Traction open boundary condition for incompressible, turbulent, single- or multi-phase flows, and surface wave simulations

Abstract

In simulations, artificial boundaries need to be introduced to limit the size of computational domains and thereby lower computational cost. At these boundaries, flow variables need to be calculated in a way that will not induce any perturbation of the interior solution, which poses a great challenge in incompressible flows. In this paper, we demonstrate the potential of a new traction open boundary condition to address the classical problems encountered in simulations with open boundary conditions: backflow instability, wave reflections, and confinement caused by the proximity of the outlet. This novel boundary treatment, based on a Lagrangian estimation of the traction in the outlet section coupled to a stabilization term, is shown to provide accuracy and stability for turbulent, single- or multi-phase flows, test cases. Using a simulation of surface gravity waves, we show that if special care is given to the computation of the estimated traction, it is possible to get a fully non-reflective open boundary condition.