The process of noise generation in a flow-excited Helmholtz resonator involves strong interaction between a time-dependent fluid flow and acoustic resonance. Quantitative prediction of this effect, requiring accurate prediction of time-dependent features of a flow over complex three-dimensional bodies, turbulence modeling, compressibility and Mach number effects, is one of the major challenges to computational fluid dynamics. In this paper a numerical procedure based on the lattice kinetic equation, combined with the RNG turbulence model, is applied to describe a well-controlled experiment on acoustic resonance excitation by a grazing flow [Nelson et al., J. Sound Vib. 78, 15-27 (1981)]. The achieved agreement between numerical and physical experiments is very good. The simulations reveal a universality transformation enabling comparison of the data for different inlet conditions.