Boundary Integral Formulations of the Scalar and Vector Wave Equations with Arbitrary Moving Boundaries

Abstract

This paper presents an operational approach for deriving the boundary integral formulas of the scalar and vector wave equations with arbitrary moving boundary. Generalized derivatives are first introduced to the classical wave equation, the Ffowcs William—lHawkings (FW—H) equation and the Maxwell’s equations. After analyzing the nonhomogeneous terms of the resultant distributional equations, it is found that the integral representations of the scalar and vector wave equations can be expressed in terms of three general operators which represent the surface source distribution, time derivative and spatial derivatives of the surface distribution, respectively. Explicit formulas for these general operators are then derived for some scalar and vector wave equations from aerodynamics, aeroacoustics and electrodynamics.