Comptes Rendus
no. 1
A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder
Roel Verstappen1; Marc Dröge1
1 Research Institute of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
Comptes Rendus. Mécanique, High-order methods for the numerical simulation of vortical and turbulent flows , Volume 333 (2005) no. 1, pp. 51-57.

This article deals with a numerical method for solving the unsteady, incompressible Navier–Stokes equations in domains with arbitrarily-shaped boundaries, where the boundary is represented using the Cartesian grid approach. We introduce a novel cut-cell discretization which preserves the spectral properties of convection and diffusion. Here, convection is discretized by a skew-symmetric operator and diffusion is approximated by a symmetric, positive-definite coefficient matrix. Such a symmetry-preserving discretization conserves the kinetic energy (if the dissipation is turned off) and is stable on any grid. The method is successfully tested for an incompressible, unsteady flow around a circular cylinder at Re=100.

Cet article décrit une méthode numérique de résolution des équations de Navier–Stokes incompressibles instationnaires dans des domaines de géométries arbitraires. Nous partons d'une grille cartésienne, modifiée près de la frontière par une nouvelle méthode de découpage de maille, compatible avec les propriétés spectrales des opérateurs de convection et de diffusion. Ainsi, les termes de convection sont discrétisés avec un opérateur discret anti-symétrique (skew-symmetric) et les termes de diffusion sont approchés par un opérateur discret symétrique défini positif. Une telle discrétisation préservant la symétrie permet de conserver l'énergie cinétique (quand la viscosité est negligée) et elle est stable sur n'importe quelle grille. La méthode a été testée avec succès dans le cas de écoulement incompressible instationnaire autour d'un cylindre de section circulaire pour une valeur du nombre de Reynolds Re=100.

Published online:
DOI: 10.1016/j.crme.2004.09.021
Keywords: Computational fluid mechanics, Cartesian grid method, Symmetry-preserving discretization
Mots-clés : Mécanique des fluides numérique, Approximation de grille cartésienne, Discrétisation préservant la symétrie

Roel Verstappen 1; Marc Dröge 1

1 Research Institute of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands 
@article{CRMECA_2005__333_1_51_0,
     author = {Roel Verstappen and Marc Dr\"oge},
     title = {A symmetry-preserving {Cartesian} grid method for computing a viscous flow past a circular cylinder},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {51--57},
     publisher = {Elsevier},
     volume = {333},
     number = {1},
     year = {2005},
     doi = {10.1016/j.crme.2004.09.021},
     language = {en},
}
TY  - JOUR
AU  - Roel Verstappen
AU  - Marc Dröge
TI  - A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder
JO  - Comptes Rendus. Mécanique
PY  - 2005
SP  - 51
EP  - 57
VL  - 333
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crme.2004.09.021
LA  - en
ID  - CRMECA_2005__333_1_51_0
ER  - 
%0 Journal Article
%A Roel Verstappen
%A Marc Dröge
%T A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder
%J Comptes Rendus. Mécanique
%D 2005
%P 51-57
%V 333
%N 1
%I Elsevier
%R 10.1016/j.crme.2004.09.021
%G en
%F CRMECA_2005__333_1_51_0
Roel Verstappen; Marc Dröge. A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder. Comptes Rendus. Mécanique, High-order methods for the numerical simulation of vortical and turbulent flows , Volume 333 (2005) no. 1, pp. 51-57. doi : 10.1016/j.crme.2004.09.021. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.09.021/

[1] J. Purvis; J. Burkhalter Prediction of critical Mach number store configurations, AIAA J., Volume 17 (1979), pp. 1170-1177

[2] M. Berger; R. LeVeque An adaptive Cartesian mesh algorithm for the Euler equations in arbitrary geometries, Proc. 9th AIAA. CFD Conf., Buffalo, NY, 1991, pp. 1-7

[3] T. Ye; R. Mittal; H.S. Udaykumar; W. Shyy An accurate Cartesian grid method for viscous incompressible flow with complex boundaries, J. Comp. Phys., Volume 156 (1999), pp. 209-240

[4] D. Calhoun; R.J. LeVeque A Cartesian grid finite volume method for the advection–diffusion equation in irregular geometries, J. Comp. Phys., Volume 157 (2000), pp. 143-180

[5] R.W.C.P. Verstappen; A.E.P. Veldman Symmetry-preserving discretization of turbulent flow, J. Comp. Phys., Volume 187 (2003), pp. 343-368

[6] F.H. Harlow; J.E. Welsh Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, Volume 8 (1965), pp. 2182-2189

[7] A.G. Kravchenko; P. Moin; K. Shariff B-spline method and zonal grids for simulations of complex turbulent flows, J. Comp. Phys., Volume 151 (1999), pp. 757-789

[8] H. Persillon; M. Braza Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation, J. Fluid Mech., Volume 365 (1998), pp. 23-88

[9] M.M. Zdravkovich Flow Around Circular Cylinders. Vol. 1: Fundamentals, Oxford University Press, 1997

[10] R.D. Henderson Details of the drag curve near the onset of vortex shedding, Phys. Fluids, Volume 7 (1995), pp. 2102-2104

[11] D.J. Tritton Experiments on the flow past a circular cylinder at low Reynolds numbers, J. Fluid Mech., Volume 6 (1959), pp. 547-567

[12] H.G. Dimopoulos; T.J. Hanratty Velocity gradients at the wall for flow around a cylinder for Reynolds numbers between 60 and 360, J. Fluid Mech., Volume 33 (1968), pp. 303-319

Cited by Sources:

Comments - Policy