A General Multi-objective Bayesian Optimization Framework for the Design of Hybrid Schemes towards Adaptive Complex Flow Simulations

Achieving accuracy with underresolved simulation of complex compressible flows with multiscale flow structures is a challenge. Either the numerical dissipation or the resolution and thereby the numerical cost is impractically high. Also, in the design of numerical solvers, the application of a solver for specific flow classes is balanced by robustness allowing the study of a broad range of flows. In this study, we propose a hybrid fifth-order targeted essentially non-oscillatory (TENO5)-based scheme tailored to optimally simulate compressible flows with underresolved dilatational and vortical multiscale structures. For optimal design, three data-driven objectives are defined. A novel objective that derives from the numerical dissipation rate analysis is a key element to deal with underresolved complex flows in practical applications. The optimization process employs a multi-objective Bayesian optimization framework with an expected hypervolume improvement and three flow configurations representative for a broad range of two- and three-dimensional flows with genuine and non-genuine subgrid scales. The optimized hybrid scheme is validated by comparing with shock-capturing schemes of the weighted essentially non-oscillatory (WENO)- and TENO- families with flows of complex shock interactions, Kelvin-Helmholtz instabilities, shock-vortex interactions, vortical and turbulent flows