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October 4, 2005, 04:15 
Simulating square cylinder using cartesian grid?

#1 
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Hello,
I currently 've a FVM navier stokes code which uses cartesian grids. Can I simulate flow past a square cylinder using this code? Will the cartesian grid pose any problem? If can, does it mean that I need to ignore those cells which are inside the cylinder? Thank you. 

October 4, 2005, 04:33 
Re: Simulating square cylinder using cartesian gri

#2 
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Yes, you can solve the square cylinder problem with the Cartesian grid. While solving, ignore the point which are inside the square cylinder and impose the noslip boundary conditions at the surface of the cylinder.
The following reference (and reference therein) will give you enough details for this problem: # A. K. Dhiman, R. P. Chhabra, V. Eswaran (2005), Flow and Heat Transfer Across a Confined Square Cylinder in the Steady Flow Regime: Effect of Peclet Number, International Journal of Heat and Mass Transfer, 48, 4598  4614. # A. Sharma and V. Eswaran, Heat and fluid flow across a square cylinder in the twodimensional laminar flow regime, Numer. Heat Transfer Part A 45 (2004), pp. 247â€"269. #A. Sharma and V. Eswaran, Effect of adding and opposing buoyancy on the heat and fluid flow across a square cylinder at Re = 100, Numer. Heat Transfer Part A 45 (2004), pp. 601â€"624 # A. Sharma and V. Eswaran, Effect of channelconfinement on the twodimensional laminar flow and heat transfer across a square cylinder, Numer. Heat Transfer Part A 47 (2005), pp. 79â€"107. # A. Mukhopadhyay, G. Biswas and T. Sundararajan, Numerical investigation of confined wakes behind a square cylinder in a channel, Int. J. Numer. Methods Fluids 14 (1992), pp. 1473â€"1484. # A.K. Gupta, A. Sharma, R.P. Chhabra and V. Eswaran, Twodimensional steady flow of a power law fluid past a square cylinder in a plane channel: momentum and heat transfer characteristics, Ind. Eng. Chem. Res. 42 (2003), pp. 5674â€"5686. # A. Sohankar, L. Davidson, C. Norberg, Numerical simulation of unsteady flow around a square twodimensional cylinder, in: Proceedings of the 12th Australian Fluid Mechanics Conference, Sydney, Australia, 1995, pp. 517â€"520. 

October 4, 2005, 06:39 
Re: Simulating square cylinder using cartesian gri

#3 
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wow, ramp, where did u find all that info within such a short time?
Thanks you very much! 

October 4, 2005, 15:45 
Re: Simulating square cylinder using cartesian gri

#4 
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You might also check the article in Scientific American, probably in the 60's. It's by Frank Harlow and Jacob Fromm. They used stream function  vorticity.
This was certainly one of the earliest expositions of computational fluids to the scientific community. 

October 10, 2005, 06:14 
Re: Simulating square cylinder using cartesian gri

#5 
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hi, i'm in the process of implementing the BC. if i ignore the pts(cells) inside the sq. cylinder, i've 3 options 
1.i exclude the cells from the sys. of linear eqns and solve it, but the numbering of cells will be quite difficult 2. i include them in the sys. of linear eqns and solve it, but will that cause instability such as 0/0? 3. i include them in the sys. of linear eqns, assign an arbitrary value to center coefficient of the eqn (along main diagonal) and and solve it Is the 3rd option the best? or is there some other better options? thanks 

October 10, 2005, 08:12 
Re: Simulating square cylinder using cartesian gri

#6 
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I think the first option is good... anyhow u need to define the location of cylinder and the cells inside the square cylinder... and also it is not as such difficult in Cartesian grid... U directly know the coordinates numbering of the sqaure.


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