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In this paper we implement a simple strategy, based on Jin and Braza'smethod, to deal with nonreflecting outlet boundary conditions forincompressible Navier-Stokes flows using the method of smoothed particlehydrodynamics (SPH). The outflow boundary conditions are implemented using anoutflow zone downstream of the outlet, where particles are moved using anoutgoing wave equation for the velocity field so that feedback noise from theoutlet boundary is greatly reduced. For unidirectional flow across the outlet,this condition reduces to Orlanski's wave equation. The performance of themethod is demonstrated through several two-dimensional test problems, includingunsteady, plane Poiseuille flow, flow between two inclined plates, theKelvin-Helmholtz instability in a channel, and flow in a constricted conduit,and in three-dimensions for turbulent flow in a $90^{\circ}$ section of acurved square pipe. The results show that spurious waves incident from theoutlet are effectively absorbed and that steady-state laminar flows can bemaintained for much longer times compared to periodic boundary conditions. Inaddition, time-dependent anisotropies in the flow, like fluid recirculations,are convected across the outlet in a very stable and accurate manner.

Nonreflecting outlet boundary conditions for incompressible flows using SPH