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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Aquifer Injection Modeling (AIM) Toolbox User Guide

The Aquifer Injection Modeling Toolbox (“AIM Toolbox”) software was developed by the Pacific Northwest National Laboratory (PNNL) for the U.S. Environmental Protection Agency’s (EPA) to provide a collection of analytical solutions suitable for evaluating the potential extent of the area impacted by subsurface injection operations. Subsurface injection operations are regulated under the EPA’s Underground Injection Control (UIC) program and are typically related to oil/gas development, waste disposal, or subsurface mining or storage. The analytical algorithms provided in the AIM Toolbox each have different approaches/assumptions/focus with respect to the nature and processes in subsurface and the nature of the injection operations. Collectively the set of analysis algorithms provides a broader evaluation of the area that can potentially be impacted by an injection operation. By providing estimates for the injectate plume extent, the software supports technical aspects of planning, evaluation, and overseeing injection activities. That is, the results help assess when further regulatory controls (e.g., monitoring, reporting) may be required and, in the case of disposal into an underground source of drinking water, the extent of the impacted area would require exemption from protection under the Safe Drinking Water Act. The AIM Toolbox software is available as a single-page web application, providing an interface to provide the necessary inputs, and both chart and map panes for visualizing the results. This User Guide describes the AIM Toolbox software, information required, user interactions, and the underlying basis of the calculations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Aquifer Injection Modeling (AIM) Toolbox User Guide

The Aquifer Injection Modeling Toolbox (“AIM Toolbox”) software was developed by the Pacific Northwest National Laboratory (PNNL) for the U.S. Environmental Protection Agency’s (EPA) to provide a collection of analytical solutions suitable for evaluating the potential extent of the area impacted by subsurface injection operations. Subsurface injection operations are regulated under the EPA’s Underground Injection Control (UIC) program and are typically related to oil/gas development, waste disposal, or subsurface mining or storage. The analytical algorithms provided in the AIM Toolbox each have different approaches/assumptions/focus with respect to the nature and processes in subsurface and the nature of the injection operations. Collectively the set of analysis algorithms provides a broader evaluation of the area that can potentially be impacted by an injection operation. By providing estimates for the injectate plume extent, the software supports technical aspects of planning, evaluation, and overseeing injection activities. That is, the results help assess when further regulatory controls (e.g., monitoring, reporting) may be required and, in the case of disposal into an underground source of drinking water, the extent of the impacted area would require exemption from protection under the Safe Drinking Water Act. The AIM Toolbox software is available as a single-page web application, providing an interface to provide the necessary inputs, and both chart and map panes for visualizing the results. This User Guide describes the AIM Toolbox software, information required, user interactions, and the underlying basis of the calculations.

58 GEOSCIENCES↗
DOE OSTI2022

Analytical Sensitivity Analysis of a Spent Nuclear Fuel Cask

Here, we report nuclear science and engineering is a field increasingly dominated by computational studies resulting from increasingly powerful computational tools. As a result, analytical studies, which previously pioneered nuclear engineering, are increasingly viewed as secondary or unnecessary. However, analytical solutions to reduced-fidelity models can provide important information concerning the underlying physics of a problem and aid in guiding computational studies. Similarly, there is increased interest in sensitivity analysis studies. These studies commonly use computational tools. However, providing a complementary sensitivity study of relevant analytical models can lead to a deeper analysis of a problem. This work provides the analytical sensitivity analysis of the one-dimensional (1D) cylindrical mono-energetic neutron diffusion equation using the forward sensitivity analysis procedure (FSAP) developed by Cacuci. Further, these results are applied to a reduced-fidelity model of a spent nuclear fuel cask, demonstrating how computational analysis might be improved with a complementary analytic sensitivity analysis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Exact solution of the DeWitt-Brehme-Hobbs equation in copropagating electromagetic and gravitational waves

An accelerated charge interacts with its own electromagnetic field, a phenomenon known as electromagnetic radiation reaction. The DeWitt-Brehme-Hobbs (DWBH) equation describes the motion of a charged mass in the presence of combined electromagnetic and gravitational fields, taking into account electromagnetic radiation-reaction effects. Here, we find the first exact analytical solution of the DWBH equation in the case of a charged mass in the presence of copropagating and otherwise arbitrary electromagnetic and gravitational plane waves. As a consequence of the Penrose limit, the scenario considered here can be seen as a local limit around ultrarelativistic trajectories in a general curved spacetime. Finally, the paradigmatic example of an electromagnetic wave in the presence of a constant-amplitude gravitational wave is worked out explicitly and it is shown how the presence of the gravitational wave can qualitatively change electromagnetic radiation-reaction effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Optimal scheduling for profit maximization of energy storage merchants considering market impact based on dynamic programming

This paper analyzes how electricity merchants' market impact affects merchants' profit. Energy storage has long been studied for its role in maximizing profit, and merchant decisions are assumed to have no impact on market prices. However, the trading decisions of large-scale energy storage merchants (e.g., pumped storage hydro) will affect the market prices. This paper employs dynamic programming theory to investigate merchants' optimal economic dispatch considering the market impact and physical characteristics of storage systems. Our findings show that the State-of-Charge (SOC) based analytical solution significantly facilitates energy storage merchants' decision-making. The SOC range is segmented into three regions by two optimal SOC reference points, which depend on the available energy in storage, given prices, and market impact. By comparing the current storage SOC with the reference points, the merchant can get the corresponding optimal actions. We analytically show that if the merchant neglects the market impact on the power market, she will exaggerate her expected profit when the price-taker and price-maker merchants have the same generating and pumping upper limits offered to Independent System Operators (ISOs). Furthermore, the profit-maximizing merchant must, therefore, assay to balance the trade-off correctly between the intensity of market impact and the dispatched power. Our findings are verified by numerical simulation, and results demonstrate the ramifications for electricity merchants in energy arbitrage decisions.

25 ENERGY STORAGE↗
DOE OSTI2021

Solving the sample size problem for resource selection functions

Abstract Sample size sufficiency is a critical consideration for estimating resource selection functions (RSFs) from GPS‐based animal telemetry. Cited thresholds for sufficiency include a number of captured animals and as many relocations per animal N as possible. These thresholds render many RSF‐based studies misleading if large sample sizes were truly insufficient, or unpublishable if small sample sizes were sufficient but failed to meet reviewer expectations. We provide the first comprehensive solution for RSF sample size by deriving closed‐form mathematical expressions for the number of animals M and the number of relocations per animal N required for model outputs to a given degree of precision. The sample sizes needed depend on just 3 biologically meaningful quantities: habitat selection strength, variation in individual selection and a novel measure of landscape complexity, which we define rigorously. The mathematical expressions are calculable for any environmental dataset at any spatial scale and are applicable to any study involving resource selection (including sessile organisms). We validate our analytical solutions using globally relevant empirical data including 5,678,623 GPS locations from 511 animals from 10 species (omnivores, carnivores and herbivores living in boreal, temperate and tropical forests, montane woodlands, swamps and Arctic tundra). Our analytic expressions show that the required M and N must decline with increasing selection strength and increasing landscape complexity, and this decline is insensitive to the definition of availability used in the analysis. Our results demonstrate that the most biologically relevant effects on the utilization distribution (i.e. those landscape conditions with the greatest absolute magnitude of resource selection) can often be estimated with much fewer than animals. We identify several critical steps in implementing these equations, including (a) a priori selection of expected model coefficients and (b) regular sampling of background (pseudoabsence) data within a given definition of availability. We discuss possible methods to identify a priori expectations for habitat selection coefficients, effects of scale on RSF estimation and caveats for rare species applications. We argue that these equations should be a mandatory component for all future RSF studies.

Street, Garrett M.↗
DOE OSTI2024

Studying the Random Number Generators in MCNP6 using an Analytic Benchmark

An analytic solution to a previously studied toy problem is derived and used as a code verification benchmark. Using various Random Number Generators (RNGs) in MCNP6, including the newest SFC64 RNG available in MCNP6.3.1, and their various properties (e.g., RNG stride), we show how these RNGs perform and how to correct or workaround potential issues with respect to the analytic benchmark problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An extended numerical manifold method for unsaturated soil-water interaction analysis at micro-scale

To investigate unsaturated soil-water interaction at micro-scale, this work extends the numerical manifold method (NMM) by incorporating a soil-water coupling model considering specific capillary water distribution and capillary force calculation. The soil skeleton is constructed by a soil skeleton generation algorithm with random polygons. To more realistically capture the interaction between soil grains and capillary water, a capillary mechanics-based geometric algorithm is proposed to iteratively calculate the capillary water distribution. The capillary forces corresponding to the capillary water distribution are calculated based on the Young-Laplace equation. The proposed capillary water solving framework is first verified by reproducing the soil-water characteristic curve and the capillary water distribution of an ideal contact-disk model against analytical solutions. To further validate the ability of the capillary water solving framework to predict hydraulic behavior of the real soil, a laboratory test on the Toyoura sand is reproduced numerically. Then an ideal direct shear test is performed to further validate the two-way soil-water coupling procedure, in which a comparison between the numerical and analytical results regarding the shear strength and matric suction is presented. Finally, microscopic hydraulic and compression tests are conducted on two soil specimens with the same porosity and mean grain diameter but different uniformity coefficients. The results elucidate that the extended method is a potential tool to explore unsaturated soil behaviors at micro-scale.

58 GEOSCIENCES↗
DOE OSTI2024

Optical second harmonic generation in anisotropic multilayers with complete multireflection of linear and nonlinear waves using ♯SHAARP.ml package

Abstract Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP. si , can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at a single interface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry in Multilayers (♯SHAARP. ml ). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: General Solutions

Fractional calculus is a relatively old yet emerging field of mathematics with the widest range of engineering and biomedical applications. Despite being an incredibly powerful tool, it, however, requires promotion in the engineering community. Rheology is undoubtedly one of the fields where fractional calculus has become an integral part of cutting-edge research. There exists extensive literature on the theoretical, experimental, and numerical treatment of various fractional viscoelastic flows in constraint geometries. However, the general theoretical approach that unites several most commonly used models is missing. Here we present exact analytical solutions for fractional viscoelastic flow in a circular pipe. We find velocity profiles and shear stresses for fractional Maxwell, Kelvin–Voigt, Zener, Poynting–Thomson, and Burgers models. The dynamics of these quantities are studied with respect to normalized pipe radius, fractional orders, and elastic moduli ratio. Three different types of behavior are identified: monotonic increase, resonant, and aperiodic oscillations. The models developed are applicable in the widest material range and allow for the alteration of the balance between viscous and elastic properties of the materials.

Gritsenko, Dmitry (ORCID:0000000248181512)↗
DOE OSTI2026

Thermo-hydro-mechanical analysis of subsurface ice-based thermal energy storage

Ice-based thermal energy storage systems are widely utilized for cooling and managing peak electrical demand globally, offering daily or weekly storage capabilities for both individual homes and larger office buildings. However, scaling these systems for district-level cooling or integrating them with renewable energy sources presents challenges, especially in accommodating larger volumes and addressing seasonal storage requirements in densely populated urban areas. This paper proposes a novel solution by evaluating subsurface ice-based thermal energy storage, in which the underground is subjected to seasonal freeze/thaw cycles. However, these cycles may influence ground behavior, affecting pore pressure and inducing ground movement. To systematically investigate these challenges, we enhance the TOUGH-FLAC simulator by integrating water/ice phase change capabilities and updating the effective stress–strain constitutive relation. Both modifications are validated against analytical solutions or experimental data. Through numerical simulations spanning a decade with ten seasonal freeze/thaw cycles, we evaluate the performance and long-term stability of a generic subsurface ice-based thermal energy storage system, considering factors such as ground permeability, freezing pipe spacing, freeze/thaw damage, and glycol solution temperature. The simulations indicate that ice formation induces pore pressure variations that drive seasonal surface heave and settlement, controlled by ground permeability, pipe spacing, and glycol solution temperature, along with tensile and localized shear deformation around freeze pipes. This highlights the need for accurate ground property characterization and geomechanical analysis for subsurface ice-based thermal energy storage.

Ground freezing↗
DOE OSTI2024

DECOVALEX-2023: Task C Final Report

The Full-scale Emplacement (FE) heater experiment at the Mont Terri Underground Rock Laboratory (URL) was designed and conducted by Nagra to replicate an emplacement tunnel of Nagra’s reference repository design at 1:1 scale. Alongside testing the technical feasibility of constructing disposal tunnels, emplacing waste containers in the tunnels and then backfilling them, the main goals of the FE experiment are (1) to obtain a better understanding of the coupled effects of induced thermo-hydro-mechanical (THM) processes that may occur and (2) to validate existing coupled THM models (Müller et al., 2017). A key aspect of ensuring safety for repositories located in low-permeability rock involves minimizing any damage to the rock itself, thereby preserving its integrity and promoting a stable environment Amongst a number of processes that could damage the rock is the increase in pore pressure due to thermal loading caused by heat emitted from the waste. To reduce the potential damage of the rock, it is important to analyse the evolution of heat over time due to the heat load of the containers and assess possible consequences by coupled THM models. The aim of Task C of DECOVALEX-2023 was to build 3D numerical models of the FE experiment, focussing in particular on the heating induced pore pressure change in the Opalinus Clay. Data from a large number of sensors were available from the FE experiment for model comparison. These sensors measured temperature and relative humidity in the bentonite around the heaters, and temperature, pressure and displacement/strain in the surrounding Opalinus clay. Data were available from the start of excavation (April 2012) up to August 2020 for most sensors (more than 5 years from the start of heating in December 2014). To fulfil the overall aim of the task, the work was broken down into a number of steps, starting with simpler models to build confidence in each team’s approach and then moving to more complex models that better represent the FE experiment. Step 0 consisted of 2D benchmark models, gradually increasing the number of processes that are represented from thermal (T) only models in Step 0a, to coupled thermal hydraulic (TH) models in Step 0b with a representation of changing porosity, to coupled thermo-hydro-mechanical (THM) models in Step 0c, where porosity changes are calculated by the mechanical model. A detailed specification of processes, parameters, initial and boundary conditions was provided for this step, with the ambition that all teams would work towards close agreement in their model results, thus building confidence in the model implementations. vi It was not straightforward to achieve agreement between the teams, so additional steps (Step 0b2, 0b3, 0c2, 0c3) were added along with derivation of some analytical solutions against which the models could be compared. The reasons for the differences between teams were investigated and found to be caused primarily by different conceptual model assumptions (including temperature dependence of the thermal expansion of water), different model formulations (including porosity evolution) and differences in modelled domain sizes, boundary conditions and grid discretisation. This demonstrates that comparisons between multiple modelling teams and/or comparison with analytical results and experimental data are highly beneficial in providing an indication of uncertainty in model predictions. At the conclusion of Step 0, almost all teams had achieved a close agreement in model results and those that had not achieved an agreement knew the reason for this. Step 1 moved from 2D models to 3D models of the FE experiment without adding technical features like shotcrete or EDZ, and only considering the heating phase. Initially the 3D model was tightly specified to continue to build confidence in the model implementations (Step 1a). The results of Step 1a were compared to the data from the FE-experiment without the teams seeing the data. The teams were then provided with a sub-set of the data from the FE-experiment and invited to consider how best to use the large dataset for model comparison (Step 1b). Teams were then asked to use the data provided to calibrate their models, only changing material property values rather than adding features or processes to their models (Step 1c). In Step 1, teams were asked to only model the heating phase of the experiment, so pressure in the Opalinus Clay was reported as change in pressure since the initial conditions were specified rather than modelled. The change from 2D to 3D models was accompanied by an increase in the dispersion of results between the teams. Some of this was resolved during the task, but some remained and is potentially due to model discretisation. Calibration of parameters was useful in improving the fit of the models to the data but the remaining differences indicated that the models were missing features or processes. In Step 2, the teams were asked to update their models with additional features and processes as well as calibrating parameters to try and improve the fit of the models to the data. Teams were encouraged to represent ventilation of the open FE tunnel prior to backfilling with heaters and bentonite and in Step 2, the absolute pressure in the Opalinus Clay was compared between the teams. Teams took different approaches, but there was consideration of adding shotcrete and an EDZ into the model, representing stress change during excavation and different approaches to modelling ventilation of the FE tunnel. Overall, the documented results showed a very good agreement for temperature. The results for porewater pressure evolution showed a significant improvement for most teams compared to Step 1c with a good agreement to the measurements for several teams whereas some teams overpredicted the pressure increase and others overpredicted the drainage effect especially for the sensors close to the heater. Step 3 was an opportunity for teams to use the models developed in Step 1 and Step 2 to make predictions about the temperature and pressure changes that will be expected at the FE experiment over the next few years in light of the planned changes in thermal output of the heaters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

CICE on a C-grid: new momentum, stress, and transport schemes for CICEv6.5

Abstract. This article presents the C-grid implementation of the CICE sea ice model, including the C-grid discretization of the momentum equation, the boundary conditions (BCs), and the modifications to the code required to use the incremental remapping transport scheme. To validate the new C-grid implementation, many numerical experiments were conducted and compared to the B-grid solutions. In idealized experiments, the standard advection method (incremental remapping with C-grid velocities interpolated to the cell corners) leads to a checkerboard pattern. A modal analysis demonstrates that this computational noise originates from the spatial averaging of C-grid velocities at corners. The checkerboard pattern can be eliminated by adjusting the departure regions to match the divergence obtained from the solution of the momentum equation. We refer to this novel approach as the edge flux adjustment (EFA) method. The C-grid discretization with edge flux adjustment allows for transport in channels that are one grid cell wide – a capability that is not possible with the B-grid discretization nor with the C-grid and standard remapping advection. Simulation results match the predicted values of a novel analytical solution for one-grid-cell-wide channels.

Lemieux, Jean-François (ORCID:0000000320845759)↗
DOE OSTI2021

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An extended trajectory-mechanics approach for calculating two-phase flow paths

A technique originating in quantum dynamics is used to derive a trajectory-based, semi-analytical solution for two-phase flow. The partial differential equation governing the evolution of the aqueous phase is equivalent to a family of ordinary differential equations defined along a path through the porous medium. The trajectories may be found by solving the differential equations directly or by post-processing the output of a numerical solution to the full set of governing equations. The trajectories, which differ from conventional streamlines, are found to bend downward in response to gravitational forces. The curvature is more pronounced as the dip of the porous layer containing the flow increases. Subtle changes in the relative permeability curve can lead to significant variations in the trajectories. The ordinary differential equation for the trajectory provides an expression for the travel time along the path. The expression produces a semi-analytical approximation to the model parameter sensitivities, the partial derivatives of the travel times with respect to changes in the permeability model. The semi-analytical trajectory-based sensitivities generally agree with those computed using a numerical reservoir simulator and a perturbation approach. The sensitivities are useful in tomographic imaging algorithms designed to estimate the spatial variation in permeability within a porous medium using multiphase observations.

58 GEOSCIENCES↗
DOE OSTI2024

Kubo-Anderson theory of polariton line shape

We apply the Kubo-Anderson stochastic theory of molecular spectral line shapes to the case of polaritons formed in the collective strong-coupling regime. We investigate both the fast and slow limits of the random frequency modulation of the emitter as well as the intermediate regime and show how the interplay between the characteristic timescales of the cavity and the molecular disorder is expressed in the observed polaritons line shapes. The analytical solution obtained for the slow limit is valid for any ratio between the inhomogeneous broadening of the molecules and the Rabi splitting, which is especially relevant for molecular polaritons where these two quantities can be of the same order of magnitude.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A minimally invasive, efficient method for propagation of full-field uncertainty in solid dynamics

In this work, we present a minimally invasive method for forward propagation of material property uncertainty to full-field quantities of interest in solid dynamics. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known a priori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the evolution equations based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the driving term of the evolution equations. The implementation is model independent, storage and communication efficient, and straightforward. We demonstrate its efficiency, accuracy, scaling with dimension of the parameter space, and convergence in distribution with two problems: a quasi-one-dimensional bar impact, and a two material notched plate impact. For the bar impact problem, we provide an analytical solution to PDF of the solution fields for method validation. With the notched plate problem, we also demonstrate good parallel efficiency and scaling of the method.

42 ENGINEERING↗