Abstract

High-fidelity scale-resolving simulations of turbulent flows can be prohibitively expensive, especially at high Reynolds numbers. Therefore, multifidelity models (MFM) can be highly relevant for constructing predictive models for flow quantities of interest (QoIs), uncertainty quantification, and optimization. For numerical simulation of turbulence, there is a hierarchy of methodologies. On the other hand, there are calibration parameters in each of these methods which control the predictive accuracy of the resulting outputs. Compatible with these, the hierarchical MFM strategy which allows for simultaneous calibration of the model parameters as developed by Goh et al. [7] within a Bayesian framework is considered in the present study. The multifidelity model is applied to two cases related to wall-bounded turbulent flows. The examples are the prediction of friction at different Reynolds numbers in turbulent channel flow, and the prediction of aerodynamic coefficients for a range of angles of attack of a standard airfoil. In both cases, based on a few high-fidelity datasets, the MFM leads to accurate predictions of the QoIs as well as an estimation of uncertainty in the predictions.

Abstract

In this paper we develop a family of arbitrarily high-order non-oscillatory hybrid Finite Volume/Discontinuous Galerkin schemes for turbulent flows on mixed-element unstructured meshes. The schemes are inherently compact in the sense that the central stencils employed are as compact as possible, and that the directional stencils are reduced in size, simplifying their implementation. Their key ingredient is the switch between a DG method and a FV method based on the CWENOZ scheme when a troubled cell is detected. Therefore, in smooth regions of the computational domain, the high order of accuracy offered by DG is preserved, while in regions with sharp gradients, the robustness of FV is utilized. This paper also presents the time evolution of troubled cells in unsteady test cases and the use of extended bounds for troubled cell detection. We assess the performance of these schemes in terms of accuracy, robustness and computational cost through a series of stringent 2D and 3D test problems. The results obtained demonstrate the accuracy and robustness that the schemes offer and highlight areas of future improvements that are considered.