Transmission line matrix in computational mechanics / Donard de Cogan, William J. O'Connor, Susan Pulko.

Includes bibliographical references and index.

Also available on the Internet.

Chapter 2 TLM and the 1-D Wave Equation 9 -- 2.2 The Vibrating String 10 -- 2.3 A Simple TLM Model 11 -- 2.4 Boundary and Initial Conditions 13 -- 2.5 Wave Media, Impedance, and Speed 15 -- 2.6 Transmission Line Junctions 18 -- 2.7 Stubs 19 -- 2.8 The Forced Wave Equation 20 -- 2.9 Waves in Moving Media: The Moving Threadline Equation 21 -- 2.10 Gantry Crane Example 21 -- 2.11 Rotating String: Differential Equation and Analytical Solution 22 -- 2.11.1 Rotating String: TLM Model 23 -- 2.11.2 Rotating String: Results 24 -- 2.12 TLM in 2-D (Extension to Higher Dimensions) 24 -- Chapter 3 The Theory of TLM: An Electromagnetic Viewpoint 27 -- 3.2 The Building Blocks: Electrical Components 28 -- 3.2.1 Resistor 28 -- 3.2.2 Capacitor 28 -- 3.2.3 Inductor 30 -- 3.2.4 Transmission Line 31 -- 3.3 Basic Network Theory 32 -- 3.4 Propagation of a Signal in Space (Maxwell's Equations) 33 -- 3.5 Distributed and Lumped Circuits 36 -- 3.6 Transmission Lines Revisited 37 -- 3.6.1 Time Discretization 37 -- 3.7 Discontinuities 39 -- 3.8 TLM Nodal Configurations 40 -- 3.9 Boundaries 43 -- Chapter 4 TLM Modeling of Acoustic Propagation 47 -- 4.2 1-D TLM Algorithm 47 -- 4.3 2-D TLM Algorithm for Acoustic Propagation 52 -- 4.4 Driven Sine-Wave Excitation 56 -- 4.5 The 2-D Propagation of a Gaussian Wave-Form 60 -- 4.6 Moving Sources 63 -- 4.7 Propagation in Inhomogeneous Media 66 -- 4.8 Incorporation of Stub Lines 68 -- 4.9 Boundaries 74 -- 4.10 Surface Conforming Boundaries 74 -- 4.11 Frequency-Dependent Absorbing Boundaries 77 -- 4.12 Open-Boundary Descriptions 80 -- 4.13 Absorption within a PML Region 84 -- Chapter 5 TLM Modeling of Thermal and Particle Diffusion 87 -- 5.2 Spatial Discretizations and Electrical Networks for Thermal and Particle Diffusion 88 -- 5.3 TLM Algorithm for a 1-D Link-line Nodal Arrangement 90 -- 5.4 1-D Link-Resistor Formulation 91 -- 5.5 Boundaries 92 -- 5.5.1 Insulating Boundary 92 -- 5.5.2 Symmetry Boundary 92 -- 5.5.3 Perfect Heat-Sink Boundary 93 -- 5.5.4 Constant Temperature Boundaries 93 -- 5.6 Temperature/Heat/Matter Excitation of the TLM Mesh 95 -- 5.6.1 Constant T Boundary as an Input 95 -- 5.6.2 Single Shot Injection into Bulk Material 96 -- 5.7 Flux Injection into Bulk Material 100 -- 5.7.1 Single Heat Source 100 -- 5.8 Multiple Flux Sources 101 -- 5.9 The Extension to Two and Three Dimensions 102 -- 5.9.1 Link-Line Formulations 102 -- 5.9.2 Link-Resistor Formulations 104 -- 5.10 Non-Uniformities in Mesh and Material Properties 106 -- 5.11 Stubs and the Avoidance of Internodal Reflections 111 -- 5.12 Time-Step Variation 114 -- 5.13 Some Aspects of the Theory of Lossy TLM 117 -- 5.13.1 TLM and Finite Difference Formulations for the Telegrapher's and Diffusion Equations 117 -- 5.13.2 Anomalous "Jumps-To-Zero" In Link-Line TLM 121 -- 5.13.3 TLM Diffusion Models as Binary Scattering Processes 126 -- 5.13.4 Mesh Decimation 128 -- 5.14 The Statistics of TLM Diffusion Models 130 -- 5.15 TLM and Analytical Solutions of the Laplace Equation 132 -- 5.15.1 Solution of the Diffusion Equation with Fixed-Value Boundaries 132 -- 5.15.2 Solution of the Telegrapher's Equation with Fixed-Value Boundaries 133 -- Chapter 6 TLM Models of Elastic Solids 137 -- 6.1 The Behavior of Elastic Materials 137 -- 6.2 The Analogy between TLM and State Space Control Theory 140 -- 6.3 Nodal Structure for Modeling Elastic Behavior 143 -- 6.4 Implementation 149 -- 6.5 Boundaries 152 -- 6.6 Force Boundaries 153 -- Chapter 7 Simple TLM Deformation Models 159 -- 7.2 Review of the Behavior of Materials 159 -- 7.3 Trouton's Descending Fluid and a TLM Treatment of a Vertically Supported Column 161 -- 7.4 A Model of Viscous Bending 165 -- 7.5 Numerical Issues and Model Convergence 169 -- 7.6 TLM Models of Viscoelastic Deformation 170 -- 7.6.1 The Parallel Viscoelastic Model 170 -- Chapter 8 TLM Modeling of Hydraulic Systems 177 -- 8.2 Symbols, Analogues, and Parameters 178 -- 8.3 Compressional Waves in Fluids 181 -- 8.4 A Transmission Line Analysis of Fluid Flow 181 -- 8.5 Time-Domain Transmission Line Models of Fluid Systems 183 -- 8.6 Transients in Elastic Pipes 193 -- 8.7 Open-Channel Hydraulics 196 -- Chapter 9 Application of TLM to Computational Fluid Mechanics 203 -- 9.2 Viscosity 204 -- 9.3 Viscosity in the TLM Algorithm 205 -- 9.4 Results 206 -- 9.5 Incompressible Fluids and Velocity Fields 207 -- 9.6 Convective Acceleration and the TLM Model 208 -- 9.7 Comments on the Procedure 211 -- 9.8 Implementation Issues 212 -- Chapter 10 State of the Art Examples 213 -- 10.2 The Hanging Cable and Gantry Crane Problems 213 -- 10.2.1 Hanging Cable: Analytical Analysis and Results 213 -- 10.2.2 Hanging Cable: TLM Model 214 -- 10.2.3 Gantry Crane: Results 215 -- 10.3 The Modeling of Rigid Bodies Joined by Transmission Line Joints 216 -- 10.4 Klein-Gordon Equation 220 -- 10.5 Acoustic Propagation and Scattering (Two-Dimensions) 223 -- 10.6 Condenser Microphone Model 225 -- 10.7 Propagation in Polar Meshes 226 -- 10.8 Acoustic Propagation in Complex Ducts (A 3-D TLM Model) 227 -- 10.9 A 3-D Symmetrical Condensed TLM Node for Acoustic Propagation 229 -- 10.10 Waves in Moving Media 233 -- 10.11 Some Recent Developments in TLM Modeling of Doppler Effect 235 -- 10.12 Simulation of a Thermal Environment for Chilled Foods during Transport: An Example of Three-Dimensional Thermal Diffusion with Phase-Change 237 -- 10.12.1 Recent Advances in Inverse Thermal Modeling using TLM 239 -- 10.12.2 Inverse scattering 239 -- 10.12.3 Amplification Factor 241 -- 10.12.4 TLM and Spatio-Temporal Patterns -- The Present and the Future 242 -- 10.12.5 TLM and Diffusion Waves 246 -- 10.12.6 The Logistic Equation in the Presence of Diffusion 248.