Semi-analytical spectral methods in generalized curvilinear coordinates for analyzing sound fields in axisymmetric cavities

This paper provides semi-analytical spectral methods for efficiently analyzing three-diminsional non-axisymmetric sound fields within axisymmetric cavities subject to arbitrary boundary conditions. By expanding the velocity potential using Fourier series in the circumferential direction, the problem is reduced to a set of two-dimensional equations. The introduction of generalized curvilinear coordinates enables the application of spectral methods to irregular axisymmetric domains, overcoming the limitations of conventional spectral methods restricted to regular geometries. Two types of spectral methods―the spectral collocation method and the spectral nodal Galerkin method―are formulated and applied to sound field analyses in cylindrical and kettledrum-shaped cavities. Numerical results demonstrate that the proposed methods achieve high accuracy with a small number of unknowns. Among the proposed approaches, the nodal Galerkin method exhibits the fastest convergence and highest accuracy.