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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

PARTIAL ERUPTION OF A FILAMENT WITH TWISTING NON-UNIFORM FIELDS

The eruption of a filament in a kinklike fashion is often regarded as a signature of kink instability. However, the kink instability threshold for the filament’s magnetic structure is not widely understood. Using Hα observations from the New Vacuum Solar Telescope, we present a partial eruptive filament. During the eruption, the filament thread appeared to split from its middle and to break out in a kinklike fashion. In this period, the remaining filament material stayed below and erupted without the kinking motion later on. The coronal magnetic field lines associated with the filament are obtained from nonlinear force-free field extrapolations using the twelve-minute-cadence vector magnetograms of the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory. We studied the extrapolated field lines passing through the magnetic dips which are in good agreement with the observed filament. The field lines are non-uniformly twisted and appear to be composed of two twisted flux ropes winding around each other. One of them has a higher twist than the other, and the flux rope with the higher twist has its dips aligned with the kinking eruptive thread at the beginning of its eruption. Before the eruption, moreover, the flux rope with the higher twist was found to expand with an approximately constant field twist. In addition, the helicity flux maps deduced from the HMI magnetograms show that some helicity is injected into the overlying magnetic arcade, but no significant helicity is injected into the flux ropes. Accordingly, we suggest that the highly twisted flux rope became kink unstable when the instability threshold declined with the expansion of the flux rope.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The spherically symmetric gravitational collapse of a clump of solids in a gas

In the subject of planetesimal formation, several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Fully nonlinear simulations using the two-fluid model are carried out (almost) up to the time when a central density singularity forms. We refer to this as the collapse time. The end result of the study is a parametrization of the collapse time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject in a particular situation. An important effect that determines the collapse time is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure, which retards particle collapse and can lead to oscillation in the size and density of the clump. In the limit of particles perfectly coupled to the gas, the characteristic ratio of gravitational force to gas pressure becomes relevant and defines a two-phase Jeans parameter, J{sub t}, which is the classical Jeans parameter with the speed of sound replaced by an effective wave speed in the coupled two-fluid medium. The parameter J{sub t} remains useful even away from the perfect coupling limit because it makes the simulation results insensitive to the initial density ratio of particles to gas (Φ{sub 0}) as a separate parameter. A simple ordinary differential equation model is developed. It takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit J{sub t}→0, collapse time equals the self-sedimentation time, which is inversely proportional to the Stokes number. As J{sub t} increases, the collapse time decreases with J{sub t} and eventually becomes approximately equal to the dynamical time. Values of collapse time versus clump size are given for a minimum-mass solar nebula. Finally, the timescale of clump erosion due to turbulent strain is estimated.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Active Radiative Thermal Switching with Graphene Plasmon Resonators

We theoretically demonstrate a near-field radiative thermal switch based on thermally excited surface plasmons in graphene resonators. The high tunability of graphene enables substantial modulation of near-field radiative heat transfer, which, when combined with the use of resonant structures, overcomes the intrinsically broadband nature of thermal radiation. In canonical geometries, we use nonlinear optimization to show that stacked graphene sheets offer improved heat conductance contrast between “ON” and “OFF” switching states and that a >10× higher modulation is achieved between isolated graphene resonators than for parallel graphene sheets. In all cases, we find that carrier mobility is a crucial parameter for the performance of a radiative thermal switch. Furthermore, we derive shape-agnostic analytical approximations for the resonant heat transfer that provide general scaling laws and allow for direct comparison between different resonator geometries dominated by a single mode. The presented scheme is relevant for active thermal management and energy harvesting as well as probing excited-state dynamics at the nanoscale.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2025

PhaseT3M: 3D imaging at 1.6 Å resolution via electron cryo-tomography with nonlinear phase retrieval

Electron cryo-tomography (cryo-ET) enables 3D imaging of complex, radiation-sensitive structures with molecular detail. However, image contrast from the interference of scattered electrons is nonlinear with atomic density and multiple scattering further complicates interpretation. These effects degrade resolution, particularly in conventional reconstruction algorithms, which assume linearity. Particle averaging can reduce such issues but is unsuitable for heterogeneous or dynamic samples ubiquitous in biology, chemistry, and materials sciences. Here, we develop a phase retrieval-based cryo-ET method, PhaseT3M. We experimentally demonstrate its application to an approximately 7 nm Co3O4 nanoparticle on an approximately 30 nm carbon substrate, achieving a maximum resolution of 1.6 Å, surpassing conventional limits using standard cryo-TEM equipment. PhaseT3M uses a multislice model for multiple scattering and Bayesian optimization for alignment and computational aberration correction, with a positivity constraint to recover ‘missing wedge’ information. Applied directly to biological particles, it enhances reconstruction quality and reduces artifacts, establishing a standard for routine 3D imaging with phase contrast.

Biophysics↗
DOE OSTI2017

Multistep inversion workflow for 3D long-offset damped elastic waves in the Fourier domain

We present a new workflow for imaging damped three-dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short-offset and low-frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine-scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite-difference frequency-domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full-waveform inversion workflow is applied to the 3D Marmousi-2 and SEG/EAGE Salt models with long-offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one-third of the maximum offset length at a resolution consistent with the inverted frequencies.

3D full waveform inversion↗
DOE OSTI2017

Surfatron accelerator in the local interstellar cloud

Taking into account results of numerous experiments, the variability of the energy spectra of cosmic rays (protons and helium nuclei) in the energy range of 10 GeV to ~10{sup 7} GeV is explained on the basis of a hypothesis of the existence of two variable sources close to the Sun. The first (soft) surfatron source (with a size of ~100 AU) is located at the periphery of the heliosphere. The second (hard) surfatron source (with a size of ~1 pc) is situated in the Local Interstellar Cloud (LIC) at a distance of <1 pc. The constant background is described by a power-law spectrum with a slope of ~2.75. The variable heliospheric surfatron source is described by a power-law spectrum with a variable amplitude, slope, and cutoff energy, the maximum cutoff energy being in the range of E{sub CH}/Z < 1000 GeV. The variable surfatron source in the LIC is described by a power-law spectrum with a variable amplitude, slope, and cut-off energy, the maximum cut-off energy being E{sub Ð}¡{sub L}/Z ≤ 3 × 10{sup 6} GeV. The proposed model is used to approximate data from several experiments performed at close times. The energy of each cosmic-ray component is calculated. The possibility of surfatron acceleration of Fe nuclei (Z = 26) in the LIC up to an energy of E{sub CL} ~ 10{sup 17} eV and electron and positrons to the “knee” in the energy spectrum is predicted. By numerically solving a system of nonlinear equations describing the interaction between an electromagnetic wave and a charged particle with an energy of up to E/Z ~ 3 × 10{sup 6} GeV, the possibility of trapping, confinement, and acceleration of charged cosmic-ray particles by a quasi-longitudinal plasma wave is demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Kramers–Kronig relation in attosecond transient absorption spectroscopy

The Kramers–Kronig relation (KKR) has a wide range of applications in extreme ultraviolet (XUV) and x-ray spectroscopy. However, the validity of KKR for many of these applications has not been systematically studied, while it is known to require careful attention in nonlinear and pump–probe experiments in optical domain spectroscopy. Here, we study the validity of KKR in XUV attosecond transient absorption spectroscopy pump–probe measurements both experimentally and theoretically using argon Fano resonances as a case study. Experiments are enabled by a phase-resolved method dubbed Complex Attosecond Transient-absorption Spectroscopy (CATS). Although the estimations based on the rotating-wave approximation suggest that KKR violation could be expected in the studied case, our results validate KKR and provide a solid basis for its application in a broad range of attosecond spectroscopy experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

RELAP-7 Development Updates

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory, and is the next generation tool in the RELAP reactor safety/systems analysis application series. RELAP-7 development began in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway of the Light Water Reactor Sustainability (LWRS) program. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. The code is being developed based on Idaho National Laboratory’s modern scientific software development framework – MOOSE (the Multi-Physics Object-Oriented Simulation Environment). The initial development goal of the RELAP-7 approach focused primarily on the development of an implicit algorithm capable of strong (nonlinear) coupling of the dependent hydrodynamic variables contained in the 1-D/2-D flow models with the various 0-D system reactor components that compose various boiling water reactor (BWR) and pressurized water reactor nuclear power plants (NPPs). During Fiscal Year (FY) 2015, the RELAP-7 code has been further improved with expanded capability to support boiling water reactor (BWR) and pressurized water reactor NPPs analysis. The accumulator model has been developed. The code has also been coupled with other MOOSE-based applications such as neutronics code RattleSnake and fuel performance code BISON to perform multiphysics analysis. A major design requirement for the implicit algorithm in RELAP-7 is that it is capable of second-order discretization accuracy in both space and time, which eliminates the traditional first-order approximation errors. The second-order temporal is achieved by a second-order backward temporal difference, and the one-dimensional second-order accurate spatial discretization is achieved with the Galerkin approximation of Lagrange finite elements. During FY-2015, we have done numerical verification work to verify that the RELAP-7 code indeed achieves 2nd-order accuracy in both time and space for single phase models at the system level.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Compactly‐Supported Nonstationary Kernels for Computing Exact Gaussian Processes on Big Data

The Gaussian process (GP) is a widely used method for analyzing large-scale data sets, including spatio-temporal measurements of nonlinear processes that are now commonplace in the environmental sciences. Traditional implementations of GPs involve stationary kernels (also termed covariance functions) that limit their flexibility, and exact methods for inference that prevent application to data sets with more than about 10,000 points. Modern approaches to address stationarity assumptions generally fail to accommodate large data sets, while all attempts to address scalability focus on approximating the Gaussian likelihood, which can involve subjectivity and lead to inaccuracies. In this work, we explicitly derive an alternative kernel that can discover and encode both sparsity and nonstationarity. We embed the kernel within a fully Bayesian GP model and leverage high-performance computing resources to enable the analysis of massive data sets. We demonstrate the favorable performance of our novel kernel relative to existing exact and approximate GP methods across a variety of synthetic data examples. Furthermore, we conduct space–time prediction based on more than 1 million measurements of daily maximum temperature and verify that our results outperform state-of-the-art methods in the Earth sciences. More broadly, having access to exact GPs that use ultra-scalable, sparsity-discovering, nonstationary kernels allows GP methods to truly compete with a wide variety of machine learning methods.

Gaussian processes↗
DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗
DOE OSTI2018

High Initial Sputter Rate Found for Vaccinia Virions Using Isotopic Labeling, NanoSIMS, and AFM

High-lateral-resolution secondary ion mass spectrometry (SIMS) has the potential to provide functional and depth resolved information from small biological structures, such as viral particles (virions) and phage, but sputter rate and sensitivity are not characterized at shallow depths relevant to these structures. Here we combine stable isotope labeling of the DNA of vaccinia virions with correlated SIMS imaging depth profiling and atomic force microscopy (AFM) to develop a nonlinear, nonequilibrium sputter rate model for the virions and validate the model on the basis of reconstructing the location of the DNA within individual virions. Our experiments with a Cs+ beam show an unexpectedly high initial sputter rate (~100 um 2 ·nm·pA –1 ·s –1 ) with a rapid decline to an asymptotic rate of 0.7 um 2 ·nm·pA –1 ·s –1 at an approximate depth of 70 nm. Correlated experiments were also conducted with glutaraldehyde-fixed virions, as well as O – and Ga + beams, yielding similar results. Based on our Cs + sputter rate model, the labeled DNA in the virion was between 50 and 90 nm depth in the virion core, consistent with expectations, supporting our conclusions. Virion densification was found to be a secondary effect. In conclusion, accurate isotopic ratios were obtained from the initiation of sputtering, suggesting that isotopic tracers could be successfully used for smaller virions and phage.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2011

TURBULENT CELLS IN STARS: FLUCTUATIONS IN KINETIC ENERGY AND LUMINOSITY

Three-dimensional (3D) hydrodynamic simulations of shell oxygen burning exhibit bursty, recurrent fluctuations in turbulent kinetic energy. These are shown to be due to a general instability of the convective cell, requiring only a localized source of heating or cooling. Such fluctuations are shown to be suppressed in simulations of stellar evolution which use the mixing-length theory. Quantitatively similar behavior occurs in the model of a convective roll (cell) of Lorenz, which is known to have a strange attractor that gives rise to chaotic fluctuations in time of velocity and, as we show, luminosity. Study of simulations suggests that the behavior of a Lorenz convective roll may resemble that of a cell in convective flow. We examine some implications of this simplest approximation and suggest paths for improvement. Using the Lorenz model as representative of a convective cell, a multiple-cell model of a convective layer gives total luminosity fluctuations which are suggestive of irregular variables (red giants and supergiants), and of the long secondary period feature in semiregular asymptotic giant branch variables. This '{tau}-mechanism' is a new source for stellar variability, which is inherently nonlinear (unseen in linear stability analysis), and one closely related to intermittency in turbulence. It was already implicit in the 3D global simulations of Woodward et al. This fluctuating behavior is seen in extended two-dimensional simulations of CNeOSi burning shells, and may cause instability which leads to eruptions in progenitors of core-collapse supernovae prior to collapse.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Optimal Transmission Switching Using the IV-ACOPF Linearization

In this paper we seek to investigate the performance of transmission switching using the iterative linear program approximation to the Current Voltage AC Optimal Power Flow (IV-ACOPF). Several different methods of using this switching are investigated to find a method that addresses the MIP challenges and is both fast and accurate. We consider opening only one line, opening up to five lines, and progressively opening one line at a time. The linear method with switching is much faster than the nonlinear ACOPF and generally finds solutions within 1% of the nonlinear ACOPF.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2014

Statistical model based iterative reconstruction (MBIR) in clinical CT systems. Part II. Experimental assessment of spatial resolution performance

Purpose: Statistical model based iterative reconstruction (MBIR) methods have been introduced to clinical CT systems and are being used in some clinical diagnostic applications. The purpose of this paper is to experimentally assess the unique spatial resolution characteristics of this nonlinear reconstruction method and identify its potential impact on the detectabilities and the associated radiation dose levels for specific imaging tasks. Methods: The thoracic section of a pediatric phantom was repeatedly scanned 50 or 100 times using a 64-slice clinical CT scanner at four different dose levels [CTDI{sub vol} =4, 8, 12, 16 (mGy)]. Both filtered backprojection (FBP) and MBIR (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for image reconstruction and results were compared with one another. Eight test objects in the phantom with contrast levels ranging from 13 to 1710 HU were used to assess spatial resolution. The axial spatial resolution was quantified with the point spread function (PSF), while the z resolution was quantified with the slice sensitivity profile. Both were measured locally on the test objects and in the image domain. The dependence of spatial resolution on contrast and dose levels was studied. The study also features a systematic investigation of the potential trade-off between spatial resolution and locally defined noise and their joint impact on the overall image quality, which was quantified by the image domain-based channelized Hotelling observer (CHO) detectability index d′. Results: (1) The axial spatial resolution of MBIR depends on both radiation dose level and image contrast level, whereas it is supposedly independent of these two factors in FBP. The axial spatial resolution of MBIR always improved with an increasing radiation dose level and/or contrast level. (2) The axial spatial resolution of MBIR became equivalent to that of FBP at some transitional contrast level, above which MBIR demonstrated superior spatial resolution than FBP (and vice versa); the value of this transitional contrast highly depended on the dose level. (3) The PSFs of MBIR could be approximated as Gaussian functions with reasonably good accuracy. (4) Thez resolution of MBIR showed similar contrast and dose dependence. (5) Noise standard deviation assessed on the edges of objects demonstrated a trade-off with spatial resolution in MBIR. (5) When both spatial resolution and image noise were considered using the CHO analysis, MBIR led to significant improvement in the overall CT image quality for both high and low contrast detection tasks at both standard and low dose levels. Conclusions: Due to the intrinsic nonlinearity of the MBIR method, many well-known CT spatial resolution and noise properties have been modified. In particular, dose dependence and contrast dependence have been introduced to the spatial resolution of CT images by MBIR. The method has also introduced some novel noise-resolution trade-off not seen in traditional CT images. While the benefits of MBIR regarding the overall image quality, as demonstrated in this work, are significant, the optimal use of this method in clinical practice demands a thorough understanding of its unique physical characteristics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗