Commun. Comput. Phys., 2 (2007), pp. 477-500.

A Numerical Comparison of Outflow Boundary Conditions for Spectral Element Simulations of Incompressible Flows

Chuanju Xu 1*, Yumin Lin 1

1 School of Mathematical Sciences, Xiamen University, Xiamen 361005, China.

Received 21 July 2005; Accepted (in revised version) 25 September 2006
Communicated by Jie Shen
Available online 31 October 2006


Outflow boundary conditions (OBCs) are investigated for calculation of incompressible flows by spectral element methods. Several OBCs, including essential-type, natural-type, periodic-type and advection-type, are compared by carrying out a series of numerical experiments. Especially, a simplified form of the so-called Orlanski's OBCs is proposed in the context of spectral element methods, for which a new treatment technique is used. The purpose of this paper is to find stable low-reflective OBCs, suitable and flexible for use of spectral element methods in simulation of incompressible flows in complex geometries. The computation is firstly carried out for a 2D simulation of Poiseuille-Benard channel flow with Re=10, Ri=150 and Pr=2/3. This flow serves as a useful example to demonstrate the applicability of the proposed OBCs because it exhibits a feature of vortex shedding propagating through the outflow boundary. Then a 3D flow around an obstacle is computed to show the efficiency in the case of more general geometries. Among the tested OBCs, the advection-type OBCs are proven to have better behavior as compared with the others.

AMS subject classifications: 65M70, 74S25, 76M22

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Key words: Spectral element methods, outflow boundary conditions, incompressible flows.

*Corresponding author.
Email: (C. Xu), (Y. Lin) † This work was partially supported by NSF China under Grant 10531080, the 973 High Performance Scientific Computation Research Program, and the Program of 985 Innovation Engineering on Information by Xiamen University.

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