A LBIE-RBF solution to the convected wave equation for flow acoustics

In this paper, the meshless local boundary integral equation (LBIE) method is implemented for the solution of convected wave equation in frequency domain. Such a problem plays an important role for the noise prediction in flow acoustics. The case of a uniform flow in x-direction is analyzed. For the resultant convected Helmholtz equation, the free-space Green's function has a more complicated form than the Green's function for the classical Helmholtz equation, though it reduces to the latter when a coordinate (Prandtl–Glauert) transformation is applied. Furthermore, the LBIE method requires the determination of the solution of the corresponding Dirichlet's problem in local subdomains (companion solution). Therefore, the relevant companion solution is derived. Radial basis functions are used for the interpolations of the field variable. Numerical examples are shown for cases up to frequency of 5000 Hz and Mach number of 0.5, and the results are compared with FEM software (COMSOL).