Aluminum alloys are used abundantly in industries, such as aerospace, that melt at temperatures (500-700 degrees C depending on alloy) well below typical fire temperatures. Relocation of the melted aluminum is partly inhibited by aluminum oxide formation, which melts at much higher temperatures (about 2051 degrees C) than aluminum itself. To model the effect of this self-healing oxide layer on the motion of melting aluminum requires further data on the behavior of melting aluminum. We present experiments that capture full-field position and temperature, while minimizing surface contact, using synchronous digital image correlation (DIC) and infrared (IR) thermometry on melting aluminum cantilever bars. Three bar sizes are studied to vary the relative importance of the oxide skin. Experiments show that each bar size has qualitatively different melting behavior, quantitatively different rate of collapse, and a "thermal slowdown" after passing 610 degrees C regardless of size. All bars collapse significantly above the liquidus temperature, with large bars collapsing at higher temperatures than small bars. We describe a melt layer model, with different tiers of complexity where each tier explains more phenomenology. We show this model can explain observed phenomena, and provide mathematical theory amenable to other sizes, geometries, and loading.

Thermal diffusivity is an important material property for understanding and characterizing transient behavior in many heat transfer applications. This study investigates the accuracy and approximations of inverse mathematical models for measuring thermal diffusivity of materials via the widely used Flash Method. High-fidelity simulations of the Flash Method in copper, silicon carbide, silicon, and glass were performed as numerical experiments and included physics such as in-depth absorption, radial conduction, and surface convection. Data from those numerical experiments were used to estimate material thermal diffusivity using seven traditional and new inverse models. Parker’s original model had relative errors ϵ <5% when the approximations it makes were enforced in numerical experiments. Newer models performed well even when experimental restrictions were relaxed. Models that include radial heat conduction were capable of accurately measuring thermal diffusivity ( ϵ <1% ) when a Gaussian energy source was used. Models with radial conduction and in-depth material absorption of the laser source could calculate thermal diffusivity for semi-transparent materials such as silicon ( ϵ <1% ) and even transparent materials like glass ( ϵ <10% ). Convective losses from the material’s front surface had a negligible impact on measurements except for very low thermal diffusivity materials. Using temperatures from many locations of the test material’s surface increased resilience to noise, reducing the distribution of thermal diffusivity measurements by more than an order of magnitude. The models developed in this study could enable a more relaxed Flash Method experimental setup that maintains thermal diffusivity accuracy and extend the utility of the Flash Method to semi-transparent materials.

This work presents a physics-infused reduced-order modeling (PIROM) framework toward the design optimization of non-linear dynamical systems. It is demonstrated via the modeling of transient thermal behavior in multi-layered hypersonic thermal protection systems. The PIROM architecture integrates a reduced-physics backbone, based on the lumped capacitance model, with data-driven correction dynamics formulated via a coarse-graining approach rooted in the Mori–Zwanzig formalism. While the lumped capacitance model captures the dominant heat transfer mechanisms, the correction terms compensate for residual dynamics arising from higher-order non-linear interactions and heterogeneities across material layers. The proposed PIROM is benchmarked against a non-intrusive ROM (i.e., operator inference) and a surrogate model (i.e., neural ordinary differential equations). The PIROM consistently achieves errors below 1

Uncertainty quantification is important for the use of simulations for munitions design and testing. However, uncertainty quantification is a computationally expensive task. Multifidelity uncertainty quantification reduces that computational cost by introducing correlated models that sacrifice some accuracy for lower computational expense to supplement information obtained from high-fidelity simulations. This study explores the use of a multifidelity uncertainty quantification technique using reduced order models to accelerate the estimation of the mean and standard deviation of two quantities of interest for a simulation of a notional munition in a fire accident scenario with uncertain material properties. Results are obtained with multiple computational budgets with a multifidelity uncertainty quantification technique and the traditional Monte Carlo uncertainty quantification technique. The errors in these estimates are computed relative to a large-budget Monte Carlo uncertainty quantification study. It was found that the multifidelity technique produced mean estimates with significantly lower errors with smaller budgets and similar errors with the largest budget when compared to Monte Carlo estimates. The multifidelity technique and Monte Carlo both had similarly large errors in the estimates of the standard deviation with all budgets.

Focused ultrasound (FUS) is a thermal therapy used to noninvasively destroy diseased tissues. Computational tools are being explored to plan faster, safer, and more effective focused ultrasound treatments by using simulations to predict their outcomes. For simulations to be used with confidence, the uncertainties in their predicted outcomes must be characterized. This is challenging because the simulations have a large computational cost and performing uncertainty quantification (UQ) typically requires evaluating the simulations many times. Multifidelity uncertainty quantification uses techniques that aim to reduce the computational cost of uncertainty quantification. This is done by combining results from computationally expensive and accurate high-fidelity models with lower-fidelity models that sacrifice some accuracy to reduce computational expense. In this work, a multifidelity uncertainty quantification technique using projection-based reduced order models (ROMs) as the low-fidelity model is used on thermal simulations of two focused ultrasound sonications performed as part of breast cancer treatments. The errors in mean response estimates of multiple quantities of interest (QoIs) using this multifidelity uncertainty quantification technique are compared against those using traditional Monte Carlo uncertainty quantification. The mean, standard deviation, and skewness estimated using the multifidelity and Monte Carlo techniques are fit to Pearson Type III distributions to compare their predictions of quantity of interest distributions. It is found that multifidelity uncertainty quantification predicts the mean response of the quantities of interest with up to 50% lower error while maintaining similar accuracy in distribution predictions when compared to Monte Carlo.

This is an in-memoriam honoring Professor Darrell W. Pepper as an exceptional researcher, educator, and engineer.

A computational model of aluminum melting is proposed which captures both the thermal fluid-solid phase transition and the mechanical effects of oxidation. The model hybridizes ideas from smoothed particle hydrodynamics and bonded particle models to simulate both hydrodynamic flows and solid elasticity. Oxidation is represented by dynamically adding and deleting spring-like bonds between surface fluid particles to represent the formation and rupture of the oxide skin. Various complex systems are simulated to demonstrate the adaptability of the method and to illustrate the significant impact of skin properties on material flow. Initial comparison to experiments of a melting aluminum cantilever highlights that the computational model can reproduce key qualitative features of aluminum relocation.

Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning and showcase improved accuracy over traditional linear subspace-reduced order models. A disadvantage of the previously proposed methods is the potential high computational costs of training the networks on high-fidelity solution snapshots. In this work, we propose and analyze a novel method that overcomes this disadvantage by training a neural network only on subsampled versions of the high-fidelity solution snapshots. This method coupled with collocation-based hyper-reduction and Gappy-POD allows for efficient and accurate surrogate models. We demonstrate the validity of our approach on a 2d Burgers problem.

In order to impact physical mechanical system design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages of the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics, as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods avoid the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. These methods work by leveraging the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies that are individually modified or replaced to define new system designs. By doing so, these methods enable rapid model development and the incorporation of uncertainty quantification earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models, which exchange solution information at component boundaries. We present a pair of approaches for propagating uncertainty in this type of decomposed system and provide implementations in the form of an open-source software library. We demonstrate these tools on a variety of applications and demonstrate the impact of problem-specific details on the performance and accuracy of the resulting UQ analysis. This work represents the most comprehensive investigation of these network uncertainty propagation methods to date.

The design of thermal protection systems (TPS), including heat shields for reentry vehicles, rely more and more on computational simulation tools for design optimization and uncertainty quantification. Since high-fidelity simulations are computationally expensive for full vehicle geometries, analysts primarily use reduced-physics models instead. Recent work has shown that projection-based reduced-order models (ROMs) can provide accurate approximations of high-fidelity models at a lower computational cost. ROMs are preferable to alternative approximation approaches for high-consequence applications due to the presence of rigorous error bounds. The following paper extends our previous work on projection-based ROMs for ablative TPS by considering hyperreduction methods which yield further reductions in computational cost and demonstrating the approach for simulations of a three-dimensional flight vehicle. We compare the accuracy and potential performance of several different hyperreduction methods and mesh sampling strategies. This paper shows that with the correct implementation, hyperreduction can make ROMs up to 1-3 orders of magnitude faster than the full order model by evaluating the residual at only a small fraction of the mesh nodes.

AbstractWe present a novel framework for automatically detecting spatial and temporal events of interest in situ while running high performance computing (HPC) simulations. The new framework – composed from signature, measure, and decision building blocks with well-defined semantics – is tailored for parallel and distributed computing, has bounded communication and storage requirements, is generalizable to a variety of applications, and operates in an unsupervised fashion. We demonstrate the efficacy of our framework on several cases spanning scientific domains and applications of event detection: optimized input/output (I/O) in computational fluid dynamics simulations, detecting events that can lead to irreversible climate changes in simulations of polar ice sheets, and identifying optimal space-time subregions for projection-based model reduction. Additionally, we demonstrate the scalability of our framework using a HPC combustion application on the Cori supercomputer at the National Energy Research Scientific Computing Center (NERSC).

The breakup of liquid drops is an important phenomenology for many applications. We approach this problem with the objective of improving methods for modeling the impulse and impact dispersal of liquids in transportation accident scenarios. These scenarios can be distinguished from many other simpler problems due to the quantity of liquid and the complexity of the intermediate liquid morphology. These differences necessitate alternative (lower computational cost and lower fidelity) approaches to the problem compared to much of the historical modeling work. This work leverages a recently implemented model for inter-particle forces in a Lagrangian/Eulerian computational fluid dynamics (CFD) code. The inter-particle force model is inspired by molecular dynamics methods. It employs a Lennard-Jones (LJ) attractive force and a spring-based repulsive force that is governed by LJ parameters. The LJ parameters are related to the bulk fluid properties through a theoretical relationship to the surface tension. Methods are developed for modifying the single particle aerodynamic drag term, depending on the new notion of particle connectivity. These methods are evaluated for potential utilization in practical simulations. Breakup experiments for drops in flows from prior studies suggest a critical Weber number relating to the onset of breakup for a drop. These data are replicated with the proposed model and it is shown that the proposed method can reasonably reproduce aspects of breakup for a range of scales with only a single tuned parameter.

A projection-based reduced order model (pROM) methodology has been developed for transient heat transfer problems involving coupled conduction and enclosure radiation. The approach was demonstrated on two test problems of varying complexity. The reduced order models demonstrated substantial speedups (up to 185x) relative to the full order model with good accuracy (less than 3% L-infinity error). An attractive feature of pROMs is that there is a natural error indicator for the ROM solution: the final residual norm at each time-step of the converged ROM solution. Using example test cases, we discuss how to interpret this error indicator to assess the accuracy of the ROM solution. The approach shows promise for many-query applications, such as uncertainty quantification and optimization. The reduced computational cost of the ROM relative to the full-order model (FOM) can enable the analysis of larger and more complex systems as well as the exploration of larger parameter spaces.

In order to impact design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages in the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods preclude the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. This is accomplished by taking advantage of the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies which are individually modified or replaced to define new system designs. We leverage this hierarchical structure to enable rapid model development and the incorporation of uncertainty quantification and rigorous sensitivity analysis earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models which exchange stochastic solution information at component boundaries. We utilize Jacobi iteration with Anderson acceleration to converge stochastic representations of system level quantities of interest through successive evaluations of component or subassembly forward problems. We publish our open-source tools for uncertainty propagation in networks remarking that these tools are extensible and can be used with any simulation tool (including arbitrary surrogate modeling tools) through the construction of a simple Python interface class. Additional interface classes for a variety of simulation tools are currently under active development. The performance of the uncertainty quantification method is determined by the number of iterations needed to achieve a desired level of accuracy. Performance of these networks for simple canonical systems from both a heat transfer and solid mechanics perspective are investigated; the models are examined with thermal and mechanical Dirichlet and Neumann type boundary conditions separately imposed and the impact of varying governing equations and boundary condition type on the performance of the networks is analyzed. The form of the boundary conditions is observed to have a large impact on the convergence rate with Neumann-type boundary conditions corresponding to significant performance degradation compared to the Dirichlet boundary conditions. Nonmonotonicity is observed in the solution convergence in some cases.