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Context. Recent, nonlinear simulations of wave generation and propagation in full-star models have been carried out in the anelastic approximation using spectral methods. Although it makes long time steps possible, this approach excludes the physics of sound waves completely and rather high artificial viscosity and thermal diffusivity are needed for numerical stability. Direct comparison with observations is thus limited. Aims. We explore the capabilities of our compressible multidimensional hydrodynamics code SLH to simulate stellar oscillations. Methods. We compare some fundamental properties of internal gravity and pressure waves in 2D SLH simulations to linear wave theory using two test cases: (1) an interval gravity wave packet in the Boussinesq limit and (2) a realistic $3\mathrm{M}_\odot$ stellar model with a convective core and a radiative envelope. Oscillation properties of the stellar model are also discussed in the context of observations. Results. Our tests show that specialized low-Mach techniques are necessary when simulating oscillations in stellar interiors. Basic properties of internal gravity and pressure waves in our simulations are in good agreement with linear wave theory. As compared to anelastic simulations of the same stellar model, we can follow internal gravity waves of much lower frequencies. The temporal frequency spectra of velocity and temperature are flat and compatible with observed spectra of massive stars. Conclusion. The low-Mach compressible approach to hydrodynamical simulations of stellar oscillations is promising. Our simulations are less dissipative and require less luminosity boosting than comparable spectral simulations. The fully-compressible approach allows the coupling of gravity and pressure waves to be studied too.