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Three issues related to good computational fluid dynamics (CFD) practice are discussed. First, adaptive methods are shown to be a simple tool to perform systematic grid refinement studies needed to achieve solutions with controlled accuracy (verification of simulations). Second, it is shown that the sensitivity equation method provides insights about which parameters critically affect the flow response. Finally, flow sensitivities are used to propagate model parameter uncertainties through the CFD code to yield uncertainty estimates of the CFD predictions. This provides a rigorous framework for comparing predictions to measurements (validation of predictions). These combined approaches help to build confidence in CFD predictions and develop good CFD practice. The resulting uncertainty bars put CFD on par with experimental techniques. The approaches are demonstrated on two-dimensional problems: a k-[epsilon] model of the flow in an annular turn-around duct and conjugate free convection with variable fluid properties. Taken together, these approaches offer a good prospect for developing families of computing methods that can be viewed as standards of good practice in CFD, ensuring that verification and validation studies are performed on solid grounds.

Compressible aerodynamic turbulent flows have been solved using a new adaptive finite element method. The procedure is aimed at flow problems in which incompressibility is a significant factor. Logarithmic variables are used to ensure the positivity of turbulence variables throughout the domain and through the course of the iterations. Error estimates are also employed in all the field variables including the eddy viscosity. As such, the proposed scheme reacts to shocks, shear layers, stagnation points, boundary layers and wakes. This improves the accuracy for all field variables.

A novel method for the analysis of turbulent free shear flows was developed based on adaptive remeshing using kappa-epsilon turbulence models. The adaptive remeshing finite element procedure for solving turbulent free shear flows has a robust and reliable finite element solution algorithm. The adaptivity methodology provides significant computational saving and it can be utilized in a black-box fashion that enhances accuracy and computational efficiency.

Grid convergence studies are conducted to assess four error estimators for their asymptotic behavior: explicit residual, solution reconstruction, Richardson extrapolation, and solution of the error equations. Their accuracy, reliability, and efficitivity to predict the true error are verified on the quasi-one-dimensional Euler equations solved by a second-order accurate finite volume method.