Tailored nearfield Green's functions for arbitrary geometries

Area of Science:

• Acoustics
• Computational Fluid Dynamics
• Optics

Background:

• Turbulent flow near solid boundaries generates complex pressure fluctuations.
• Accurate nearfield evaluation is crucial for understanding acoustic phenomena.
• Conventional methods like Boundary Element Method (BEM) can be computationally intensive.

Purpose of the Study:

• To introduce and evaluate an iterative technique for calculating nearfield pressure fluctuations.
• To compare the iterative method's performance against analytical solutions and conventional BEM.
• To assess the computational efficiency and accuracy of the novel approach.

Main Methods:

• An iterative technique adapted from optics is employed.
• Green's functions are tailored for nearfield pressure fluctuation evaluation.
• Comparisons are made with analytical solutions (solid sphere) and conventional BEM (semi-infinite plate).
• A relaxation factor is introduced to resolve divergence issues.

Main Results:

• The iterative approach yields results comparable to conventional BEM.
• A divergence issue for a solid sphere was successfully resolved.
• The iterative method demonstrates a slightly larger error bandwidth at irregular frequencies compared to BEM.
• Significant reduction in computational cost was observed.

Conclusions:

• The iterative technique provides a viable and computationally efficient alternative for nearfield pressure fluctuation analysis.
• Reduced computational cost allows for denser surface meshes and extended frequency ranges.
• The method shows promise for applications involving turbulent flow acoustics.