Two Modified QUICK Schemes for Advection-Diffusion Equation of Pollutants on Unstructured Grids
Linghang XING
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DOI: 10.4236/jwarp.2009.15043   PDF    HTML     7,615 Downloads   13,805 Views   Citations

Abstract

In this paper, two modified QUICK schemes, namely Q-QUICK and UQ-QUICK, for improving the preci-sion of convective flux approximation are verified in advection-diffusion equation of pollutants on unstruc-tured grids. The constructed auxiliary nodes for Q-QUICK/UQ-QUICK are composed of two neighboring nodes plus the next upwind node, the later node is generated from intersection of the line of current neighboring nodes and their corresponding interfaces. 2D unsteady advection-diffusion equation of pollut-ants is conducted for their verifications on unstructured grids. The numerical results show that Q-QUICK and UQ-QUICK have similar computational accuracy to the central difference scheme and similar numerical stability to upwind difference scheme after applying the deferred correction method. In addition, their corre-sponding CPU times are approximately equivalent to those of traditional difference schemes and their abili-ties for adapting high grid deformation are robust.

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L. XING, "Two Modified QUICK Schemes for Advection-Diffusion Equation of Pollutants on Unstructured Grids," Journal of Water Resource and Protection, Vol. 1 No. 5, 2009, pp. 362-367. doi: 10.4236/jwarp.2009.15043.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] R. S. mkiewiez, “Oscillation-free solution of shallow water equations for nonstaggered grid,” Journal of Hy-draulic Engineering, ASCE, Vol. 119, No. 10, pp. 1118?1137, 1993.
[2] J. Fletcher, “Computational techniques for fluid dyrta-ralcs,” 8pfinger-Vedag, Berlin, No. 1, 1991.
[3] J. Shi and E. F. Toro, “Fully discrete high-order shock-eaptunng numerical schemes,” Internationa1 Jour-nal for Numerical Methods in Fluids, Vol. 23, pp. 241?269, 1996.
[4] S. Sankaranarayanan, N. J. Shankar, and H. F. Cheoag, “Three-dimensional finite difference model for transport conservative pollutants,” Ocean Engneering, Vol. 25, No. 6, pp. 425?442, 1998.
[5] R. J. Sobey, “Fraetional step algorithm for estruaine mass transport,” International Journal for Numerical Methods in Fluids, Vol. 3, pp. 567?581, 1983.
[6] B. P. Leonard, “Simple high accuracy resolution program for convective modelling of discontinuities” International Journal for Numerical Methods in Fluids, Vol. 8, pp. 1291?1318, 1988.
[7] B. J. Noye and H. H. Tan, “A third-order semi-implicit finite difference method for solving one-dimensional eon-vectlon-dlffusion equation,” International Journal for Numerical Method in Engineering, Vol. 26, pp. 1615? 1629, 1988.
[8] B. J. Noye and H. H. Tan, “Finite difference method for the two-dimensional advetion difusion equation” Interna-tional Journal for Numerical Methods in Fluids, Vol. 9, pp. 75?98, 1989.
[9] A. Pollard, A. L. Siu, and L. W. Siu, “The calculation of some laminar flows using various discretization schemes,” Comp. Meth. Appl. Mech. Eng., Vol. 35, pp. 293?313, 1982.
[10] S. V. Pantankar, Numerical Heat Transfer, McGraw?Hill, New York, 1980.
[11] M. K. Patel and N. C. Markatos, “An evaluation of eight discretization schemes for two-dimensional convec-tion-diffusion equations,” International Journal for Nu-merical Methods in Fluids, Vol. 6, pp. 129?154, 1986.
[12] L. Davidson, “A pressure correction method for unstruc-tured meshes with arbitrary control volumes,” Interna-tional Journal for Numerical Methods in Fluids, Vol. 22, pp. 265?281, 1996.
[13] Y. Saad and M. H. Schultz, “Gmres: A generalized mini-mal residual algorithm for solving nonsymmetric linear systems,” SIAM. J. Sci. Stat. Comput., Vol. 7, 1986.
[14] B. P. Leonard, “Third-order finite-difference method for steady two-dimensional convection,” Numerical Methods in Laminar and Turbulent Flow, pp. 807?819, 1978.
[15] S. I. Karaa and J. Zhan, “High order ADI method for solving unsteady convection diffusion problems,” Journal of Computational Physics, Vol. 198, No. 1, pp. 1?9, 2004.
[16] H. Jasak, “Error analysis and estimation for the finite volume method with applications to fluid flows,” Ph.D. thesis, Imperial College, University of London, London, 1996.
[17] B. Basara, “Employment of the second-moment turbu-lence closure on arbitrary unstructured grids,” Interna-tional Journal of Numerical Methods in Fluids, Vol. 44, pp. 377?407, 2001.
[18] Y. Y. Tsui and Y. F. Pan, “A pressure-correction method for incompressible flows using unstructured methes,” Nu-merical Heat Transfer, Part B, Vol. 49, pp. 43?65, 2006.

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