Least-squares Legendre spectral element solutions to sound propagation problems

Area of Science:

• Computational Aeroacoustics (CAA)
• Numerical Analysis of Wave Propagation

Background:

• Accurate simulation of sound wave propagation is crucial in various engineering fields.
• Existing numerical methods face challenges in accurately capturing acoustic phenomena, especially in flows.

Purpose of the Study:

• To present a novel algorithm for sound wave propagation.
• To validate the algorithm's accuracy and capability using benchmark problems from the NASA Computational Aeroacoustics (CAA) Workshop.

Main Methods:

• Employs a least-squares Legendre spectral element approach for spatial discretization.
• Utilizes Crank-Nicolson and Adams-Bashforth schemes for temporal discretization.
• Solves linearized acoustic field equations for sound propagation.

Main Results:

• The algorithm demonstrates low numerical dispersion and dissipation for a one-dimensional sound wave.
• It effectively handles sound propagation in a uniform flow (Mach 0.5) for a two-dimensional acoustic pulse reflection.
• Computed results show good agreement with analytical solutions and other established numerical methods.

Conclusions:

• The proposed algorithm is accurate and robust for simulating sound wave propagation.
• It shows significant potential for applications in computational aeroacoustics, particularly in scenarios involving fluid flow.