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Abstract

This paper reports numerical experiments for propagating a continuous acoustic pressure signal by means of the linearized Euler equations with both a uniform flow and a parallel jet as the base or mean flow. The numerical domain is embedded in a surrounding damping layer, and the outer boundaries of the damping layer are treated with weak Giles type nonreflecting boundary conditions that are introduced in this paper as interpolation constraints. We view this combination of the damping layer with the nonreflecting outer boundary conditions as the complete boundary treatment. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, which would be improved by grid refinement, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error from the complete boundary treatment can be controlled. These computational experiments show that the weak boundary conditions are stable, and the complete boundary treatment is conditionally stable, for long simulation times, and that the damping layer width and the damping amplitude can be adjusted to produce maximum relative errors that are O[10⁻⁶]. The complete boundary treatment is in this sense consistent with the numerical simulation of the propagation dynamics.

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Experiments in Numerical Error Control for Sound Propagation in a 2D Jet Using a dAmping Layer and Nonreflecting Outer Boundaries

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