Generalized characteristic boundary conditions for computational aeroacoustics

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 flows 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, and mean drag coefficient are evaluated correctly in comparison,vith 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.