7.8 Examples
211
Fig. 7.12. Velocity profiles at the vertical centerline of the lid-driven cavity at
Re = 1000, calculated on various grids using: midpoint rule and UDS (upper left),
CDS (upper right) and cubic polynomial (lower left); Simpson's rule and cubic
polynomials (lower right)
For all of the methods used, the grids had to be refined to 80 x 80
CV in order to judge the accuracy with confidence. If errors of the order
of 1% are acceptable, then using CDS is the most efficient method (it is the
simplest to implement and needs less computing time per iteration). Higher
order methods are effective if small discretization errors are required (below
0.1%). On Cartesian grids, the fourth order scheme increases the memory
requirement by about 30% and computing time per outer iteration by a
factor of two; on irregular grids the cost increase would be much higher. The
number of required iterations is roughly the same for all schemes (Lilek and
PeriC, 19%).
211
Fig. 7.12. Velocity profiles at the vertical centerline of the lid-driven cavity at
Re = 1000, calculated on various grids using: midpoint rule and UDS (upper left),
CDS (upper right) and cubic polynomial (lower left); Simpson's rule and cubic
polynomials (lower right)
For all of the methods used, the grids had to be refined to 80 x 80
CV in order to judge the accuracy with confidence. If errors of the order
of 1% are acceptable, then using CDS is the most efficient method (it is the
simplest to implement and needs less computing time per iteration). Higher
order methods are effective if small discretization errors are required (below
0.1%). On Cartesian grids, the fourth order scheme increases the memory
requirement by about 30% and computing time per outer iteration by a
factor of two; on irregular grids the cost increase would be much higher. The
number of required iterations is roughly the same for all schemes (Lilek and
PeriC, 19%).