Nonreflecting Boundary Conditions for the Nonlinear

nonreflecting boundary conditions are derived for time-dependent internal flows. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of the Fourier-Bessel modes. This leads to a onedimensional convected wave equation for the perturbation pressure for which an ‘exact’ nonreflecting boundary condition, local in space but nonlocal in time, has been derived. 6 The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Four test problems were carried out: propagation of acoustic, vortical and entropic waves and the scattering of a vortical wave by a cascade of flat plates. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that unlike the local boundary conditions, whose accuracy depends on the group velocity of the scattered or propagating waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities.