A multi-objective Bayesian optimization environment for systematic design of numerical schemes for compressible flow

Multi-objective Bayesian optimization (MOBO) is an efficient and robust optimization framework for expensive functions. In this work, we use MOBO to optimize the free parameters of a high-order nonlinear weighted essentially non-oscillatory (WENO) reconstruction scheme to devise a model for implicit large eddy simulations. We concurrently optimize for a low dispersion error and sufficient shock-capturing ability for compressible flows as well as for physically consistent transition occurring in under-resolved flow regions. With our approach, we follow the genealogy of designing implicit sub-grid models. Yet, in contrast to previous works that were limited to incompressible flows, our model is also applicable to compressible flows. Validated results show that the model is able to decrease excessive dissipation in continuous flow regimes, to capture shocks with little dispersive and dissipative errors while achieving a well shaped vortical structures. The proposed framework is general and can be used to design a physically consistent numerical scheme for under-resolved compressible-flow simulations.