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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 ( N h f ) 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. [ABSTRACT FROM AUTHOR]

Macro-scale computations of shocked particulate flows require closure laws that model the exchange of momentum/energy between the fluid and particle phases. Closure laws are constructed in this work in the form of surrogate models derived from highly resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the least number of mesoscale simulations. It is shown that if the input data is noise-free, the DKG method converges monotonically; convergence is less robust in the presence of noise. The MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments. This work is the first step towards a full multiscale modeling of interaction of shocked particle laden flows. [ABSTRACT FROM AUTHOR]

The effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. This is done with the express purpose of using metamodels to bridge scales between micro- and macro-scale models in a multi-scale multimaterial simulation. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver. [ABSTRACT FROM AUTHOR]