Numerical solution of the steady incompressible Navier—Stokes equations for the flow past a sphere by a multigrid defect correction technique

1990 ◽  
Vol 11 (4) ◽  
pp. 379-395 ◽  
Author(s):  
Gh. Juncu ◽  
R. Mihail
Keyword(s):  
Numerical Solution ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Defect Correction ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Correction Technique ◽  
Flow Past A Sphere

Higher-Order Compact Scheme for the Incompressible Navier-Stokes Equations in Spherical Geometry

2012 ◽  
Vol 11 (1) ◽  
pp. 99-113 ◽  
Author(s):  
T. V. S. Sekhar ◽  
B. Hema Sundar Raju ◽  
Y. V. S. S. Sanyasiraju
Keyword(s):  
Stokes Equations ◽  
Higher Order ◽  
Compact Scheme ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Uniform Grid ◽  
Axially Symmetric ◽  
Flow Past ◽  
Correction Technique ◽  
Flow Past A Sphere

AbstractA higher-order compact scheme on the nine point 2-D stencil is developed for the steady stream-function vorticity form of the incompressible Navier-Stokes (N-S) equations in spherical polar coordinates, which was used earlier only for the cartesian and cylindrical geometries. The steady, incompressible, viscous and axially symmetric flow past a sphere is used as a model problem. The non-linearity in the N-S equations is handled in a comprehensive manner avoiding complications in calculations. The scheme is combined with the multigrid method to enhance the convergence rate. The solutions are obtained over a non-uniform grid generated using the transformation r=e? while maintaining a uniform grid in the computational plane. The superiority of the higher order compact scheme is clearly illustrated in comparison with upwind scheme and defect correction technique at high Reynolds numbers by taking a large domain. This is a pioneering effort, because for the first time, the fourth order accurate solutions for the problem of viscous flow past a sphere are presented here. The drag coefficient and surface pressures are calculated and compared with available experimental and theoretical results. It is observed that these values simulated over coarser grids using the present scheme are more accurate when compared to other conventional schemes. It has also been observed that the flow separation initially occurred at Re = 21.

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Subgrid Stabilized Defect Correction Methods for the Navier–Stokes Equations

2006 ◽  
Vol 44 (4) ◽  
pp. 1639-1654 ◽  
Author(s):  
Songul Kaya ◽  
William Layton ◽  
Béatrice Rivière
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Defect Correction ◽  
Navier Stokes Equations
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