Preface

The book is a result of the Advanced School Computational Acoustics, which took place at the International Centre for Mechanical Sciences (CISM), Udine, Italy, in May 2016. The aim of this book is to present state-of-the-art overview of numerical schemes efficiently solving the acoustic conservation equations, the acoustic wave equation, and its Fourier-transformed Helmholtz equation. Thereby, the different equations model both vibrational and flow-induced sound generation and its propagation. Chapter “Fundamental Equations of Acoustics” sets the scene by providing the mathematical/physical modeling of acoustic fields. Thereby, the equations of acoustics are based on the general equations of fluid dynamics: conservation of mass, momentum, energy, and closed by the appropriate constitutive equations defining the thermodynamic state. The use of a perturbation ansatz, which decomposes the physical quantities such as density, pressure, and velocity into mean, incompressible fluctuating and compressible fluctuating ones, allows to derive linearized acoustic conservation equations and its state equation. Thereby, we derive acoustic wave equations for both homogeneous and inhomogeneous media. Chapter “Non-conforming Finite Elements for Flexible Discretization with Applications to Aeroacoustics” focuses toward non-conforming finite elements for flexible discretization. Therewith, we allow for each subdomain an optimal grid. The two proposed methods—Mortar and Nitsche-type mortaring—fulfill the physical conditions along the non-conforming interfaces. We exploit this capability and apply it to real engineering applications in aeroacoustic. The results demonstrate the superiority of the nonconforming finite elements over standard finite elements concerning preprocessing, mesh generation flexibility, accuracy, and computational time. Chapter “Boundary Element Method for Time–Harmonic Acoustic Problems” presents the solution of time–harmonic acoustic problems by the boundary element method (BEM). Specifically, the Helmholtz equation with admittance boundary conditions is solved in three-dimensional space. The chapter starts with a derivation of the Kirchhoff–Helmholtz integral equation from a residual formulation of the