The SONATE vibro acoustic simulation suite

Hard sound barrier simulation in Time Domain BEM
(Boundary Element Method)

  • The sound barrier is a wall (5m high x 10m long), represented in transparency mode.
  • The noise source is modeled by a point source (the yellow point) with a Gaussian volume velocity (standard deviation = 0.3ms).

This video shows the evolution of the pressure on 2 orthogonal planes. One can distinguish the reflection by the ground and the wall and the diffraction from the top and lateral edges.

This simulation was performed using SONATE© Time Domain BEM solver.

SONATE© is an operational software developed by IMACS and dedicated to the simulation of vibro-acoustic phenomena with applications in automotive, aeronautic and other transport industries. SONATE© is based on a revolutionary approach of Time Domain Boundary Element Method (TD-BEM). That leads to excellent performances for wide frequency band responses, which result in an important gain of productivity and make possible projects computational costs were prohibitive. These performances open the door to multiphysics coupling in time domain as for engine run up process or for aeroacoustic applications. SONATE is well-suited to solve many acoustic phenomena. Typical current Analysis cases are:
  • Acoustic Analysis Case: given an acoustic mesh, SONATE computes response to acoustic sources (plane waves, monopoles, dipoles...).
  • Blocked Pressure Analysis Case: the same as the previous one, followed by the use of a projection module to obtain pressure load on a structural mesh for a strutural analysis, or interior vibro-acoustic coupled analysis.
  • Weakly Coupled Analysis Case: given a structural and acoustic meshes, atructural modes, time-domain or frequency domain loads (forces), SONATE computes structural response, use projection module to infer normal velocity load and computes the acoustic response. This Analysis Case is well suited forengine noise simulation. <
  • Strongly Coupled Analysis Case: given structural and acoustic meshes and structural modes, SONATE computes vibro-acoustic response to acoustic or structural sources.

Retarded Potentials and Time Domain BEM

Various waves can be represented by the so-called retarded (or delayed) potential integral representation formulae. This can serve to reduce different wave problems  to integral equations in the time domain that could be solved using an appropriate Boundary Element Method. Compared to the more traditional frequency domain, solving these problems in the time domain have the interesting property of providing the result in a wide range of frequencies with one simulation by means of a Fast Fourier Transform. Time marching schemes have been considered for a long time very delicate when applied to integral equations in the time domain arising from various wave problems. Stability issue has been and seems to remain at the centre of investigations. Almost all (vain) attempts to stabilize the scheme have been based on spatial and temporal averaging procedures during the time stepping, or try to extrapolate the beginning of the response signals using different techniques as Prony's or autoregressive models. This type of approach only delays the onset of the instability and/or seriously compromise the precision of the results. Recent studies are dedicated to improve the precision by high order time approximation. Thus complete time-space variational approximation leads to unconditionally stable and precise schemes. Several PhD thesis (under supervision of Prof. Jean-Claude Nédélec at École Polytechnique and Prof. Alain Bachelot at Université de Bordeaux I) have been dedicated to study of this theory and its application to different situations in electromagnetism, acoustics and elastodynamics. A rigorous functional framework and the first 3D electromagnetic EFIE stable computation without any averaging trick have been published in the thesis of Isabelle Terrasse in 1993. IMACS has contributed to a deaper comprehension and improvement of these techniques, and made a continuous and important research effort since 1995 with 3 PhD theses. Today, delayed potentials have been applied and studied in many situations, and accelaration techniques have been transposed from previous frequency domain studies. Today, delayed potentials are very well understood. Interesting issues concern coupling with other numerical methods, multiphysics coupling, dispersion laws in the time domain for special materials, inverse problems and multipole acceleration techniques.

SONATE© is the result of IMACS' works on TD BEM. It implements a precise, robust and inconditionally stable numerical scheme.  SONATE© solves acoustic and vibroacoustic problems.SONATE© has been used in an industrial context since 2000, and benefits from an important feedback that contributes to improve its robustness and extend its field of applications.

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