Outflow Boundary Condition and Algorithm for Single-Phase Incompressible Flows

<p>We present a robust and accurate outflow boundary condition&nbsp;and an associated numerical algorithm&nbsp;for incompressible flow simulations on&nbsp;unbounded physical domains, aiming at&nbsp;maximizing the domain truncation&nbsp;without adversely affecting&nbsp;the flow physics.&nbsp;The proposed outflow boundary condition allows&nbsp;for the influx of kinetic energy&nbsp;into the domain through the outflow&nbsp; boundaries,&nbsp;and prevents un-controlled growth in the&nbsp;energy of the&nbsp;domain in such situations.

The&nbsp;numerical algorithm for the outflow boundary&nbsp;condition is developed&nbsp;on top of a rotational velocity-correction type&nbsp;strategy to de-couple the pressure and velocity&nbsp;computations,&nbsp;and a special construction in the algorithmic formulation&nbsp;prevents the numerical locking&nbsp;at the outflow boundaries for time-dependent problems.&nbsp;Extensive numerical tests for flow problems with bounded and&nbsp;semi-bounded physical domains&nbsp;demonstrate that&nbsp;this outflow boundary condition and the numerical&nbsp;algorithm produce stable and accurate simulations &nbsp;on even severely truncated computational&nbsp;domains,&nbsp;where strong vortices may be present at or exit&nbsp;the outflow boundaries.