Adaptivity, sensitivity, and uncertainty: toward standards of good practice in computational fluid dynamics

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.