On the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates

https://doi.org/10.1016/0021-9991(91)90293-TGet rights and content

Abstract

The issues of adopting the velocity components as dependent velocity variables, including the Cartesian and culvilinear ones, for the Navier-Stokes flow computations are investigated. The viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form. It is demonstrated that with the curvilinear velocity vectors the curvatures of the grid lines introduce extra source terms into the governing equations. With the Cartesian velocity vector, on the other hand, the governing equations in curvilinear coordinates can retain the full conservation-law form and honor the physical conservation laws. The nonlinear combinations of the metric terms also cause the algorithms based on curvilinear velocity components to be more difficult to satisfy the geometric conservation law and, hence, more sensitive to grid skewness effect. For the combined utilization of the Cartesian velocity vector and the staggered grid arrangement, the implications of spurious pressure oscillation arising from the 90° turning are discussed. It is demonstrated that these spurious oscillations can possibly appear only under a very specific circumstance, namely, the meshes in the region with 90° turning must be parallel to the Cartesian coordinates and of uniform spacing along coordinates; otherwise no spurious oscillations can appear. Several flow solutions for domain with 90° and 360° turnings are presented to demonstrate that satisfactory results can be obtained by using the Cartesian velocity components and the staggered grid arrangement.

References (27)

  • W. Shyy

    Comput. Methods Appl. Mech. Engng.

    (1985)
  • W. Shyy et al.

    Int. J. Heat Mass Transf.

    (1990)
  • R. Peyret et al.

    Computational Methods for Fluid Flow

    (1983)
  • K.C. Karki
  • S.V. Patankar

    ASME J. Heat Transf.

    (1988)
  • H.Q. Yang et al.

    Int. J. Numer. Methods Engng.

    (1988)
  • W. Shyy et al.

    Numer. Heat Transf.

    (1985)
  • M.E. Braaten et al.

    Numer. Heat Transf.

    (1986)
  • W. Shyy et al.

    Int. J. Numer. Methods Fluids

    (1986)
  • S.V. Patankar

    Numerical Heat Transfer and Fluid Flow

    (1980)
  • S. Wittig et al.

    AGARD CP. No. 422

    (1988)
  • T.C. Vu et al.

    ASME J. Fluids Engng.

    (1988)
  • W. Shyy et al.

    Combust. Sci. Tech.

    (1988)
  • Cited by (67)

    • Numerical study of turbulent wall jet over multiple-inclined flat surface

      2014, Computers and Fluids
      Citation Excerpt :

      These islands are not found for plane wall jet or wall jet on single inclined flat surface. Shyy and Vu [62] observed similar type of cellular structure in the wall static pressure contours for flow of water in a hydraulic turbine casing with segmented wall geometry. Sub-atmospheric pressure region is found throughout the domain except near the exit boundary for uniform and trapezoidal inlet profiles.

    • Analysis of semi-staggered finite-difference method with application to Bingham flows

      2009, Computer Methods in Applied Mechanics and Engineering
    View all citing articles on Scopus
    View full text