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.

Sanyasiraju V.S.S. Yedida

Department of Mathematics

V. Manjula

Approximation theory

Computational methods

Finite difference method

Incompressible flow

KINEMATICS

Mathematical transformations

Poisson distribution

Reynolds number

Two dimensional

Viscosity

Viscous flow

Vortex flow

Computational domains

HIGHER ORDER COMPACT (HOC)

PARABOLIC EQUATIONS

Viscous fluids

Navier Stokes equations

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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

Computational Mechanics

This paper presents an exponential compact higher order scheme for Convection-Diffusion Equations (CDE) with variable and nonlinear convection coefficients. The scheme is O(h4) for one-dimensional problems and produces a tri-diagonal system of equations which can be solved efficiently using Thomas algorithm. For twodimensional problems, the scheme produces an O(h4+k4) accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit procedure. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be positive. Wave number analysis has been carried out to establish that the scheme is comparable in accuracy with spectral methods. The higher order accuracy and better rate of convergence of the developed scheme have been demonstrated by solving numerous model problems for one and two-dimensional CDE, where the solutions have the sharp gradient at the solution boundary. © 2011 Global-Science Press.

Communications in Computational Physics

Exponential compact higher order scheme for nonlinear steady convection-diffusion equations

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.

Journal of Scientific Computing

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

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

Numerical Solution of Partial Differential Equations

Preface to the second edition

International Journal for Numerical Methods in Fluids

Numerical solution of incompressible flows by discrete singular convolution

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

International Journal for Numerical Methods in Engineering

High-order compact scheme for the steady stream-function vorticity equations

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

Journal	Data powered by TypesetComputational Mechanics
Publisher	Data powered by TypesetSpringer Verlag
ISSN	01787675
Open Access	No