Comparison of numerical upwinding schemes for flows involving steep gradients

Abstract EN

A comparative study is done on six convective schemes used to model flows with steep gradients.

First-order and second-order upwinding, Fromm’s, Johnson & Mackinnon’s, QUICK, and QUICK with transverse curvature term are considered.

The results of the study are tested by the bench-mark problem first introduced by Smith and Hutton, which contains many of the essential features common to practical convection-diffusion problems.

A 40 x 20 staggered grid mesh is used with prescribed stream function values at the boundaries.

The temperature at the inlet boundary is given in terms of a hyperbolic tangent function with a parameter, a, to control the steepness of this function.

Values of 10 and 100 for a are used representing sharp and very sharp transition, respectively.

The exact analytical solution for the case of no diffusion Pe' - is compared with numerical solutions from the six schemes studied.

Two other values of Pe' = 10 and Pe' =500 are investigated in order to demonstrate the effect of diffusion on the two-dimensional steady state convection-diffusion equation.

A grid-refinement analysis is done by considering two other mesh sizes, 20 x 10 and 80 x 40.

Based on a computational cost, accuracy, and error analysis, QUICK with the transverse curvature term is found to be the most efficient scheme for convection dominant problems.