A conservative finite difference method and its application for the analysis of a transient flow around a square prism

Detailed results of numerical calculations of transient, 2D incompressible flow around and in the wake of a square prism at Re = 100, 200 and 500 are presented. An implicit finite‐difference operator‐splitting method, a version of the known SIMPLEC‐like method on a staggered grid, is described. Appropriate theoretical results are presented. The method has second‐order accuracy in space, conserving mass, momentum and kinetic energy. A new modification of the multigrid method is employed to solve the elliptic pressure problem. Calculations are performed on a sequence of spatial grids with up to 401 × 321 grid points, at sequentially halved time steps to ensure grid‐independent results. Three types of flow are shown to exist at Re = 500: a steady‐state unstable flow and two which are transient, fully periodic and asymmetric about the centre line but mirror symmetric to each other. Discrete frequency spectra of drag and lift coefficients are presented.

[1]  T. Tamura,et al.  ON THE RELIABILITY OF TWO-DIMENSIONAL SIMULATION FOR UNSTEADY FLOWS AROUND A CYLINDER-TYPE STRUCTURE , 1990 .

[2]  G. Karniadakis,et al.  Three-dimensional dynamics and transition to turbulence in the wake of bluff objects , 1992, Journal of Fluid Mechanics.

[3]  Cornelis Vuik,et al.  How fast the Laplace equation was solved in 1995 , 1997 .

[4]  Atsushi Okajima,et al.  Numerical simulation of flow around rectangular cylinders , 1990 .

[5]  R. W. Douglass,et al.  Perspective: Future Research Directions in Computational Fluid Dynamics , 1994 .

[6]  J. Wissink.  DNS of Transitional Flow Around a Square Cylinder , 1995 .

[7]  N. Kondo,et al.  Third-order upwind finite element computation of the incompressible Navier-Stokes equations Part I. Computation of flow around rectangular cylinders , 1995 .

[8]  A. Leonard.  Vortex methods for flow simulation , 1980 .

[9]  R. P. Fedorenko.  The speed of convergence of one iterative process , 1964 .

[10]  Hugh W. Coleman,et al.  Uncertainties and CFD Code Validation , 1997 .

[11]  R. W. Davis,et al.  A numerical-experimental study of confined flow around rectangular cylinders , 1984 .

[12]  T. Igarashi.  Characteristics of the Flow around a Square Prism , 1984 .

[13]  Michael Schumm,et al.  Self-excited oscillations in the wake of two-dimensional bluff bodies and their control , 1994, Journal of Fluid Mechanics.

[14]  R. W. Davis,et al.  A numerical study of vortex shedding from rectangles , 1982, Journal of Fluid Mechanics.

[15]  T. Shih,et al.  Effects of grid staggering on numerical schemes , 1989 .

[16]  C. Williamson.  The Existence of Two Stages in the Transition to Three-Dimensionality of a Cylinder Wake , 1988 .

[17]  T. Sarpkaya.  Computational Methods With Vortices—The 1988 Freeman Scholar Lecture , 1989 .

[18]  Danesh K. Tafti,et al.  Comparison of some upwind-biased high-order formulations with a second-order central-difference scheme for time integration of the incompressible Navier-Stokes equations , 1996 .

[19]  P. N. Vabishchevich,et al.  Operator‐splitting methods for the incompressible Navier‐Stokes equations on non‐staggered grids. Part 1: First‐order schemes , 1995 .

[20]  Turgut Sarpkaya,et al.  Vorticity, Free Surface, and Surfactants , 1996 .

[21]  G. Pedrizzetti,et al.  Vortex Dynamics , 2011 .

[22]  S. Nagano,et al.  A numerical analysis of two-dimensional flow past a rectangular prism by a discrete vortex model , 1981 .

[23]  Jan G. Wissink,et al.  DNS of 2D turbulent flow around a square cylinder , 1997 .

[24]  M. Fiebig.  Vortex Generators for Compact Heat Exchangers , 1995 .

[25]  A. Okajima.  Strouhal numbers of rectangular cylinders , 1982, Journal of Fluid Mechanics.

[26]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[27]  B. Schoenung,et al.  NUMERICAL CALCULATION OF LAMINAR VORTEX-SHEDDING FLOW PAST CYLINDERS , 1990 .

[28]  Christophe Leys,et al.  Three-dimensional modelling of processes in the fast-axial-flow CO2laser , 1994 .

[29]  P. Roache.  QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS , 1997 .

[30]  J. Humphrey,et al.  Vortex shedding from a bluff body adjacent to a plane sliding wall , 1991 .

[31]  S. Balachandar,et al.  Computations of flow and heat transfer in parallel-plate fin heat exchangers on the CM-5: effects of flow unsteadiness and three-dimensionality , 1997 .

[32]  Turgut Sarpkaya,et al.  Vortex Element Methods for Flow Simulation , 1994 .

[33]  Lars Davidson,et al.  Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition , 1998 .

[34]  C. Williamson.  Vortex Dynamics in the Cylinder Wake , 1996 .

[35]  Numerical study of aerodynamic behavior of a square cylinder , 1990 .

[36]  T. Igarashi,et al.  Heat transfer from a square prism to an air stream , 1985 .

[37]  Arthur E. P. Veldman.  "Missing" Boundary Conditions? Discretize First, Substitute Next, and Combine Later , 1990, SIAM J. Sci. Comput..

[38]  J. Humphrey,et al.  Numerical modelling of confined flow past a cylinder of square cross‐section at various orientations , 1995 .

[39]  S. Karlsson,et al.  On the phenomenon of vortex street breakdown , 1971, Journal of Fluid Mechanics.

[40]  A. Arakawa.  Computational design for long-term numerical integration of the equations of fluid motion: two-dimen , 1997 .

[41]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[42]  Atsushi Okajima,et al.  Numerical simulation of laminar and turbulent flows around rectangular cylinders , 1992 .

[43]  Vidyadhar Y Mudkavi.  The phenomenon of vortex breakdown , 1993 .