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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Pore-Scale Study on the Positive Feedback Between Stress and Porosity Caused by Pressure Solution in Porous Media

Pressure solution is an important process in the evolution of sedimentary rocks, which provide storage space for most of our petroleum resources. It directly influences the generation, migration, and storage of petroleum fluids in subsurface sedimentary rocks. Here, in this paper, we develop a pore-scale, mechanochemical model to demonstrate a possible positive feedback between the local porosity and pore surface stress, in which a higher local porosity causes a higher local pore surface stress, thus enhancing pressure solution and consequently further increasing the local porosity. Pore surface stress represents stress on a solid grain adjacent to a pore. Specifically, the pore-scale, mechanochemical model directly simulates the stress distribution over solid and pore surfaces using a finite element model. The dissolution of solids at the solid-pore interfaces under a far-from-equilibrium condition is simulated using a first-order kinetics model that accounts for the local stress distribution. The updated pore geometry, caused by pore surface dissolution, is then used in the stress simulation in the next numerical iteration. Two types of porous media, the Oriskany sandstone and an artificial porous medium with spherical pores, were tested in the mechanochemical simulation. The positive stress-porosity feedback during pressure solution was observed in both samples. In addition, the model quantitatively illustrated the distribution of local mineral dissolution rates on all pore surfaces, as well as its relation to the effective mineral dissolution rate of the entire sample. Based on the comparison between the two porous media, the local mineral dissolution was regulated by pore space distribution, geometry, and coalescence during pressure solution. This work is the first that uses direct, pore-scale numerical simulation to demonstrate the positive stress-porosity feedback during pressure solution, which has the potential to advance the understanding of the mechanical-chemical (MC) coupling in many geological processes that are relevant to subsurface energy systems, such as the recovery of petroleum hydrocarbons and geothermal energy.

CT scanning↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

Here, in this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Advantages of the Samarskii-type schemes on the Shishkin mesh

The schemes of the Samarskii type are simple modifications of the upwind scheme. We use them on the Shishkin mesh and discuss their advantages over the upwind scheme when applied to the linear one-dimensional singularly perturbed convection–diffusion problem. One of the advantages is that the Samarskii-type schemes have exact first-order accuracy uniform in the perturbation parameter, as opposed to the upwind scheme which is almost first-order uniformly accurate because its accuracy is diminished by logarithmic factors. Although this is not a new result, we re-emphasize it in the paper. We also demonstrate another advantage, that the Samarskii-type schemes are almost second-order uniformly accurate on the layer component of the solution. Motivated by this fact, we present a further improvement of the numerical method.

Convection–diffusion↗
DOE OSTI2020

An Eulerian multimaterial framework for simulating high-explosive aquarium tests

Aquarium tests of cylindrical high-explosive charges provide optical data of the detonation front velocity and shape, propagation of the shock wave in the surrounding water, and expansion rates of the detonation products behind the front. Data from aquarium experiments is often used for calibration of reactive burn models based on phenomenological equations of state (EOS) and reaction rate laws. This paper presents a multimaterial numerical modeling framework to solve the 2D axisymmetric reactive Euler equations for high-explosive aquarium tests, in particular for ammonium nitrate - fuel oil (ANFO) explosives. An extension of the Ghost Fluid Method (GFM) is used to handle the dynamic material interfaces for the ANFO explosion products, the charge-confining material (polymethyl methacrylate PMMA), and the surrounding water. This study analyzes the sensitivity of calculations (both computational efficiency and numerical accuracy) to different algorithms for the material interface models including the original GFM versus Riemann solver-based strategies. A novel method for defining the left and right states in the interfacial Riemann problem eliminates the need for sorting or nodal interpolation during the projection along the material interface. Numerical tests indicate that populating the interface node values using the Riemann solution mitigate the overheating error observed in steady-state calculations. Solution convergence and computational efficiency are explored as a function of the spatial and temporal order of the schemes. Results from the computational model with analytical equations of state and fitted reaction rate parameters show very good quantitative agreement with experimentally observed detonation front velocity, reaction products expansion, and shock wave propagation in the surrounding water for a cylindrical ANFO charge encased in PMMA. Finally, the proposed modeling framework, in conjunction with experimental tests, provides a reliable tool to assess equations of state and reaction rate expressions for reactive burn models of confined high explosives.

42 ENGINEERING↗
DOE OSTI2025

Direct Discontinuous Galerkin methods for the reacting multi-component flow equations

The Direct Discontinuous Galerkin (DDG (Liu and Yan, 2008)) method and a counterpart with Interface Correction (DDGIC (Danis and Yan, 2022)) are extended to compute diffusion terms that arise when solving the compressible multi-component flow equations in thermochemical nonequilibrium. Thermodynamic properties, transport properties, chemical reaction rates, and energy exchange terms are computed using Mutation++ (Scoggins et al., 2020). The DG method is applied on unstructured grids, where the accuracy and convergence rates can be sensitive to the numerical method chosen for parabolic terms. A method for determining the homogeneity tensor of the flow equations required for DDGIC is shown. The convergence properties of the DDG methods are studied and compared to the Interior Penalty (IP) method. A number of numerical experiments are conducted to assess the accuracy and performance of the method. The numerical results and convergence studies indicate that DDG and DDGIC provide accurate solutions and perform well for general flows in thermochemical nonequilibrium.

Diffusion↗
DOE OSTI2025

Multi-physics melt pool modeling and process optimization for laser direct energy deposition of Nb-based refractory C103: Defect formation, geometric precision, and process mapping

Recent developments in additive manufacturing (AM) technology have reignited interest in the fabrication of the Nb-based refractory C103 alloy offering solutions to the challenges posed by traditional manufacturing methods. However, the limited numerical and experimental studies on laser direct energy deposition (DED) of C103 have hindered the understanding of the relationships between process parameters and build quality. This has made it challenging to consistently produce parts with the desired quality and microstructure suitable for critical applications. In this study, we focus on optimizing the laser DED process for C103 by employing a hybrid approach that combines experimental techniques and computational fluid dynamics (CFD). This approach facilitates the development of process maps for defect detection and geometric precision. To achieve this, multi-layer C103 samples were fabricated using laser DED under various process parameters, enabling the creation of a process map for defect detection. Additionally, a multi-physics, multiphase simulation framework was developed within a high-performance computing (HPC) environment to establish process maps for geometric precision. Using these process maps, printability windows were identified for achieving both the desired geometric accuracy and defect-free prints. It was observed that prints with a power-to-velocity (P/V) ratio close to unity resulted in defect-free outcomes. This study provides a foundation for reducing design lead time and rejected parts, ultimately optimizing the laser DED process for C103.

Defect formation and geometric precision↗
DOE OSTI2021

Conditional Point Sampling: A Monte Carlo Method for Radiation Transport in Stochastic Media.

Current methods for stochastic media transport are either computationally expensive or, by nature, approximate. Moreover, none of the well-developed, benchmarked approximate methods can compute the variance caused by the stochastic mixing, a quantity especially important to safety calculations. Therefore, we derive and apply a new conditional probability function (CPF) for use in the recently developed stochastic media transport algorithm Conditional Point Sampling (CoPS), which 1) leverages the full intra-particle memory of CoPS to yield errorless computation of stochastic media outputs in 1D, binary, Markovian-mixed media, and 2) leverages the full inter-particle memory of CoPS and the recently developed Embedded Variance Deconvolution method to yield computation of the variance in transport outputs caused by stochastic material mixing. Numerical results demonstrate errorless stochastic media transport as compared to reference benchmark solutions with the new CPF for this class of stochastic mixing as well as the ability to compute the variance caused by the stochastic mixing via CoPS. Using previously derived, non-errorless CPFs, CoPS is further found to be more accurate than the atomic mix approximation, Chord Length Sampling (CLS), and most of memory-enhanced versions of CLS surveyed. In addition, we study the compounding behavior of CPF error as a function of cohort size (where a cohort is a group of histories that share intra-particle memory) and recommend that small cohorts be used when computing the variance in transport outputs caused by stochastic mixing.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

The Fragility of Bedform‐Induced Hyporheic Zones: Exploring Impacts of Dynamic Groundwater Table Fluctuations

Abstract Hyporheic zones are commonly regarded as resilient and enduring interfaces between groundwater and surface water in river corridors. In particular, bedform‐induced advective pumping hyporheic exchange (bedform‐induced exchange) is often perceived as a relatively persistent mechanism in natural river systems driving water, solutes, and energy exchanges between the channel and its surrounding streambed sediments. Numerous studies have been based on this presumption. To evaluate the persistence of hyporheic zones under varying hydrologic conditions, we use a multi‐physics framework to model advective pumping bedform‐induced hyporheic exchange in response to a series of seasonal‐ and event‐scale groundwater table fluctuation scenarios, which lead to episodic river‐aquifer disconnections and reconnections. Our results suggest that hyporheic exchange is not as ubiquitous as generally assumed. Instead, the bedform‐induced hyporheic exchange is restricted to a narrow range of conditions characterized by minor river‐groundwater head differences, is intermittent, and can be easily obliterated by minor losing groundwater conditions. These findings shed light on the fragility of bedform‐induced hyporheic exchange and have important implications for biogeochemical transformations along river corridors.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Empirical correlations between the function of entropy ( Z S ) and net artificial viscous work in a shock physics hydrocode

Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy Z S , and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Simultaneous determination of electrical conductivity and thickness of nonmagnetic metallic foils using two-sided multifrequency eddy current techniques

Here, in this paper, we describe a simple method for performing multifrequency eddy current characterization of free-standing uniform-thickness metallic foils using a forked inductive coil arrangement. The method involves measuring the mutual inductance between two coils when a foil is present between the coils, and when it is not present; the ratio of these mutual inductances is compared with an analytical solution, and foil conductivity, thickness, and sheet resistance are simultaneously estimated using numerical inversion and least-squares fitting. This method was used to characterize 34 non-ferrous metallic samples with thicknesses between 50 and 640 μm and with conductivities between 0.8 × 10 7 and 5.8 × 10 7 S/m. The estimated thicknesses from eddy current characterization agreed well with those measured using confocal optical techniques; the two approaches agreed to within 1 μm for samples that were thinner than 200 μm, and to within 0.5% for samples that had a thickness of 200 μm or greater. The estimated conductivities from eddy current characterization were in close agreement with expected values, given knowledge of the materials used. A particular strength of this approach is that the instrumentation needed is broadly available in research and development laboratories and the associated fixturing is easy to manufacture and assemble. A calibration procedure is described that can be used to reduce errors from geometric uncertainties. This calibration requires a sample that has only a known conductivity or thickness; both do not need to be known. The method described herein is likely extensible to conductivities and thickness well outside the ranges measured as part of this work.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities

Cluster perturbation theory (CPT) is a computationally economic method commonly used to estimate the momentum- and energy-resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. Finally, we benchmark the method with the one-dimensional Fermi-Hubbard model by comparing with known results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Resonant propagation of extreme-ultraviolet pulses through strongly driven high-density media

We show that by combining strong-field dressing and resonant propagation of XUV pulses, the transition of absorption lines from their natural Lorentzian profiles through Fano and complex multipeak shapes all the way back to broadened near-Lorentzian profiles can be achieved, in the limit of optically thick samples. The final stage of this spectral modification can be understood in terms of a significant temporal stretching and delay of the resonant XUV pulse as it propagates through the dense gas, which alters the ultrafast absorption that is modified by the time-synchronized few-femtosecond laser pulse. We first demonstrate this concept in numerical calculations, both using a model system and through a fully coupled solution of the time-dependent Schrödinger equation and the Maxwell wave equation. The applicability and generality of the underlying mechanism is then illustrated in proof-of-principle attosecond transient absorption measurements in a helium gas with a widely varying atomic density. These results provide insights into the interaction of ultrashort laser pulses with dense media and its coherent control. Published by the American Physical Society 2025

He, Yu (ORCID:0000000152120176)↗
DOE OSTI2020

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. In this report we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

42 ENGINEERING↗
DOE OSTI2020

Three-Phase Modeling in Sockeye

The heat pipe simulation tool Sockeye is given the capability to allow the presence of the solid phase of the heat pipe working fluid, which is necessary for modeling transients to and from room temperature, since microreactor designs feature high-temperature heat pipes employing metal working fluids. The liquid phase equations are converted to equations for the mixture of liquid and solid phases, with a simple latent heat relation determining the fractions of these phases. This capability is introduced while preserving equivalent solutions for the liquid-vapor regime. Theory is presented, along with numerical examples to illustrate the propagation of a melt front and startup from the solid state.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Scattering Observables from Few-Body Densities and Compton Scattering on $^6$Li

The dynamics of scattering on light nuclei is numerically expensive using standard methods. Fortunately, recent developments allow one to factor the relevant quantities for a given probe into a convolution of an n -body Transition Density Amplitude (TDA) and the interaction kernel for a given probe. These TDAs depend only on the target, and not the probe; they are calculated once for each set of kinematics and can be used for different interactions.\ % in the same kinematics. The kernels depend only on the probe, and not on the target; they can be reused for different targets and different kinematics. The calculation of TDAs becomes numerically difficult for more than four nucleons, but we discuss a new solution through the use of a Similarity Renormalization Group transformation, and a subsequent back-transformation. This technique allows for extending the TDA method to heavier nuclei such as 6 Li. We present preliminary results for Compton scattering on 6 Li and compare with available data, anticipating an upcoming, more thorough study. We also discuss ongoing extensions to pion-photoproduction and other reactions on light nuclei.

Long, Alexander [George Washington University, Was↗