In this paper, the local grid refinement is focused by
using a nested grid technique. The Cartesian grid numerical method is
developed for simulating unsteady, viscous, incompressible flows
with complex immersed boundaries. A finite volume method is used in
conjunction with a two-step fractional-step procedure. The key aspects
that need to be considered in developing such a nested grid solver are
imposition of interface conditions on the inter-block and accurate
discretization of the governing equation in cells that are with the
inter-block as a control surface. A new interpolation procedure is
presented which allows systematic development of a spatial
discretization scheme that preserves the spatial accuracy of the
underlying solver. The present nested grid method has been tested by
two numerical examples to examine its performance in the two
dimensional problems. The numerical examples include flow past a
circular cylinder symmetrically installed in a Channel and flow past
two circular cylinders with different diameters. From the numerical
experiments, the ability of the solver to simulate flows with
complicated immersed boundaries is demonstrated and the nested grid
approach can efficiently speed up the numerical solutions.
[1] L. Chacon, and G. Lapenta, "A fully implicit, nonlinear adaptive grid
strategy," J. Comput. Phys., vol. 212, pp 703-717, 2006.
[2] H. Ding, and C. Shu, "A stencil adaptive algorithm for finite difference
solution of incompressible viscous flows," J. Comput. Phys., vol. 214, pp
397-420, 2006.
[3] Y. F. Peng, Y. H. Shiau, and R. R. Hwang, "Transition in a 2-D lid-driven
cavity flow," Comput. & Fluids, vol. 32, pp 337-352, 2003.
[4] J. F. Ravoux, A. Nadim, and H. Hariri, "An Embedding Method for Bluff
Body Flows: Interactions of Two Side-by-Side Cylinder Wakes," Theo.
Comput. Fluid Dyn., vol. 16, pp. 433-466, 2003
[5] T. Ye, R. Mittal, H. S. Udaykumar, and W. Shyy, "An accurate Cartesian
grid method for viscous incompressible flows with complex immersed
boundaries," J. Comput. Phys., vol. 156, pp 209-240, 1999.
[6] J. H. Chen, W. G. Pritchard, and S. J. Tavener, "Bifurcation for flow past
a cylinder between parallel planes," J. Fluid Mech., vol. 284, pp 23-52,
1995.
[7] B. J. Strykowski, and K. R. Sreenivasan, "On the formation and
suppression of vortex ÔÇÿshedding- at low Reynolds numbers," J. Fluid
Mech., vol. 218, pp 71-107, 1990.
[8] H. Sakamoto, K. Tan, and H. Haniu, "An optimum suppression of fluid
forces by controlling a shear layer separated from a square prism," J.
Fluid Eng., vol. 113, pp 183-189, 1991.
[9] H. Sakamoto, and H. Haniu, "Optimum suppression of fluid forces acting
on a circular cylinder," J. Fluid Eng., vol. 116, pp 221-227, 1994.
[10] C. Dalton, Y. Xu, and J. C. Owen, "The Suppression of lift on a circular
cylinder due to vortex shedding at moderate Reynolds numbers," J. Fluid
Struct., vol. 15, pp 61-128, 2001.
[11] M. Zhao, L. Cheng, B. Teng, and D. Liang, "Numerical simulation of
viscous flow past two circular cylinders of different diameters," Appl.
Ocean Res., vol. 27, pp 39-55, 2005.
[12] Y. Delaunay, and L. Kaiktsis, "Control of circular cylinder wakes using
base mass transpiration," Phys. Fluid, vol. 13, pp 3285-302, 2001.
[13] D. L. Young, J. L. Huang, and T. I. Eldho, "Simulation of laminar vortex
shedding flow past cylinders using a coupled BEM and FEM model,"
Comput. Method Appl. Mech. Eng., vol. 190, pp 5975-5998, 2001.
[14] C. Lei, L. Cheng, K. and Kavanagh, "A finite difference solution of the
shear flow over a circular cylinder," Ocean Eng, vol. 27, pp 271-90, 2000.
[1] L. Chacon, and G. Lapenta, "A fully implicit, nonlinear adaptive grid
strategy," J. Comput. Phys., vol. 212, pp 703-717, 2006.
[2] H. Ding, and C. Shu, "A stencil adaptive algorithm for finite difference
solution of incompressible viscous flows," J. Comput. Phys., vol. 214, pp
397-420, 2006.
[3] Y. F. Peng, Y. H. Shiau, and R. R. Hwang, "Transition in a 2-D lid-driven
cavity flow," Comput. & Fluids, vol. 32, pp 337-352, 2003.
[4] J. F. Ravoux, A. Nadim, and H. Hariri, "An Embedding Method for Bluff
Body Flows: Interactions of Two Side-by-Side Cylinder Wakes," Theo.
Comput. Fluid Dyn., vol. 16, pp. 433-466, 2003
[5] T. Ye, R. Mittal, H. S. Udaykumar, and W. Shyy, "An accurate Cartesian
grid method for viscous incompressible flows with complex immersed
boundaries," J. Comput. Phys., vol. 156, pp 209-240, 1999.
[6] J. H. Chen, W. G. Pritchard, and S. J. Tavener, "Bifurcation for flow past
a cylinder between parallel planes," J. Fluid Mech., vol. 284, pp 23-52,
1995.
[7] B. J. Strykowski, and K. R. Sreenivasan, "On the formation and
suppression of vortex ÔÇÿshedding- at low Reynolds numbers," J. Fluid
Mech., vol. 218, pp 71-107, 1990.
[8] H. Sakamoto, K. Tan, and H. Haniu, "An optimum suppression of fluid
forces by controlling a shear layer separated from a square prism," J.
Fluid Eng., vol. 113, pp 183-189, 1991.
[9] H. Sakamoto, and H. Haniu, "Optimum suppression of fluid forces acting
on a circular cylinder," J. Fluid Eng., vol. 116, pp 221-227, 1994.
[10] C. Dalton, Y. Xu, and J. C. Owen, "The Suppression of lift on a circular
cylinder due to vortex shedding at moderate Reynolds numbers," J. Fluid
Struct., vol. 15, pp 61-128, 2001.
[11] M. Zhao, L. Cheng, B. Teng, and D. Liang, "Numerical simulation of
viscous flow past two circular cylinders of different diameters," Appl.
Ocean Res., vol. 27, pp 39-55, 2005.
[12] Y. Delaunay, and L. Kaiktsis, "Control of circular cylinder wakes using
base mass transpiration," Phys. Fluid, vol. 13, pp 3285-302, 2001.
[13] D. L. Young, J. L. Huang, and T. I. Eldho, "Simulation of laminar vortex
shedding flow past cylinders using a coupled BEM and FEM model,"
Comput. Method Appl. Mech. Eng., vol. 190, pp 5975-5998, 2001.
[14] C. Lei, L. Cheng, K. and Kavanagh, "A finite difference solution of the
shear flow over a circular cylinder," Ocean Eng, vol. 27, pp 271-90, 2000.
@article{"International Journal of Architectural, Civil and Construction Sciences:52899", author = "Yih-Ferng Peng", title = "Study on a Nested Cartesian Grid Method", abstract = "In this paper, the local grid refinement is focused by
using a nested grid technique. The Cartesian grid numerical method is
developed for simulating unsteady, viscous, incompressible flows
with complex immersed boundaries. A finite volume method is used in
conjunction with a two-step fractional-step procedure. The key aspects
that need to be considered in developing such a nested grid solver are
imposition of interface conditions on the inter-block and accurate
discretization of the governing equation in cells that are with the
inter-block as a control surface. A new interpolation procedure is
presented which allows systematic development of a spatial
discretization scheme that preserves the spatial accuracy of the
underlying solver. The present nested grid method has been tested by
two numerical examples to examine its performance in the two
dimensional problems. The numerical examples include flow past a
circular cylinder symmetrically installed in a Channel and flow past
two circular cylinders with different diameters. From the numerical
experiments, the ability of the solver to simulate flows with
complicated immersed boundaries is demonstrated and the nested grid
approach can efficiently speed up the numerical solutions.", keywords = "local grid refinement, Cartesian grid, nested grid,fractional-step method.", volume = "2", number = "10", pages = "225-8", }