Actual impedance of nonreflecting boundary conditions: Implications for computation of resonators
Résumé
Nonreflecting boundary conditions are essential elements in the computation of many compressible flows. Such simulations are very sensitive to the treatment of acoustic waves at boundaries. Nonreflecting conditions allow acoustic waves to propagate through boundaries with zero or small levels of reflection into the domain. However, perfectly nonreflecting conditions must be avoided because they can lead to ill-posed problems for the mean flow. Various methods have been proposed to construct boundary conditions that can be sufficiently nonreflecting for the acoustic field while still making the mean flow problem well-posed. A widely used technique for nonreflecting outlets is analyzed (Poinsot, T., and Lele, S., "Boundary Conditions for Direct Simulations of Compressible Viscous Flows," Journal of Computational Physics, Vol. 101, No.1,1992, pp. 104-129; Rudy, D. H., and Strikwerda, J. C., "A Non-Reflecting Outflow Boundary Condition for Subsonic Navier-Stokes Calculations," Journal of Computational Physics, Vol. 36, 1980, pp. 55-70). It shows that the correction introduced by these authors can lead to large reflection levels and resonant behavior that cannot be observed in the experiment. A simple scaling is proposed to evaluate the relaxation coefficient used in these methods for a nonreflecting outlet. The proposed scaling is tested for simple cases (ducts) both theoretically and numerically.
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