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A low-Mach-number, compressible flow, simulation model is used to compute unsteady oscillatory flow in the neighborhood of a thermoacoustic stack. The model relies on a vorticity-based formulation of the mass, momentum, and energy conservation equations. The numerical scheme incorporates a highly efficient construction which combines a domain decomposition boundary Green’s function formulation with fast Fourier inversion methods. Computed results are used to calculate the effective impedance of the device, which accounts for contributions of both linearized acoustic phenomena and nonlinear inertial effects. The dependence of this effective impedance on stack configuration and on acoustic driving amplitudes and frequencies is also analyzed. [Work supported by the Office of Naval Research.]