A Convective-like Energy-Stable Open Boundary Condition for Simulations of Incompressible Flows

TL;DR

This paper introduces a new energy-stable open boundary condition for incompressible flow simulations that effectively handles backflows and vortices, improving stability and control at outflow boundaries.

Contribution

It proposes a novel energy-stable open boundary condition with velocity control and an associated numerical algorithm using a rotational velocity-correction strategy.

Findings

Ensures energy stability even with strong vortices and backflows.

Provides velocity control at the outflow boundary, unlike previous methods.

Demonstrates effectiveness through extensive numerical experiments at various Reynolds numbers.

Abstract

We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even when strong vortices or backflows occur at the outflow boundary. Under certain situations it can be reduced to a form that can be analogized to the usual convective boundary condition. One prominent feature of this boundary condition is that it provides a control over the velocity on the outflow/open boundary. This is not available with the other energy-stable open boundary conditions from previous works. Our numerical algorithm treats the proposed open boundary condition based on a rotational velocity-correction type strategy. It gives rise to a Robin-type condition for the discrete pressure and a Robin-type condition for the discrete velocity on the outflow/open boundary, respectively at the pressure and the velocity sub-steps. We present extensive numerical experiments on a canonical wake flow and a jet flow in open domain to test the effectiveness and performance of the method developed herein. Simulation results are compared with the experimental data as well as with other previous simulations to demonstrate the accuracy of the current method. Long-time simulations are performed for a range of Reynolds numbers, at which strong vortices and backflows occur at the outflow/open boundaries. The results show that our method is effective in overcoming the backflow instability, and that it allows for the vortices to discharge from the domain in a fairly natural fashion even at high Reynolds numbers.