Evaluation of multifidelity surrogate modeling techniques to construct closure laws for drag in shock-particle interactions

Meta- (or surrogate-) models constructed from meso-scale simulations can be used in place of empirical correlations to close macro-scale equations. In shocked particulate flows, surrogate models for drag are constructed as functions of shock Mach number (Ma), particle volume fraction (ϕ), Reynolds number (Re), etc. The computational cost of the high-fidelity meso-scale simulations is a challenge in construction of surrogates in such hierarchical multi-scale frameworks. Here multifidelity surrogate-modeling techniques are evaluated as inexpensive alternatives to high-fidelity surrogate models for obtaining closure laws for drag in shock-particle interactions. Preliminary surrogates for drag as a function of Ma and ϕ are constructed from ensembles of low-fidelity (coarse grid) mesoscale computations. The low-fidelity surrogates are subsequently corrected using only a few (Nhf) high-fidelity computations to obtain multifidelity surrogate models. The paper evaluates three different methods for correcting an initial low-fidelity surrogate; Space Mapping (SM), Radial Basis Functions (RBF) and Modified Bayesian Kriging (MBKG). Of these methods, MBKG is found to provide the best multi-fidelity surrogate model, simultaneously minimizing the computational cost and error in the constructed surrogate.