Issue1. Vol.1 (April, 2013) - IIT Mandi

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ESSENT Society for Collaborative Research and Innovation, IIT MandiFig 3(b): Streamlines for Re = 500 fromDennis et al. [5].Fig 4(a): Vorticity contours for αm = 2.0, Sf = 0.4 and Re= 200 where dashed and solid lines represent negative andpositive vortices respectively.Fig 4(b): Lift and Drag coefficientsFig 4(c): Phase DiagramOur scheme also very accurately captures thecomplex flow phenomena for Re as high as 500.Fig: 3(a) shows an excellent qualitativeagreement on streamlines with the numericalresult of Dennis et al. [5] in Fig: 3(b).On theother hand, fig: 4(a) clearly depicts the vorticitycontours at a particular instant when forcingfrequency increases to 0.4 for Re = 200. Acloser inspection of Fig: 4(b) discloses that thereare two frequency peaks in the lift curves andboth are of different amplitude. Near periodicityof velocity end point diagram in Fig: 4(c)further implies that size and strength of vorticesappears uneven.Conclusion:We have discussed the higher order compactscheme and its application to flow past arotationally oscillating cylinder. The presentscheme has proven to be useful to characterizethe diagnostics of two dimensional flows behinda rotationally oscillating cylinder accurately.Further there is a huge possibility to developand implement the HOC scheme to solve thereal three dimensional problems. We can extendour approach for the 2D interface problems withthe possibility of using it to tackle flows inrandom geometries governed by Navier-Stokesequations and moving interface problems. Butthe potential still remains to explore many moreareas and the flood gates can open up evenfurther.50 ESSENT|Issue1|Vol1
ESSENT Society for Collaborative Research and Innovation, IIT MandiReferences:1) Kalita JC. Dalal DC. and Dass AK., 2002, Atransformation free HOC scheme for steadystate convection diffusion on non-uniformgrids, Int. J. Numer. Methods Fluids 44, 33-53.2) Ray RK. and Kalita JC., 2010, Atransformation-free HOC scheme forimpulsively started circular cylinder. J.Comput. Phys. 228, 5207-52364) Ray R.K., 2011, A transformation free HOCscheme for incompressible viscous flowpast a rotating and translating circularcylinder, J. Sci. Comput. 46, 265-293.incompressible viscous flows on nonuniformpolar grids. Int. J. Numer. MethodsFluids, 683-708.3) Kalita JC, Ray RK. , 2009, Atransformation-free HOC scheme forincompressible viscous flows past an5) Dennis S.C.R.,Nguyen P. andKocabiyik Serpil, 2000, The flowinduced by a rotationally oscillating andtranslating circular cylinder , J. FluidMech. 407, 123-144.51 ESSENT|Issue1|Vol1
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