The calculation of some laminar flows using various discretisation schemes

Abstract

For various laminar, two-dimensional flows, the upwind, hybrid and the quadratic finite-difference schemes are evaluated. The upwind and hybrid schemes are used in their normal forms. The quadratic formulation (Leonard's QUICK scheme) has in the past been found to be less stable than these two other schemes because it can, on occasion, generate both negative and positive influence coefficients. Two new forms of the quadratic formulation, both of which always generate positive influence coefficients, are presented for a uniform grid distribution and tested by reference to the results obtained from the upwind and hybrid schemes and data from other sources. These two new schemes are found to be stable, although one form seems to be sensitive to the size of the finite-difference grid. Furthermore, the solutions obtained using these new formulations are equal to or better than those obtained using the upwind and/or the hybrid schemes. It is concluded that these new formulations require further validation; and to this end, these new formulations are provided in a form that is easy to install into existing computer codes.