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2J Q J Q absorbing boundary conditions Acoustic Gravity Waves acoustic wave propagation Akron Applications in Science approximate boundary condition atmospheric fluid flow boundary conditions 2.32 boundary operators boundary value problem computational efficiency Computer Applications conditions 2.4 Decibel Level Distribution diagonal dispersion relations dr dz eigenvectors energy estimate energy release Euler equations Figure forcing term governing equations Hankel transforms Hariharan higher order boundary initial boundary value initial conditions Institute for Computer Langley Research Center Laplace transform linear problem lower order terms neglect the lower Nondimensional Numerical results open boundary problem order boundary conditions order linearized version paper discusses numerical Performing Organization point source pressure and density pressure level distribution Pressure Wave problem that arises radiation boundary conditions Riemann invariants Science and Engineering sound pressure level stable boundary conditions theorem 3.1 truncated region University of Akron uTSCu wave equations well-posed problem yield a well-posed zeroth order condition