Generalized characteristic boundary conditions for computational aeroacoustics

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Description/Abstract

An extended conservative formalism of the characteristic boundary conditions is presented on the basis of the
generalized coordinates for practical computational aeroacoustics. The formalism is derived for solving the entire
conservative form of the compressible Euler or Navier–Stokes equations on the body-fitted grid mesh system by
using the high-order and high-resolution numerical schemes. It includes the matrices of transformation between
the conservative and the characteristic variables, which were already derived in the literature to analyze the
eigenvalue–eigenvector modes in an arbitrary direction. The conservation-form governing equations with their
full terms are solved at the boundaries, and no kind of extrapolation or simplification of the equations is included
in this formalism. Additional correction terms are devised to preserve the conservative form of flux derivative
terms in the generalized coordinates. Especially, the soft inflow conditions are presented to keep the nonreflecting
features, as well as to maintain the mean value of inflow velocity at the inlet boundary. These boundary conditions
are applied to the actual computation of two-dimensional viscous cylinder inflows with Reynolds number of 400
on the grid meshes clustered on the cylinder surface and the downstream region. The Strouhal number due to
von Karman vortex streets, root-mean-square lift coefficient, andmean drag coefficient are evaluated correctly in
comparison with experimental data. The far-field sound pressure levels are measured directly in this computation,
and the accuracy is validated by an analytic formula derived in the literature.