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Calculation of cell face velocity of non-staggered grid system


In this paper, the cell face velocities in the discretization of the continuity equation, the momentum equation, and the scalar equation of a non-staggered grid system are calculated and discussed. Both the momentum interpolation and the linear interpolation are adopted to evaluate the coefficients in the discretized momentum and scalar equations. Their performances are compared. When the linear interpolation is used to calculate the coefficients, the mass residual term in the coefficients must be dropped to maintain the accuracy and convergence rate of the solution.

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  1. Rhie, C. M. and Chow, W. L. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA Journal, 21(11), 1525–1552 (1983)

    Article  MATH  Google Scholar 

  2. Peric, M. A Finite Volume Method for the Prediction of Three-Dimensional Fluid Flow in Complex Ducts, Ph.D. dissertation, University of London, UK (1985)

    Google Scholar 

  3. Majumdar, S. Development of a Finite-Volume Procedure for Prediction of Fluid Flow Problems with Complex Irregular Boundaries, SFB-210/T-29, University of Karlsruhe, Germany (1986)

    Google Scholar 

  4. Peric, M., Kessler, R., and Scheuerer, G. Comparison of finite-volume numerical methods with staggered and collocated grids. Computers and Fluids, 16(4), 389–403 (1988)

    Article  MATH  Google Scholar 

  5. Majumdar, S. Role of underrelaxation in momentum interpolation for calculation of flow with non-staggered grids. Numerical Heat Transfer, Part B, 13(1), 125–132 (1988)

    Article  Google Scholar 

  6. Rahman, M. M., Miettinen, A., and Siikonen, T. Modified simple formulation on a collocated grid with an assessment of the simplified QUICK scheme. Numerical Heat Transfer, Part B, 30(3), 291–314 (1996)

    Article  Google Scholar 

  7. Choi, S. K. Note on the use of momentum interpolation method for unsteady flows. Numerical Heat Transfer, Part A, 36(5), 545–550 (1999)

    Article  Google Scholar 

  8. Barton, I. E. and Kirby, R. Finite difference scheme for the solution of fluid flow problems on nonstaggered grids. International Journal of Numerical Methods in Fluids, 33(7), 939–959 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Yu, B., Kawaguchi, Y., Tao, W. Q., and Ozoe, H. Checkerboard pressure predictions due to the under-relaxation factor and time step size for a nonstaggered grid with momentum interpolation method. Numerical Heat Transfer, Part B, 41(1), 85–94 (2002)

    Article  Google Scholar 

  10. Yu, B., Tao, W. Q., Wei, J. J., Kawaguchi, Y., Tagawa, T., and Ozoe, H. Discussion on momentum interpolation method for collocated grids of incompressible flow. Numerical Heat Transfer, Part B, 42(2), 141–166 (2002)

    Article  Google Scholar 

  11. Date, A. W. Solution of Navier-Stokes equations on non-staggered at all speeds. International Journal of Heat and Mass Transfer, 36(4), 1913–1922 (1993)

    Article  MATH  Google Scholar 

  12. Date, A. W. Complete pressure correction algorithm for solution of incompressible Navier-Stokes equations on a non-staggered grid. Numerical Heat Transfer, Part B, 29(4), 441–458 (1996)

    Article  Google Scholar 

  13. Wang, Q. W., Wei, J. G., and Tao, W. Q. An improved numerical algorithm for solution of convective heat transfer problems on non-staggered grid system. Heat and Mass Transfer, 33(4), 273–288 (1998)

    Article  Google Scholar 

  14. Nie, J. H., Li, Z. Y., Wang, Q. W., and Tao, W. Q. A method for viscous incompressible flows with simplified collocated grid system. Proceedings of Symposium on Energy and Engineering in the 21st Century, 1, 177–183 (2000)

    Google Scholar 

  15. Leonard, B. P. A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering, 19(1), 59–98 (1979)

    Article  MATH  Google Scholar 

  16. Khosla, P. K. and Rubin, S. G. A diagonally dominant second-order accurate implicit scheme. Computers and Fluids, 2(2), 207–218 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  17. Botella, O. and Peyret, R. Benchmark spectral results on the lid-driven cavity flow. Computers and Fluids, 27(4), 421–433 (1998)

    Article  MATH  Google Scholar 

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Correspondence to Bo Yu  (宇 波).

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Project supported by the National Natural Science Foundation of China (Nos. 51176204 and 51134006)

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Li, W., Yu, B., Wang, Xr. et al. Calculation of cell face velocity of non-staggered grid system. Appl. Math. Mech.-Engl. Ed. 33, 991–1000 (2012).

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2010 Mathematics Subject Classification