Monotonic convergence property of turbulent flow solution with central difference and quick schemes

Monotonic convergence of numerical solutions with the computational grid refinement is an essential requirement in estimating the grid-dependent uncertainty of computational fluid dynamics. If the convergence is not monotonic, the solution could be erroneously regarded as convergent at the local extremum with respect to some measure of the error. On the other hand, if the convergence is exactly mono tonic, estimation methods such as Richardson extrapolation properly evaluate the uncertainty of numerical solutions. This paper deals with the characterization of numerical schemes based on the property of the monotonic convergence of numerical solutions. Two typical discretization schemes of convective terms were considered; the second-order central difference scheme and the third-order Leonards QUICK scheme. A fully developed turbulent flow through a square duct was calculated via a SIMPLER based finite volume method without a turbulence model. The convergence of the numerical solution with the grid refinement was investigated for the mean flow property as well as fluctuations. The comparison of convergence process between the discretization schemes has revealed that the QUICK scheme results in preferable monotonic convergence, while the second-order central difference scheme undergoes non-monotonic convergence. The latter possibly misleads the determination of convergence with the grid refinement, or causes trouble in applying the Richardson extrapolation procedure to estimate the numerical uncertainty.