Description
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary conditions, which all ensure the energy stability of the system, even in situations where strong vortices or backflows occur at the open/outflow boundaries. Our numerical algorithm for treating these open boundary conditions is based on a rotational pressure correction-type strategy, with a formulation suitable for $C^0$ spectral-element spatial discretizations. We have introduced a discrete equation and associated boundary conditions for an auxiliary variable. The algorithm contains constructions that prevent a numerical locking at the open/outflow boundary. In addition, we have also developed a scheme with a provable unconditional stability for a sub-class of the open boundary conditions. Extensive numerical experiments have been presented to demonstrate the performance of our method for several flow problems involving open/outflow boundaries. We compare simulation results with the experimental data to demonstrate the accuracy of our algorithm. Long-time simulations have been performed for a range of Reynolds numbers at which strong vortices or backflows occur at the open/outflow boundaries. We show that the open boundary conditions and the numerical algorithm developed herein produce stable simulations in such situations.
Cite this work
Researchers should cite this work as follows:
- Suchuan Dong (2015). Generalized Energy-Stable Open Boundary Conditions for Incompressible Flows. Purdue University Research Repository. doi:10.4231/R7RV0KM6
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Data files for paper "S. Dong & J. Shen, A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows, Journal of Computational Physics, 291, 254-278, 2015".