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The accuracy of two direct coupled two-step CFD/CAA methods is discussed. For the flow field either a finite-volume (FV) method for the solution of the Navier–Stokes equations or a lattice Boltzmann (LB) method is coupled to a discontinuous Galerkin (DG) method for the solution of the acoustic perturbation equations. The coupling takes advantage of a joint Cartesian mesh allowing for the exchange of the acoustic sources without MPI communication. An immersed boundary treatment of the acoustic scattering from solid bodies by a novel solid wall formulation is implemented and validated in the DG method. Results for the case of a spinning vortex pair and the low Reynolds number unsteady flow around a circular cylinder show that a solution with comparable accuracy is obtained for the two direct-hybrid methods when using identical mesh resolution.