In the present investigation, the newly developed Higher Order Semi-Compact (HOSC) finite difference scheme has been tested for its capability in capturing the very complex flow phenomenon of unsteady flow past a rotating and translating circular cylinder. The physical problem has been modeled in stream function and vorticity formulation and the obtained governing equations are transformed into curvilinear coordinates using body fitted coordinate system to enable the developed scheme to handle the non-rectangular geometry of the problem. Qualitative and quantitative comparisons have been done at low-rotation parameters and found that the results obtained are in excellent agreement with the existing literature. Then simulations have been carried out at high-rotation parameters and noticed that the HOSC scheme is able to simulate some of the flow features known experimentally but not simulated numerically to the present date. © Springer Science+Business Media, LLC 2007.

Sanyasiraju V.S.S. Yedida

Department of Mathematics

V. Manjula

Complex flow

Higher order

Rotating cylinder

SEMI COMPACT

Computer simulation

Cylinders (shapes)

Finite difference method

Incompressible flow

Numerical methods

Unsteady flow

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Journal of Scientific Computing

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 (N-S) 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 = eζ 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. © 2012 Global-Science Press.

Fulltext

Communications in Computational Physics

Higher-order compact scheme for the incompressible Navier-Stokes equations in spherical geometry

In the present investigation an attempt has been made to solve the two-dimensional incompressible viscous flow past an impulsively started circular cylinder for Reynolds numbers ranging from 20 to 5000 using higher-order semicompact scheme (HOSC). Unlike conventional higher-order compact schemes the HOSC scheme has been developed to handle the circular geometry of the chosen problem and the intensive algebraic manipulations have been reduced considerably by relaxing the compactness of the computational stencil for few terms (but retained for most of the terms) of the discretized equations. For the flow past an impulsively started circular cylinder the results obtained at low and moderate Reynolds numbers have been validated with the experimental and numerical observations available in the literature. For high Reynolds number flows, the present scheme rightly captures the α phenomenon at Re=1000 and both β and α phenomena one after the other at Re=5000. © 2005 The American Physical Society.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Flow past an impulsively started circular cylinder using a higher-order semicompact scheme

A fourth order semi compact finite difference scheme has been developed to solve unsteady incompressible Navier-Stokes equations in stream function and vorticity formulation. The governing equations are transformed into curvilinear coordinates using body fitted coordinate system to enable the developed scheme to handle non-regular domains. Two test problems are utilized to explore the efficiency of the scheme. It is found that the solutions obtained with the present scheme are in good agreement with the analytical results or with the existing results depending on the availability. © Springer-Verlag 2005.

Computational Mechanics

Higher order semi compact scheme to solve transient incompressible Navier-Stokes equations

Numerical Computation of Internal and External Flows

Numerical Methods for Partial Differential Equations

Extension of high-order compact schemes to time-dependent problems

Handbook of Grid Generation

Mathematics of Space and Surface Grid Generation

Fourth-order semi-compact scheme for flow past a rotating and translating cylinder

Journal	Journal of Scientific Computing
ISSN	08857474
Open Access	No