequency dependant absorption profile corresponding to absorption coefficients of planes as commonly used in hall data. The current implementation of the software can parse and voxellise ODEON, CATT and X3D files. For more information see ... I. A. Drumm, Y. W. Lam, 'Development and assessment of a finite difference time domain room acoustic prediction model that uses hall data in popular formats', Proceedings, Internoise-Turkey, (2007)
I've also been hybridising the technique with a Finite Element Time Domain
based method to model surfaces as meshes of interconnected nodes whose interactions
can be given in terms of a global stiffness matrix which is hence solved in
the time domain via Newmark integration. By iterating the two methods concurrently
FDTD and FETD is hybridised to model the coupling of vibrating surfaces within
an aero-acoustic medium. The approach has the potential to model the likes of
panel absorbers, bass traps, etc and active systems including loudspeakers.
For more information see ... I. A. Drumm, 'A hybrid finite element / finite
difference time domain technique for modelling the acoustics of surfaces within
a medium', Acta Acustica, Vol 93, p804-809 (2007)
Some examples and movies...
3D Man
Here a 600 polygon X3D file of a man was voxellised into the FDTD software and the source modelled. The movie man3DFDTD.wmv shows slice views followed by a 3D view of a sound field's propagation around the man.
Elmia Concert Hall
The CATT file of Elmia Concert Hall made available in recent round robins was voxellised and room acoustic predictions performed. The surfaces were modelled as fourth order IIR filters whose least pth designed frequency responses correspond to the absorption coefficients of the hall model. Pressure impulse responses can be recorded at specified detector positions, filtered for octave bands and hence room acoustics parameters (such as T30, EDT, C80, D50, Centre Time and Bass Ratio) predicted. Such
The accompanying movie elima1.wmv shows plan and elevation views of a Gaussian pulse propagating within the hall with the corresponding pressure impulse at a detector recorded. The surfaces reflect the remaining energy back into which hasn't been absorbed. You will also see sound propagating out of the hall, this unwanted residual is absorbed by the PML boundary and doesn't effect the room acoustic prediction. Note one would expect the direct sound to show the loudest spike but this isn't seen on the movie because the graphing I use is very crude (I just plot points every so many samples along the impulse to fit the impulse into the few pixels I have room to draw to) also pressures from multiple reflections paths can contribute to the same sample so impulse responses from FDTD predictions tend to look a little different from those from say an image source prediction even though the overall energy profile is the same.
Noise Panel
A simple demonstration of a hybrid FDTD and FETD approach to modelling a surface. This method is superior to filtering in that it models the modal response of the panel and it's interaction with the medium.
Flow
A demonstration of FDTD being used to model flow by essential descretising Navier Stoke's differential equations.
Flute
By using FDTD with flow and a very small amount of noise at the mouthpiece a simple flute can be modelled. The pressure release termination at the end of the flute causes a reflection and hence standing wave which in turn controls flow into the system.
Some futher reading
If you are interested in getting started with Finite Difference Time Domain here is a matlab based tutorial I recently wrote for an EPSRC summer school. Have fun.
Implementing FDTD Tutorial.doc