Sanyasiraju VSS Yedida

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.

A spectral resolutioned exponential compact higher order scheme (SRECHOS) is developed to solve stationary convection-diffusion type of differential equations with constant convection and diffusion coefficients. The scheme is O (h6) for one-dimensional problems and produces a tri-diagonal system of equations that can be solved efficiently using Thomas algorithm. For two-dimensional 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 (ADI) procedure. The efficiency of the developed scheme is measured using wave number analysis. The analysis shows that the SRECHOS has a much better spectral resolution than any of the existing higher order schemes. Numerical examples are solved and better performance of the SRECHOS in terms of accuracy over the existing schemes in the literature is demonstrated. © 2008 Elsevier B.V. All rights reserved.

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.