A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains

We present a robust and accurate outflow boundary condition and an associated numerical algorithm for incompressible flow simulations on unbounded physical domains, aiming at maximizing the domain truncation without adversely affecting the flow physics. The proposed outflow boundary condition allows for the influx of kinetic energy into the domain through the outflow boundaries, and prevents un-controlled growth in the energy of the domain in such situations. The numerical algorithm for the outflow boundary condition is developed on top of a rotational velocity-correction type strategy to de-couple the pressure and velocity computations, and a special construction in the algorithmic formulation prevents the numerical locking at the outflow boundaries for time-dependent problems. Extensive numerical tests for flow problems with bounded and semi-bounded physical domains demonstrate that this outflow boundary condition and the numerical algorithm produce stable and accurate simulations on even severely truncated computational domains, where strong vortices may be present at or exit the outflow boundaries. The method developed herein has the potential to significantly expedite simulations of incompressible flows involving outflow or open boundaries, and to enable such simulations at Reynolds numbers significantly higher than the state of the art.