Computational Mechanics

, Volume 58, Issue 1, pp 45–57 | Cite as

Time domain BEM for sound radiation of tires

  • Lothar Banz
  • Heiko Gimperlein
  • Zouhair Nezhi
  • Ernst P. Stephan
Original Paper


This work investigates a time domain boundary element method for the acoustic wave equation in an exterior domain in the half-space \(\mathbb {R}^3_+\). The Neumann problem is formulated as a boundary integral equation of the second kind, and the convergence and stability of conforming Galerkin approximations is studied in the complex geometry of a car or truck tire above a street. After a validation experiment, numerical results are presented in time or frequency domain for realistic benchmarks in traffic noise: the sound emission of vibrating tires, noise amplification in the horn-like geometry between the tire and the road, as well as the Doppler effect of a moving tire. The results are compared with calculations in frequency domain.


Time domain BEM Sound radiation  Horn effect Computational acoustics Boundary elements 



Zouhair Nezhi was funded by BMWi under the project SPERoN 2020, part II, Leiser Straßenverkehr, Grant number 19 U 10016 F. Heiko Gimperlein acknowledges partial support by the Danish National Research Foundation (DNRF) through the Centre for Symmetry and Deformation, the Danish Science Foundation (FNU) research Grant 10-082866 and the ERC Advanced Grant HARG 268105.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Lothar Banz
    • 1
  • Heiko Gimperlein
    • 2
    • 3
  • Zouhair Nezhi
    • 4
  • Ernst P. Stephan
    • 4
  1. 1.Department of MathematicsUniversity of SalzburgSalzburgAustria
  2. 2.Maxwell Institute for Mathematical Sciences and Department of MathematicsHeriot-Watt UniversityEdinburghUK
  3. 3.Institut für MathematikUniversität PaderbornPaderbornGermany
  4. 4.Institute of Applied MathematicsLeibniz University HannoverHannoverGermany

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