A variable transformation approach for boundary element solutions of wave propagation in non-uniform potential flows

ABSTRACT A boundary element method in a transformed Taylor-Lorentz space-time is presented to solve sound propagation and scattering in weakly non-uniform subsonic potential flows. Boundary element solutions are conventionally provided for sound propagation and scattering in quiescent media. On the other hand, an effective approach to solve wave propagation in a non-uniform mean flow using boundary element methods has yet to be demonstrated. Although either the Taylor or Lorentz transform being applied separately has been commonly used to provide boundary integral solutions including mean flow effects on wave propagation, in this work a combination of these transformations is proposed. The Taylor-Lorentz transform allows an approximate formulation of the full potential linearized wave equation to be reduced to the standard wave equation in a deformed space-time, where a conventional boundary element method can then be devised. The boundary conditions for the formulation in the transformed space are also presented. Numerical experiments are performed to validate the present method.