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The Acoustics Module User's Guide

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The Acoustics Module User's Guide Acoustics Module User’s Guide Acoustics Module User’s Guide © 1998–2018 COMSOL Protected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. Version: COMSOL 5.4 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates • COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community • Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number: CM020201 Contents Chapter 1: Introduction Acoustics Module Capabilities 23 What Can the Acoustics Module Do? . 23 What are the Application Areas? . 25 Which Problems Can You Solve?. 28 Fundamental of Acoustics 30 Acoustics Explained . 30 Mathematical Models for Acoustic Analysis . 31 Damping . 33 Artificial Boundaries. 35 Acoustics Module Physics Interface Guide 36 Common Physics Interface and Feature Settings and Nodes . 41 Where Do I Access the Documentation and Application Libraries? . 41 Overview of the User’s Guide 46 Chapter 2: Pressure Acoustics Interfaces The Pressure Acoustics, Frequency Domain Interface 52 Domain, Boundary, Edge, Point, and Pair Nodes for the Pressure Acoustics, Frequency Domain Interface . 57 Pressure Acoustics . 59 Poroacoustics . 65 Narrow Region Acoustics . 72 Background Pressure Field . 75 Initial Values . 78 Monopole Domain Source . 78 Dipole Domain Source . 79 Heat Source . 79 CONTENTS | 3 Sound Hard Boundary (Wall) . 80 Axial Symmetry . 80 Normal Acceleration . 80 Normal Velocity . 81 Normal Displacement . 81 Sound Soft Boundary . 82 Pressure . 82 Impedance . 83 Symmetry . 88 Periodic Condition . 88 Matched Boundary . 90 Exterior Field Calculation . 91 Port. 93 Circular Port Reference Axis . 98 Plane Wave Radiation . 99 Spherical Wave Radiation . 99 Cylindrical Wave Radiation . 100 Incident Pressure Field. 100 Interior Sound Hard Boundary (Wall) . 103 Interior Normal Acceleration . 103 Interior Normal Velocity . 104 Interior Normal Displacement. 105 Interior Impedance/Pair Impedance . 105 Interior Perforated Plate/Pair Perforated Plate. 106 Continuity . 108 Line Source . 108 Line Source on Axis. 111 Monopole Point Source . 112 Dipole Point Source. 114 Quadrupole Point Source . 115 Point Sources (for 2D Components) . 118 Circular Source (for 2D axisymmetric components) . 120 The Pressure Acoustics, Transient Interface 122 Domain, Boundary, Edge, and Point Nodes for the Pressure Acoustics, Transient Interface . 124 Transient Pressure Acoustics Model . 125 Nonlinear Acoustics (Westervelt) . 126 4 | CONTENTS Background Pressure Field (for Transient Models) . 129 Incident Pressure Field (for Transient Models). 130 The Gaussian Pulse Source Type Settings. 131 Normal Acceleration . 132 Normal Velocity . 133 Normal Displacement . 133 Exterior Field Calculation (for Transient Models) . 133 Interior Normal Acceleration . 134 Interior Normal Velocity . 135 Interior Normal Displacement. 135 The Pressure Acoustics, Boundary Mode Interface 137 Initial Values . 138 Boundary, Edge, Point, and Pair Nodes for the Pressure Acoustics, Boundary Mode Interface . 139 The Pressure Acoustics, Boundary Elements Interface 140 Domain, Boundary, Edge, and Pair Nodes for the Pressure Acoustics, Boundary Elements Interface . 147 Pressure Acoustics . 147 Background Pressure Field . 148 Initial Values . 149 Sound Hard Boundary (Wall) . 149 Normal Acceleration . 149 Normal Velocity . 150 Normal Displacement . 150 Sound Soft Boundary . 151 Impedance . 151 Pressure . 151 Interior Sound Hard Boundary (Wall) . 151 Interior Normal Acceleration . 152 Interior Normal Velocity . 153 Interior Normal Displacement. 153 Continuity . 154 The Pressure Acoustics, Time Explicit Interface 155 Domain, Boundary, Edge, and Point Nodes for the Pressure Acoustics, Time Explicit Interface . 158 CONTENTS | 5 Pressure Acoustics, Time Explicit Model . 158 Background Acoustic Field . 160 Initial Values . 162 Mass Source . 162 Heat Source . 162 Volume Force Source . 163 Sound Hard Wall. 163 Sound Soft Boundary . 164 Pressure . 164 Symmetry . 164 Normal Velocity . 164 Impedance . 165 Exterior Field Calculation . 165 Interior Sound Hard Boundary (Wall) . 166 Interior Normal Velocity . 166 General Flux/Source . 167 Modeling with the Pressure Acoustics Branch (FEM-Based Interfaces) 168 Meshing (Resolving the Waves) . 168 Lagrange and Serendipity Shape Functions . 170 Time Stepping in Transient Models . 171 Frequency Domain, Modal and AWE . 173 Solving Large Acoustics Problems Using Iterative Solvers. 174 Perfectly Matched Layers (PMLs) . 177 Postprocessing Variables . 181 Evaluating the Acoustic Field in the Exterior: Near- and Far-Field . 186 Dedicated Acoustics Plots for Postprocessing . 188 About the Material Databases for the Acoustics Module . 193 Specifying Frequencies: Logarithmic and ISO Preferred . 193 Modeling with the Pressure Acoustics Branch (BEM-Based Interface) 194 When to Use BEM . 194 Selections: Infinite Void and Finite Voids . 195 Solvers for BEM Models . 196 Meshing BEM Models . 196 Postprocessing BEM Results. 197 6 | CONTENTS Modeling with the Pressure Acoustics Branch (dG-FEM-Based Interface) 198 Meshing, Discretization, and Solvers . 198 Postprocessing: Variables and Quality . 198 Absorbing Layers. 198 Storing Solution on Selections for Large Models . 199 Theory Background for the Pressure Acoustics Branch 200 The Governing Equations. 200 Pressure Acoustics, Frequency Domain Equations . 204 Pressure Acoustics, Transient Equations . 207 The Nonlinear Westervelt Equation . 208 Pressure Acoustics, Boundary Mode Equations . 209 Theory for the Plane, Spherical, and Cylindrical Radiation Boundary Conditions . 210 Theory for the Exterior Field Calculation: The Helmholtz-Kirchhoff Integral . 213 Theory for the Boundary Impedance Models 217 Impedance Conditions . 217 RCL Models. 218 Physiological Models . 220 Waveguide End Impedance Models . 228 Porous Layer Models . 229 Characteristic Specific Impedance Models . 230 Theory for the Interior Impedance Models 232 Interior Perforated Plate Models . 232 Theory for the Equivalent Fluid Models 238 Introduction to the Equivalent Fluid Models. 238 About the Pressure Acoustics Fluid Models . 240 About the Poroacoustics Models . 242 About the Narrow Region Acoustics Models . 256 Theory for the Perfectly Matched Layers in the Time Domain 262 Introduction to Perfectly Matched Layers . 262 CONTENTS | 7 Perfectly Matched Layers in the Time Domain. 263 References for the Pressure Acoustics Branch 264 Chapter 3: Acoustic-Structure Interaction Interfaces The Acoustic-Solid Interaction, Frequency Domain Interface 270 The Acoustic-Solid Interaction, Transient Interface 273 The Acoustic-Piezoelectric Interaction, Frequency Domain Interface 276 The Acoustic-Piezoelectric Interaction, Transient Interface 279 The Solid Mechanics (Elastic Waves) Interface 282 The Poroelastic Waves Interface 283 Domain, Boundary, and Pair Nodes for the Poroelastic Waves Interfaces . 285 Poroelastic Material . 285 Porous, Free . ..
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