Coupling of Micro-Scale and Macro-Scale Eulerian-Lagrangian Models for the Computation of Shocked Particle-Laden Flows

The accuracy and efficiency of several algorithms that couple output from full resolution micro-scale Direct Numerical Simulation computations to input for macro-scale Eulerian-Lagrangian (EL) methods for the computation of high-speed, particle-laden flow are assessed. A Stochastic Collocation method, a Gaussian Radial Basis Function (RBF) Artificial Neural Network (ANN), and an improved RBF-ANN are compared for the fitting of an analytical drag coefficient formula that depends on Mach number and Reynolds number. The improved RBF-ANN uses a clustering algorithm to enhance conditioning of interpolation matrices. The fitted drag coefficient mantle, used to trace point particles in macro-scale computations, is in excellent agreement with the analytical drag formula. The SC method requires fewer micro-scale realizations to obtain comparable accuracy of the drag coefficient. The Gaussian RBF does not converge monotonically, while the improved RBF-ANN converges algebraically and has the potential to provide error estimates.