A pressure correction scheme for generalized form of energy-stable open boundary conditions for incompressible flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:291

Article

Dong, S.¹  Shen, J.¹ 

[1] Purdue Univ, Ctr Computat & Appl Math, Dept Math, W Lafayette, IN 47907 USA

关键词: Pressure correction scheme;    Outflow;    Open boundary condition;    Outflow boundary condition;    Unbounded domain;    Backflow instability;    Spectral element;   

DOI  :  10.1016/j.jcp.2015.03.012

来源: Elsevier

【 摘 要 】

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 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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