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Numerical model for nonlinear standing waves and weak shocks in thermoviscous fluids
1E.S.C.E.T. Universidad Rey Juan Carlos, Madrid, Spain. c.vanhille@escet.urjc.es
The Journal of the Acoustical Society of America
|June 27, 2001
Summary
This study numerically models nonlinear standing waves in tubes using a finite-difference algorithm. Results show accurate acoustic field simulations, including absorption effects, for various excitation levels.
Area of Science:
- Acoustics
- Fluid Dynamics
- Computational Physics
Background:
- Nonlinear standing waves in tubes are crucial for understanding acoustic resonators.
- Previous studies often relied on simplified models or experimental data.
- Accurate numerical modeling of thermoviscous fluids is essential.
Purpose of the Study:
- To numerically investigate nonlinear standing waves in a one-dimensional tube.
- To develop and validate a time-domain finite-difference algorithm for acoustic fields.
- To analyze the effects of thermoviscous fluids and absorption on wave propagation.
Main Methods:
- A finite-difference algorithm was employed for numerical simulations.
- The study utilized Lagrangian coordinates to solve the nonlinear differential equation without truncation.
- Calculations were performed in the time domain, capturing all harmonic components.
Main Results:
- Displacement and pressure waveforms were calculated at various locations and excitation levels.
- Amplitude distributions for harmonic components along the resonator axis were evaluated.
- Simulations covered a range from linear to strongly nonlinear regimes, including weak shock waves.
Conclusions:
- The numerical code accurately models acoustic fields in resonators.
- The method demonstrated excellent agreement with existing experimental and analytical results.
- This approach provides a robust tool for studying nonlinear acoustics in thermoviscous fluids.