Oishik Sen

Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation

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.

Evaluation of kriging based surrogate models constructed from mesoscale computations of shock interaction with particles

Abstract 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.

SPARSE—A subgrid particle averaged Reynolds stress equivalent model: testing with a priori closure

A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian–Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles.

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

ABSTRACT A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.

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

Abstract 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.

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.Copyright

Multi-scale shock-to-detonation simulation of pressed energetic material: A meso-informed ignition and growth model

This work presents a multiscale modeling framework for predictive simulations of shock-to-detonation transition (SDT) in pressed energetic (HMX) materials. The macro-scale computations of SDT are performed using an ignition and growth (IG) model. However, unlike in the traditional semi-empirical ignition-and-growth model, which relies on empirical fits, in this work meso-scale void collapse simulations are used to supply the ignition and growth rates. This results in a macro-scale model which is sensitive to the meso-structure of the energetic material. Energy localization at the meso-scale due to hotspot ignition and growth is reflected in the shock response of the energetic material via surrogate models for ignition and growth rates. Ensembles of meso-scale reactive void collapse simulations are used to train the surrogate model using a Bayesian Kriging approach. This meso-informed Ignition and Growth (MES-IG) model is applied to perform SDT simulations of pressed HMXs with different porosity and void diameters. The computations are successfully validated against experimental pop-plots. Additionally, the critical energy for SDT is computed and the experimentally observed P s 2 τ s = constant relations are recovered using the MES-IG model. While the multiscale framework in this paper is applied in the context of an ignition-and-growth model, the overall surrogate model-based multiscale approach can be adapted to any macro-scale model for predicting SDT in heterogeneous energetic materials.