Computational AcousticsThe book is a result of the

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详细说明：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 conservationThe series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by Cism, the International Centre for Mechanical sciences Moreinformationaboutthisseriesathttp://www.springer.com/series/76 Manfred Kaltenbacher Editor Computational acoustics 空 Springer editor Manfred Kaltenbacher Institute of mechanics and mechatronics Vienna University of Technology Vienna austria ISSN0254-1971 issn 2309-3706(electronic) CISM International Centre for mechanical sciences ISBN978-3-319-59037-0 ISBN978-3-319-59038-7( e Book) DOⅠ10.10071978-3-319-59038-7 Library of Congress Control Number: 2017941071 C CISM International Centre for Mechanical Sciences 201 8 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse ll, 6330 Cham, Switzerland 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, ir 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 demon strate the superiority of the nonconforming finite elements over standard finite lements 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 Preface Helmholtz equation. The discretization process with introduction of basis and test functions is described and shown for the collocation and the galerkin method Throughout the chapter, numerous different examples are presented, both simple one-dimensional examples having analytical solutions, which may be used for implementation verification, and rather industrial applications such as sedan cabin compartments, diesel engine radiation, and tire noise problems demonstrating the applicability Chapter"Direct Aeroacoustic Simulations Based on High Order Discontinuous Galerkin Schemes"' focuses on direct aeroacoustic simulations based on high-order discontinuous Galerkin schemes. The framework presented is based on a particular version of the discontinuous galerkin method in which a nodal as well as dis cretely orthogonal basis is used for computational efficiency. This discretization choice allows arbitrary order in space while also supporting unstructured meshes After discussing the details of the framework, examples of direct noise computation are presented, with a special focus on the numerical simulation of acoustic feedback In a complex automotive application Numerical schemes lead to a system of algebraic equations, which needs effi cient solvers. Therefore, Chapter"Direct and Iterative Solvers"presents a compact introduction to direct and iterative solvers for systems of algebraic equations typ ically arising from the finite element discretization of partial differential equations Beside classical iterative solvers, we also consider advanced preconditioning and solving techniques like additive and multiplicative Schwarz methods, generalizing Jacobis and Gauss-Seidel's ideas to more general subspace correction methods. In particular, we consider multilevel diagonal scaling and multigrid methods We have pleasure in thanking our colleagues, Gary Cohen, Dan Givoli, Ulrich Langer, Steffen Marburg, Claus-Dieter Munz, and Martin Neumuller for presenting their lectures, and the students for attending the course and contributing to dis- cussions. Furthermore we particularly thank the rectors and officers at cism for their enthusiasm, assistance, and hospitality. Finally, we want to thank Springer for their kind assistance, and especially Sooryadeepth Jayakrishnan and his team for their great job in doing the layo Vienna. austria Manfred Kaltenbacher Contents Fundamental Equations of Acoustics Manfred Kalten bacher Non-conforming Finite Elements for Flexible Discretization with applications to aeroacoustics 35 Manfred Kaltenbacher Boundary element Method for Time-Harmonic Acoustic problems Steffen Marburg Direct Aeroacoustic Simulations Based on High Order Discontinuous Galerkin Schemes 159 Andrea beck and Claus-Dieter Munz Direct and Iterative Solvers 205 Ulrich Langer and martin Neumuller Fundamental Equations of Acoustics Manfred Kaltenbacher abstract The equations of acoustics are based on the general equations of fuid dynamics: conservation of mass, momentum, energy and closed by the appropriate constitutive equation defining the thermodynamic state. The use of a perturbation ansatz, which decomposes the physical quantities density pressure and velocity into mean,incompressible fluctuating and compressible fluctuating ones, allows to derive inearized acoustic conservation equations and its state equation. Thereby, we derive acoustic wave equations both for homogeneous and inhomogeneous media, and the equations model both vibrational- and flow-induced sound generation and its prop agation 1 Overview Acoustics has developed into an interdisciplinary field encompassing the disciplines of physics, engineering, speech, audiology, music, architecture, psychology, neuro- science, and others(see, e.g., Rossing 2007). Therewith, the arising multi-field prob ems range from classical airborne sound over underwater acoustics(e. g,ocean acoustics) to ultrasound used in medical application. Here, we concentrate on the basic equations of acoustics describing acoustic phenomena. Thereby, we start with the mass, momentum and energy conservation equations of fuid dynamics as well as the constitutive equations Furthermore we introduce the helmholtz decompo sition to split the overall fluid velocity in a pure solenoidal (incompressible part) and irrotational(compressible) part. Since, wave propagation needs a compressible medium, we associate this part to acoustics. Furthermore, we apply a perturbation method to derive the acoustic wave equation, and discuss the main physical quanti ties of acoustics, plane and spherical wave solutions finally we focus towards the two main mechanism of sound generation: aeroacoustics(flow induced sound)and vibroacoustics(sound generation due to mechanical vibrations) M. Kaltenbacher(凶 Institute of mechanics and Mechatronics Tu Wien. Vienna. austria e-mail: manfred kaltenbacher tuwien acat O CISM International Centre for mechanical sciences 2018 M. Kaltenbacher(ed, Computational Acoustics, CISM International Centre for Mechanical Sciences 579. DOi 10.1007/978-3-319-59038-7 1 M. Kaltenbacher 2 Basic equations of Fluid dynamics We consider the motion of fluids in the continuum approximation, so that a body B is composed of particles R as displayed in Fig. 1. Thereby, a particle R already represents a macroscopic element On the one hand a particle has to be small enough to describe the deformation accurately and on the other hand large enough to satisfy the assumptions of continuum theory. This means that the physical quantities density P, pressure p, velocity v, and so on are functions of space and time, and are written as density p(xi, t), pressure p(xi, t), velocity v(xi, t), etc. So, the total change of a scalar quantity like the density p is 0 dt+ dx1 t dx2+ d 0 0 ax Therefore, the total derivative(also called substantial derivative) computes by dp apap/dx dp x3 dt at ax1(dt 0x2+8x3 ax2\ dt O ∑ ap dx dx 2) O dt Note that in the last line of (2) we have used the summation rule of einstein Furthermore in literature the substantial derivative of a physical quantity is mainly denoted by the capital letter D and for an Eulerian frame of reference writes as +υ.V Dt at Fluid particle R Fluid body B Fig 1 a body B composed of particles R I In the following, we will use both vector and index notation; for the main operations see Appendix

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