0
Research Papers: Techniques and Procedures

Application of an Iterative High Order Difference Scheme Along With an Explicit System Solver for Solution of Stream Function-Vorticity Form of Navier–Stokes Equations

[+] Author and Article Information
Parviz Ghadimi

e-mail: pghadimi@aut.ac.ir

Mehdi Yousefi Fard

e-mail: yousefifard@aut.ac.ir

Abbas Dashtimanesh

e-mail: a.dashtimanesh@aut.ac.ir
Department of Marine Technology,
Amirkabir University of Technology,
Hafez Avenue, No. 424,
P.O. Box 15875-4413
Tehran, Iran

Manuscript received July 26, 2012; final manuscript received December 23, 2012; published online February 22, 2013. Assoc. Editor: Chunill Hah.

J. Fluids Eng 135(4), 041401 (Feb 22, 2013) (11 pages) Paper No: FE-12-1347; doi: 10.1115/1.4023295 History: Received July 26, 2012; Revised December 23, 2012

This paper describes the general convection-diffusion equation in 2D domain based on a particular fourth order finite difference method. The current fourth-order compact formulation is implemented for the first time, which offers a semi-explicit method of solution for the resulting equations. A nine point finite difference scheme with uniform grid spacing is also put into action for discretization purpose. The proposed numerical model is based on the Navier–Stokes equations in a stream function-vorticity formulation. The fast convergence characteristic can be mentioned as an advantage of this scheme. It combines the enhanced Fournié's fourth order scheme and the expanded fourth order boundary conditions, while offering a semi-explicit formulation. To accomplish this, some coefficients which do not influence the solutions are also omitted from Fournié's formulation. Consequently, very accurate results can be acquired with a relatively coarse mesh in a short time. The robustness and accuracy of the proposed scheme is proved using the benchmark problems of flow in a driven square cavity at medium and relatively high Reynolds numbers, flow over a backward-facing step, and flow in an L-shaped cavity.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Labeling of the nine grid points

Grahic Jump Location
Fig. 14

(a) Profile of u along CL1, and (b) profile of v along CL2 for Re = 100

Grahic Jump Location
Fig. 15

Vorticity and stream function contours: Re = 1000

Grahic Jump Location
Fig. 16

(a) Profile of u along CL1, and (b) profile of v along CL2 for Re = 1000

Grahic Jump Location
Fig. 3

Vorticity and stream function contours: Re = 1000

Grahic Jump Location
Fig. 4

(a) Profile of u along the cavity vertical centerline, and (b) profile of v along the horizontal centerline for Re = 1000

Grahic Jump Location
Fig. 2

Geometry and boundary conditions of the square cavity

Grahic Jump Location
Fig. 13

Vorticity and stream function contours: Re = 100

Grahic Jump Location
Fig. 5

Vorticity and stream function contours: Re = 5000

Grahic Jump Location
Fig. 6

(a) Profile of u along the cavity vertical centerline, and (b) profile of v along the horizontal centerline for Re = 5000, N = 256

Grahic Jump Location
Fig. 7

(a) Profile of u along the cavity vertical centerline, and (b) profile of v along the horizontal centerline for Re = 5000, N = 512

Grahic Jump Location
Fig. 8

Vorticity and stream function contours: Re = 10,000

Grahic Jump Location
Fig. 9

(a) Profile of u along the cavity vertical centerline, and (b) profile of v along the horizontal centerline for Re = 10,000, N = 512

Grahic Jump Location
Fig. 10

Vorticity and stream function contours: Re = 20,000

Grahic Jump Location
Fig. 11

(a) Profile of u along the cavity vertical centerline, and (b) profile of v along the horizontal centerline for Re = 20,000, N = 1024

Grahic Jump Location
Fig. 12

Geometry of the L-shaped cavity

Grahic Jump Location
Fig. 17

Geometry and boundary conditions of backward-facing step flow problem

Grahic Jump Location
Fig. 18

Stream function contours: Re = 100–1000

Grahic Jump Location
Fig. 19

Reattachment length

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In