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Study on a Nested Cartesian Grid Method

Authors: Yih-Ferng Peng


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: cartesian grid, local grid refinement, nested grid, fractional-step method

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[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.