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Infrasound observations are commonly used to constrain properties of subaerial volcanic eruptions. In order to better interpret infrasound observations, however, there is a need to better understand the relationship between eruption properties and sound generation. Here we perform two-dimensional computational aeroacoustic simulations where we solve the compressible Navier-Stokes equations with a large-eddy simulation approximation. We simulate idealized impulsive volcanic eruptions where the exit velocity is specified and the eruption is pressure-balanced with the atmosphere. Our nonlinear simulation results are compared with the commonly used analytical linear acoustics model of a compact monopole source radiating acoustic waves isotropically in a half space. The monopole source model matches the simulations for low exit velocities (M < 0.3 where M is the Mach number); however, the two solutions diverge as the exit velocity increases with the simulations developing lower peak amplitude and more rapid onset. For high exit velocities (M>0.8) the radiation pattern becomes anisotropic, with stronger infrasound signals recorded above the vent than on Earth's surface (50% greater peak amplitude for an eruption with M=0.95) and interpreting ground-based infrasound observations with the monopole source model can result in an underestimation of the erupted volume. We examine nonlinear effects and show that nonlinear effects during propagation are relatively minor. Instead, the dominant nonlinear effect is sound generation by the complex flow structure that develops above the vent. This work demonstrates the need to consider anisotropic radiation patterns and near-vent fluid flow when interpreting infrasound observations, particularly for eruptions with sonic or supersonic exit velocities.