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Retracted

The article has been retracted as it is found to contain a substantial amount of materials from the previously published papers for one of the coauthors: (1) Y. H. Hwang, “Development of a compact and accurate discretization for incompressible navier-stokes equations based on an equation-solving solution gradient, part I: kernel scheme fundamentals,” Numerical Heat Transfer B, vol. 58, no. 3, pp. 145–169, 2010; (2) Y. H. Hwang, “Development of a compact and accurate discretization for incompressible navier-stokes equations based on an equation-solving solution gradient, part II: formulation on unstructured polygonal grids,” Numerical Heat Transfer B, vol. 58, no. 3, pp. 170–192, 2010; (3) Y. H. Hwang, “Development of a compact and accurate discretization for incompressible Navier-Stokes equations based on an equation-solving solution gradient, part III: fluid flow simulations on staggered polygonal grids,” Numerical Heat Transfer B, vol. 58, no. 3, pp. 193–215, 2010.

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References

  1. H.-S. Huang and Y.-H. Hwang, “Fluid flow simulations based on an equation-solving solution gradient strategy,” Mathematical Problems in Engineering, vol. 2013, Article ID 409846, 19 pages, 2013.
Mathematical Problems in Engineering
Volume 2013, Article ID 409846, 19 pages
http://dx.doi.org/10.1155/2013/409846
Research Article

Fluid Flow Simulations Based on an Equation-Solving Solution Gradient Strategy

1Department of Naval Architecture and Ocean Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan
2Department of Marine Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan

Received 22 February 2013; Accepted 12 April 2013

Academic Editor: Chang-Hua Lien

Copyright © 2013 Ho-Shuenn Huang and Yao-Hsin Hwang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A compact and accurate discretization for fluid flow simulations is introduced in this paper. Contrary to the common wisdom in a convectional scheme, the solution gradient required for a high-resolution scheme is provided by solving its corresponding difference equation rather than by interpolation from solution values at neighboring computational nodes. To achieve this goal, a supplementary equation and its associated control volume are proposed to retain a compact and accurate discretization. Scheme essentials are exposed by numerical analyses on simple one-dimensional modeled problems to reveal its formal accuracy. Several test problems are solved to illustrate the feasibility of present formulation. From the obtained numerical results, it is evident that the proposed scheme will be a useful tool to simulate fluid flow problems in arbitrary domains.