A simple and efficient outflow boundary condition for the incompressible Navier-Stokes equations

Yibao Li, Jung Ii Choi, Yongho Choic, Junseok Kim

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6 Citations (Scopus)

Abstract

Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier-Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier-Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity-pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes.

Original languageEnglish
Pages (from-to)69-85
Number of pages17
JournalEngineering Applications of Computational Fluid Mechanics
Volume11
Issue number1
DOIs
Publication statusPublished - 2017

Bibliographical note

Funding Information:
Y.B. Li is supported by the Fundamental Research Funds for the Central Universities, China [No. XJJ2015068] and by the National Natural Science Foundation of China [No. 11601416]; J.-I. Choi was supported by the National Research Foundation (NRF) of Korea, grant funded by the Ministry of Science, Information and Communications Technology, and Future Planning (MSIP) of the Korea government [No. NRF-2014R1A2A 1A11053140]; J.S. Kim was supported by the National Research Foundation of Korea, grant funded by the Korea government (MSIP) [NRF-2014R1A2A2A01003683].

Publisher Copyright:
© 2016 The Author(s).

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Modelling and Simulation

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