Session B8: Focus Session: Uncertainty Quantification in Compressible High-Speed Flows I

Evaluation of Variable-fidelity Techniques for Construction of Surrogates for Drag in Multiscale Modeling for Shock-Particle Interactions

In multiscale modeling of shock-particle interactions, the macroscale is connected to the mesoscale via homogenized closure laws for drag, heat transfer etc. Closure models are obtained using metamodeling techniques; in this work a Modified Bayesian Kriging method (MBKG) is used to estimate statistical measures (such as mean, confidence intervals) of the drag on particles. The drag is computed as a function of Mach number (Ma) and Volume Fraction ($\phi )$ from high-resolution mesoscale simulations. The process is computationally expensive -- each high-fidelity mesoscale simulation is worth several hours of compute time even in multi-processer systems. Therefore, because of the cost of dimensionality, the cost of constructing surrogates becomes prohibitive for higher dimensional parameter spaces. In this work, an alternative route -- a variable fidelity technique -- is used to construct closures from mesoscale simulations. In this approach, ensembles of low-resolution mesoscale simulations are used to construct an initial surrogate for the mean drag and the confidence intervals as a function of Ma and $\phi $. The initial surrogate is then corrected using a few high-fidelity simulations. The overall computational cost for creating surrogates is low because the onus of creating surrogates lies on low-resolution computations. Several variable fidelity techniques will be evaluated for accuracy and savings in compute time for a robust technique for creating surrogates for shock-particle interactions.   

Forensic Uncertainty Quantification of Explosive Dispersal of Particles

In addition to the numerical challenges of simulating the explosive dispersal of particles, validation of the simulation is often plagued with poor knowledge of the experimental conditions. The level of experimental detail required for validation is beyond what is usually included in the literature. This presentation proposes the use of forensic uncertainty quantification (UQ) to investigate validation-quality experiments to discover possible sources of uncertainty that may have been missed in initial design of experiments or under-reported. The current experience of the authors has found that by making an analogy to crime scene investigation when looking at validation experiments, valuable insights may be gained. One examines all the data and documentation provided by the validation experimentalists, corroborates evidence, and quantifies large sources of uncertainty a posteriori with empirical measurements. In addition, it is proposed that forensic UQ may benefit from an independent investigator to help remove possible implicit biases and increases the likelihood of discovering unrecognized uncertainty. Forensic UQ concepts will be discussed and then applied to a set of validation experiments performed at Eglin Air Force Base.   

Sensitivity Analysis of strength models using~Bayesian Adaptive Splines~

Through sensitivity analysis we study how variability of the output of a strength model can be apportioned to different sources of uncertainty in the model input. Determining these relationships has become a first step in the use of strength models that precedes their calibration to experimental data. We discuss the Bayesian approach to multivariate adaptive regression splines (BMARS) as an emulator of a strength model for the purpose of sensitivity analysis without Monte Carlo error. We show that the BMARS formulation is well suited for functional output like stress-strain curves and we extend the global sensitivity indices to functional outputs.   

Bayesian model calibration of ramp compression experiments on Z

Bayesian model calibration (BMC) is a statistical framework to estimate inputs for a computational model in the presence of multiple uncertainties, making it well suited to dynamic experiments which must be coupled with numerical simulations to interpret the results. Often, dynamic experiments are diagnosed using velocimetry and this output can be modeled using a hydrocode. Several calibration issues unique to this type of scenario including the functional nature of the output, uncertainty of nuisance parameters within the simulation, and model discrepancy identifiability are addressed, and a novel BMC process is proposed. As a proof of concept, we examine experiments conducted on Sandia National Laboratories' Z-machine which ramp compressed tantalum to peak stresses of 250 GPa. The proposed BMC framework is used to calibrate the cold curve of Ta (with uncertainty), and we conclude that the procedure results in simple, fast, and valid inferences. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Boundary identification and error analysis of shocked material images

To compute quantities such as pressure and velocity from laser-induced shock waves propagating through materials, high-speed images are captured and analyzed. Shock images typically display high noise and spatially-varying intensities, causing conventional analysis techniques to have difficulty identifying boundaries in the images without making significant assumptions about the data. We present a novel machine learning algorithm that efficiently segments, or partitions, images with high noise and spatially-varying intensities, and provides error maps that describe a level of uncertainty in the partition- ing. The user trains the algorithm by providing locations of known materials within the image but no assumptions are made on the geometries in the image. The error maps are used to provide lower and upper bounds on quantities of interest, such as velocity and pressure, once boundaries have been identified and propagated through equations of state. This algorithm will be demonstrated on images of shock waves with noise and aberrations to quantify properties of the wave as it progresses. DOE/NV/25946–3126 This work was done by National Security Technologies, LLC, under Contract No. DE- AC52-06NA25946 with the U.S. Department of Energy and supported by the SDRD Program.   

Computational-hydrodynamic studies of the Noh compressible flow problem using non-ideal equations of state

The Noh problem is classic verification problem in the field of compressible flows. Simple to conceptualize, it is nonetheless difficult for numerical codes to predict correctly, making it an ideal code-verification test bed. In its original incarnation, the fluid is a simple ideal gas; once validated, however, these codes are often used to study highly non-ideal fluids and solids. In this work the classic Noh problem is extended beyond the commonly-studied polytropic ideal gas to more realistic equations of state (EOS) including the stiff gas, the Nobel-Abel gas, and the Carnahan-Starling hard-sphere fluid, thus enabling verification studies to be performed on more physically-realistic fluids. Exact solutions are compared with numerical results obtained from the Lagrangian hydrocode FLAG, developed at Los Alamos. For these more realistic EOSs, the simulation errors decreased in magnitude both at the origin and at the shock, but also spread more broadly about these points compared to the ideal EOS. The overall spatial convergence rate remained first order.