Finite difference time domain discretization

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Table of contents

Abstract
Resume
Resume Long
Acknowledgments
Notation
Acronyms
1 Introduction
1.1 Reverberation
1.2 Energy-based methods
1.3 Motivation
1.4 Outlook
I Energy-Stress Tensor Method
2 Background
2.1 Introduction
2.2 Statistical acoustics
2.2.1 Energy Density and Sound Intensity
2.3 Energy-Stress Tensor Method
2.3.1 Theory
2.3.2 Scattering and diusion
2.3.3 Dimensional reduction
2.3.4 Limitations
2.3.5 Advantages
3 Frequency Dependence and Validity of a 1D Model
3.1 Introduction
3.2 Parameter tting
3.2.1 Telegraph equation
3.2.2 Boundary conditions on ends of the hallway
3.2.3 Finite dierence time domain discretization
3.2.4 Discussion
3.3 Measurements
3.3.1 Geometry
3.3.2 Details
3.4 Results
3.4.1 Physical hallways
3.4.2 Numerical model
3.4.3 Alcove hallway
3.4.4 Plain hallway
3.5 Discussion
3.6 Future work
3.7 Conclusion
II Finite Volume Approaches
4 Sources and Finite Volume Formulation
4.1 Introduction
4.2 Sources
4.2.1 1-dimensional EST
4.3 Finite volume model
4.3.1 Spatial discretization
4.3.2 Time domain discretization
4.4 Evaluation and commentary
4.5 Conclusion
5 Auralization
5.1 Introduction
5.2 Hybrid Model
5.2.1 EST method
5.2.2 Low-frequency reverberation
5.2.3 Direct path and early reections
5.3 Calibration
5.3.1 Between simulation methodologies
5.3.2 Between simulated results and measurements
5.4 Evaluation
5.5 Results
5.6 Future work
5.7 Conclusion
6 Energy-Stress Tensor Quantities
6.1 Introduction
6.2 Toward 3-dimensional prediction
6.3 Pressure domain simulation
6.3.1 Ambisonic microphone approach
6.4 Derivation of EST terms in FVTD formalism
6.5 Measurements
6.6 Preliminary results
6.6.1 Passage sections
6.6.2 Junction and alcove sections
6.6.3 Discussion
6.7 Riemannian tessellation
6.8 Discussion
6.9 Future work
6.10 Conclusion
III Conclusions
7 Conclusions
7.1 Review
7.2 Future work
7.3 Perspectives
IV Appendices
A Publications
A.1 Lower Bound on Frequency Validity of Energy-Stress Tensor Based Diuse Sound Field Model
A.2 Implementation of Sources in an Energy-Stress Tensor Based Diuse Sound Field Model
A.3 Auralization of a Hybrid Sound Field using a Wave-Stress Tensor Based Model
A.4 Riemannian Space Tessellation with Polyhedral Room Images
B Code listing
B.1 Introduction
B.2 FVTD
B.3 Remote code execution
Bibliography