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

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

Research output: Contribution to journalArticle

3 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

Fingerprint

Incompressible Navier-Stokes Equations
Navier Stokes equations
Boundary conditions
Mass flux
Weak Formulation
Divergence-free
Projection Method
Numerical Algorithms
Numerical Scheme
Computational Results
Computational Cost
Navier-Stokes Equations
Mass transfer
Discretization
Numerical Experiment
Robustness
Grid
Fluid
Fluids
Cell

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation

Cite this

A simple and efficient outflow boundary condition for the incompressible Navier-Stokes equations. / Li, Yibao; Choi, Jung Ii; Choic, Yongho; Kim, Junseok.

In: Engineering Applications of Computational Fluid Mechanics, Vol. 11, No. 1, 2017, p. 69-85.

Research output: Contribution to journalArticle

@article{0bba4a8acf1947128eae248caf65caf5,
title = "A simple and efficient outflow boundary condition for the incompressible Navier-Stokes equations",
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.",
author = "Yibao Li and Choi, {Jung Ii} and Yongho Choic and Junseok Kim",
year = "2017",
doi = "10.1080/19942060.2016.1247296",
language = "English",
volume = "11",
pages = "69--85",
journal = "Engineering Applications of Computational Fluid Mechanics",
issn = "1994-2060",
publisher = "Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University",
number = "1",

}

TY - JOUR

T1 - A simple and efficient outflow boundary condition for the incompressible Navier-Stokes equations

AU - Li, Yibao

AU - Choi, Jung Ii

AU - Choic, Yongho

AU - Kim, Junseok

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84997822223&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84997822223&partnerID=8YFLogxK

U2 - 10.1080/19942060.2016.1247296

DO - 10.1080/19942060.2016.1247296

M3 - Article

VL - 11

SP - 69

EP - 85

JO - Engineering Applications of Computational Fluid Mechanics

JF - Engineering Applications of Computational Fluid Mechanics

SN - 1994-2060

IS - 1

ER -