Volume 11, Issue 1
Higher-Order Compact Scheme for the Incompressible Navier-Stokes Equations in Spherical Geometry

T. V. S. Sekhar, B. Hema Sundar Raju & Y. V. S. S. Sanyasiraju

Commun. Comput. Phys., 11 (2012), pp. 99-113.

Published online: 2012-11

Preview Full PDF 436 1364
Export citation
  • Abstract

A 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 (NS) 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 = eξ 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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-11-99, author = {}, title = {Higher-Order Compact Scheme for the Incompressible Navier-Stokes Equations in Spherical Geometry}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {1}, pages = {99--113}, abstract = {

A 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 (NS) 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 = eξ 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.171010.030311a}, url = {http://global-sci.org/intro/article_detail/cicp/7355.html} }
TY - JOUR T1 - Higher-Order Compact Scheme for the Incompressible Navier-Stokes Equations in Spherical Geometry JO - Communications in Computational Physics VL - 1 SP - 99 EP - 113 PY - 2012 DA - 2012/11 SN - 11 DO - http://dor.org/10.4208/cicp.171010.030311a UR - https://global-sci.org/intro/article_detail/cicp/7355.html KW - AB -

A 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 (NS) 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 = eξ 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.

T. V. S. Sekhar, B. Hema Sundar Raju & Y. V. S. S. Sanyasiraju. (2020). Higher-Order Compact Scheme for the Incompressible Navier-Stokes Equations in Spherical Geometry. Communications in Computational Physics. 11 (1). 99-113. doi:10.4208/cicp.171010.030311a
Copy to clipboard
The citation has been copied to your clipboard