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Journal of Scientific Computing

, Volume 27, Issue 1–3, pp 431–441

# High Order Accurate Solution of Flow Past a Circular Cylinder

Article

A high order method is applied to time-dependent incompressible flow around a circular cylinder geometry. The space discretization employs compact fourth-order difference operators. In time we discretize with a second-order semi-implicit scheme. A large linear system of equations is solved in each time step by a combination of outer and inner iterations. An approximate block factorization of the system matrix is used for preconditioning. Well posed boundary conditions are obtained by an integral formulation of boundary data including a condition on the pressure. Two-dimensional flow around a circular cylinder is studied for Reynolds numbers in the range 7 ≤  R   ≤ 180. The results agree very well with the data known from numerical and experimental studies in the literature.

## Keywords

Navier–Stokes equations compact fourth-order methods iterative solution circular cylinder vortex shedding

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## References

1. 1.
Braza M., Chassaing P., Minh H. (1986). Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 165, 79–130
2. 2.
Brüger A., Gustafsson B., Lötstedt P., Nilsson J. (2005). High order accurate solution of the incompressible Navier–Stokes equations. J. Comput. Phys. 203, 49–71
3. 3.
Brüger, A., Gustafsson, B., Lötstedt, P., and Nilsson, J. (2004). Splitting methods for high order solution of the incompressible Navier–Stokes equations in 3D. To appear in Int. J. Numer. Meth. Fluids.Google Scholar
4. 4.
Brüger A., Nilsson J., Kress W. (2002). A compact higher order finite difference method for the incompressible Navier–Stokes equations. J. Sci. Comput. 17, 551–560
5. 5.
Dennis S.C.R., Chang G. (1970). Numerical solution for steady flow past a circular cylinder at Reynolds numbers up to 100. J. Fluid Mech. 42, 471–489
6. 6.
Kress W., Nilsson J. (2003). Boundary conditions and estimates for the linearized Navier–Stokes equations on a staggered grid. Comput. Fluids 32, 1093–1112
7. 7.
Lele S. K. (1992). Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42
8. 8.
Park J., Kwon K., Choi H. (1998). Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160. KSME Int. J. 12, 1200–1205Google Scholar
9. 9.
Perot J. B. (1993). An analysis of the fractional step method. J. Comput. Phys. 108, 51–58
10. 10.
Piller M., Stalio E. (2004). Finite-volume compact schemes on staggered grids. J. Comput. Phys. 197, 299–340
11. 11.
Roshko A. (1954). On the development of turbulent wakes from vortex streets. NACA Rep. 1191, 1–23Google Scholar
12. 12.
Williamson C.H.K. (1989). Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds number. J. Fluid Mech. 206, 579–627
13. 13.
Williamson C.H.K., Brown G.L. (1998). A series in $$1/\sqrt{Re}$$ to represent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12, 1073–1085
14. 14.
Zhang H.L., Ko N.W.M. (1996). Numerical analysis of incompressible flow over smooth and grooved circular cylinders. Comput. Fluids 25, 263–281

## Copyright information

© Springer Science+Business Media, Inc. 2006

## Authors and Affiliations

• Erik Stålberg
• 1
Email author
• Arnim Brüger
• 1
• Per Lötstedt
• 2
• Arne V. Johansson
• 1
• Dan S. Henningson
• 1
1. 1.Department of MechanicsKTHStockholmSweden
2. 2.Department of Information Technology, Division of Scientific ComputingUppsala UniversityUppsalaSweden