The prediction performance of two computational fluid dynamics codes is compared to each other and to experimental data of a complex swirling and tumbling flow in a practical complex configuration. This configuration consists of a flow in a production-type heavy-duty diesel engine head with 130 - mm cylinder bore. One unsteady Reynolds-averaged Navier-Stokes (URANS)-based simulation and two large-eddy simulations (LES) with different inflow conditions have been performed with the KIVA-3V code. Two LES with different resolutions have been performed with the FASTEST-3D code. The parallelization of the this code allows for a more resolved mesh compared to the KIVA-3V code. This kind of simulations gives a complete image of the phenomena that occur in such configurations, and therefore represents a valuable contribution to experimental data. The complex flow structures gives rise to an inhomogeneous turbulence distribution. Such inhomogeneous behavior of the turbulence is well captured by the LES, but naturally damped by the URANS simulation. In the LES, it is confirmed that the inflow conditions play a decisive role for all main flow features. When no particular treatment of the flow through the runners can be made, the best results are achieved by computing a large part of the upstream region, once performed with the FASTEST-3D code. If the inflow conditions are tuned, all main complex flow structures are also recovered by KIVA-3V . The application of upwinding schemes in both codes is in this respect not crucial.

Verification of Calculations involves error estimation, whereas Verification of Codes involves error evaluation, from known benchmark solutions. The best benchmarks are exact analytical solutions with sufficiently complex solution structure; they need not be realistic since Verification is a purely mathematical exercise. The Method of Manufactured Solutions (MMS) provides a straightforward and quite general procedure for generating such solutions. For complex codes, the method utilizes Symbolic Manipulation, but here it is illustrated with simple examples. When used with systematic grid refinement studies, which are remarkably sensitive, MMS produces strong Code Verifications with a theorem-like quality and a clearly defined completion point.

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 1-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first-and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.