A unified modeling paradigm for turbulence, shock waves and boundary layers in computational compressible aerodynamics

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Highly accurate computer simulations of compressible flows require methods for the reliable modeling of turbulence, shock waves and boundary layers. Existing modeling approaches achieve good results when simulating every single phenomenon on its own, but they interact with each other in an undesirable manner when turbulence, shock waves and boundary layers occur together. For example, numerical methods based on artificial viscosity for treating shock waves often influence the turbulence model in such a way that the simulation result becomes unphysical. The proposed project is based on the hypothesis that an integrated approach that considers the modeling of all three phenomena together can significantly improve the simulation accuracy of turbulent compressible flows. In the context of the finite element method the variational multiscale method (VMS) constitutes a promising tool for the simulation of turbulent compressible flows, in which practical mesh widths cannot resolve sharp interior and boundary layers as well as tiny turbulent eddies. The aim of the proposed project is to develop a unified VMS-based modeling approach for turbulence, shock waves and boundary layers that is based on the underlying entropy structure of the physical model and avoids any ad hoc mechanisms. The unified modeling approach to be developed will be integrated into modern discretization techniques based on higher-order isogeometric finite element methods. Its performance in terms of accuracy and robustness and its potential for use in industrial applications will be investigated and demonstrated using challenging aerodynamic simulation problems from aircraft and turbine design.