Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “PRESERVATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Decommissioning of a facility in a historical reactor at SRS: achieving both historical significance preservation and effective in-situ decommissioning - 15275

The Savannah River Site (SRS) is an 802 square-kilometer United States Department of Energy (US DOE) nuclear facility located along the Savannah River near Aiken, South Carolina, where Management and Operations are performed by Savannah River Nuclear Solutions, LLC (SRNS). In 2004, US DOE recognized SRS as a structure within the Cold War Historic District of national, state and local significance because it is composed of the first generation of facilities constructed and operated from 1950 through 1989 to produce plutonium and tritium for our nation's defense. US DOE agreed to manage the SRS 105-C Reactor Facility as a potentially historic property due to its significance in supporting the U.S. Cold War Mission and for potential for future interpretation. The Disassembly Basin (DB) in C Reactor was evaluated for action under CERCLA. Data indicated there were over 830 curies of radioactivity associated with the basin sediments and approximately 9.1 million (M) liters (L) of contaminated water, not including a large quantity of activated reactor equipment, scrap metal, and debris on the basin floor. The release of DB water could potentially migrate to the aquifer and contaminate groundwater. The need for an action was identified to reduce risks to personnel in the facility and to eliminate the possible release of contaminants into the environment. In-situ decommissioning was selected as the remedy. The remedial action proceeded in stages: -Above-grade modifications to the interior of DB building -Relocation of irradiated scrap and reactor components to the deepest segments of the DB - Construction of a metal building to house evaporators - Forced evaporation of the DB's radiologically contaminated water - Grouting with special hybrid grouts - Removal of the evaporators and temporary building. Since the building itself was not demolished and will remain unchanged in appearance with the exception of filling the DB with grout, this ISD removal action/methodology did not adversely impact the historical significance of the 105-C Reactor Building, in accordance with the National Historic Preservation Act, nor did it adversely affect the ability to determine the full extent and details of preservation at some later date. Both special hybrid grout materials met all requirements. Overall average 7-day compressive strength for the dry area mix was 1.54 MPa (223 psi) and for the underwater mix 2.94 MPa (427 psi).Overall 28-day compressive strength for the dry area mix was 2.88 MPa (417 psi) and for the underwater mix 4.99 MPa (724 psi). A limited amount of testing was also performed at 91 days, where the overall compressive strength for the dry area mix was found to be 9.40 MPa (1363 psi) and for the underwater mix 13.98 MPa (2028 psi). All compressive strength values far exceeded the 0.34 MPa (50 psi) minimum requirements. The special, flowable-fill grouts designed and used for P- and R-Reactor ISD and used again for this 105-C ISD removal action resulted in considerable labor, cost, and schedule savings versus conventional materials. As an added bonus/benefit, the CO{sub 2} footprint of the SRS C-Reactor DB ISD was minimized by using a small amount of cement and byproduct material to produce the structural fill materials. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Groundwater remediation at the Fernald preserve, Cincinnati, Ohio modeling and resulting 2014 well field operational changes - 15324

The Fernald Preserve became a US DOE Office of Legacy Management site in November 2006, for long-term surveillance and maintenance following completion (with the exception of completing groundwater cleanup) of the Comprehensive Environmental Response, Compensation, and Liability Act; environmental remediation; and site restoration. When the site was turned over to the Office of Legacy Management, approximately 76 hectares (189 acres) of the Great Miami Aquifer (GMA) remained contaminated with uranium above the final remediation level of 30 micrograms per liter. Uranium contamination is being removed from groundwater in the GMA through a pump-and-treat operation that is predicted by groundwater modeling to continue until 2033. Certifying that cleanup objectives have been met and removing the remediation infrastructure after pump-and-treat (P and T) operations are complete will require a minimum of 3 additional years. The current P and T remedy has operated well. From August 1993 through December 2013 the remedy has been used to remove 5,345 kg (11,784 lb) of uranium from the GMA. A variety of metrics are used to track how the P and T operation is progressing and are reported each year in the Site Environmental Report for the Fernald site. The metrics show that the effectiveness of uranium removal is slowly decreasing (a common observation for P and T remedies) and that operational changes needed to be considered. Several different operational changes were modeled to determine if model-predicted cleanup dates could be shortened and if the effectiveness of the groundwater remediation could be improved. With the concurrence and support of US EPA, Ohio EPA, and site stakeholders, operational changes were agreed upon and implemented in 2014 that are predicted to increase the effectiveness of the ongoing operation and shorten cleanup times for a portion of the aquifer. Although the overall predicted length of the remediation was not shortened, modeling predicts that key areas of the uranium plume will be re-mediated sooner. This paper provides a status of the groundwater remediation under way at the Fernald Preserve near Cincinnati, presents the operational changes that were implemented in 2014, and summarizes the groundwater modeling that supported the changes. This paper also illustrates the potential benefits that can be gained by pro-actively managing a pump-and-treat operation and looking for innovative ways to adjust the operation. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Design and Construction of the Paddys Run Streambank Stabilization Project at the Fernald Preserve, Harrison, Ohio - 16165

The Fernald Preserve is a former uranium-processing plant that underwent extensive remediation pursuant to CERCLA and is now managed by the US DOE Office of Legacy Management. While remediation of buildings and soil contamination was completed in 2006, aquifer remediation is ongoing. Paddys Run is a second-order stream that runs to the south along the western side of the Fernald Preserve. The Paddys Run watershed encompasses nearly 41 km{sup 2} (16 mi{sup 2}), including most of the Fernald site. Field personnel conducting routine site inspections in March 2014 observed that Paddys Run was migrating east via bank erosion into the 'Pit 3 Swale', an area of known surface-water contamination. The soil there was certified pursuant to site regulatory agreements and meets all final remediation levels. However, weekly surface-water monitoring is conducted from two puddles within the swale area, when water that exceeds the final remediation levels is present. Paddys Run had migrated east approximately 4 m (13 ft) in 2 years and was approximately 29 m (95 ft) from the sample location. This rapid migration threatened existing conditions that allowed for continued monitoring of the swale area and also threatened Paddys Run water quality. Therefore, DOE and regulators determined that the east bank of Paddys Run required stabilization. This was accomplished with a design that included the following components: relocation of approximately 145 m (475 ft) of streambed 9 m (30 ft) west, installation of a rock toe along the east bank, installation of two cross-vane in-stream grade-control structures, stabilization of a portion of the east bank using soil encapsulated lifts, and regrading, seeding, and planting within remaining disturbed areas. In an effort to take advantage of low-flow conditions in Paddys Run, construction was initiated in September 2014. Weather delays and subsurface flow within the Paddys Run streambed resulted in an interim shutdown of the project area in December 2014. Construction activities resumed in April 2015, with completion in November 2015. To date, this stabilization project has been successful. The regraded bank and streambed have remained stable, and no compromise to installed cross-vanes, the rock toe, or the soil encapsulated lifts has been observed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Lessons Learned Concerning the Onsite Disposal Facility at the Fernald Preserve, Harrison, Ohio - 16176

An onsite disposal facility (OSDF) was constructed at the Fernald Preserve, Ohio, for the disposal of contaminated soil and debris generated during a Comprehensive Environmental Response, Compensation, and Liability Act site cleanup. Completed in October of 2006, the 30 ha facility contains 2.26 million m{sup 3} of waste materials, has a maximum height of approximately 19.8 m, and consists of eight individual cells. The dimensions of cells 1-7 are approximately 213 m x 122 m each, or 26,000 m{sup 2} (2.60 ha). The dimensions of cell 8 (the last cell constructed) are larger than those of the other cells (approximately 3.8 ha). Each cell was constructed with a leachate collection system (LCS) that collected rainwater and storm-water runoff during waste placement and prevented it from entering the underlying environment. Other engineered features include a multilayer composite liner system, a leak detection system (LDS) positioned beneath the primary liner, and a multilayer composite cover that was placed over each cell following the completion of waste-placement activities. The LCS and LDS layers are designed to convey (by gravity) any leachate/fluid that enters the system through pipes to the west side of the facility and into tanks located in valve houses. From there, leachate can be sampled and conveyed to treatment. Groundwater is monitored beneath each cell via monitoring wells. In November 2006, the US DOE Office of Legacy Management (LM) assumed responsibility for the long-term care and maintenance of the OSDF. LM has nine years of monitoring and maintenance experience with the Fernald OSDF. Monitoring data is reported each year in the Fernald Annual Site Environmental Report. The data collected and inspections conducted indicate that the facility is operating as designed. The past nine years has provided LM with the opportunity to evaluate how well many of the design and as-built features of the facility have functioned over time as they pertain to environmental monitoring, valve-house operation and maintenance, and leachate transmission. Lessons learned concerning the long-term care and maintenance of the OSDF at the Fernald Preserve are presented. The main lessons learned include the following: How bivariate plots can be used to address environmental monitoring challenges created by installing an engineered disposal facility in a location where contamination is above the background level but below cleanup standards. How valve-house design decisions can help to alleviate long-term monitoring challenges. How scale buildup can lead to leachate transmission issues. Some additional minor lessons learned are also presented. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

The Evolution of DOE/Stakeholder Relationships at the Fernald Preserve, Ohio, Site - 19559

The Fernald Preserve, Ohio, Site is managed by the US Department of Energy (DOE) Office of Legacy Management. It is approximately 29 km (18 miles) northwest of Cincinnati, Ohio, on the site of a former uranium-processing plant established by the US Atomic Energy Commission in 1951. The production mission officially ended in 1991 when it was replaced by a remediation mission. Extensive environmental remediation was subsequently conducted under the Superfund program by the DOE Office of Environmental Management. After most of the remediation was concluded in 2006, the site was transferred to the DOE Office of Legacy Management, which continued comprehensive ecological restoration and is responsible for an ongoing aquifer remediation operation. The site was renamed the Fernald Preserve and opened to the public in 2008 as an undeveloped park, encompassing a diversity of natural habitats native to the area. The site now serves as a community asset, offering a Visitors Center with exhibits that tell the site story, hiking trails, wildlife observation opportunities, meeting spaces for community groups, educational program opportunities, and Interpretive Services personnel to engage the public. There was a long history of community mistrust about government operations at the site, beginning in the 1950's when land for the site was acquired by eminent domain, and continuing when contamination and hazardous waste management concerns were revealed in the 1980's. Resulting media coverage on possible contamination and cover-up concerns was extensive. In 1986, sitewide studies to determine the nature and extent of contamination and to consider cleanup options were instigated. In 1989, the site was placed on the National Priorities List of the Superfund program. Because of the longstanding mistrust held by many stakeholders, DOE faced a very serious challenge in achieving consensus among stakeholder groups about the cleanup levels, waste disposition, and the future uses of the site. Starting in the late 1980's, DOE, the regulators, site contractors and the community took a number of steps over many years to increase trust and achieve consensus among the many stakeholder groups. These steps included establishing a single cleanup mission, involving the community early and often as a critically important stakeholder, creating a citizens taskforce and community envoys, and providing extensive educational outreach. As a result, DOE, regulators, contractors, and community members moved from a position of very little trust to one of increased trust and collaboration among all concerned parties. The lessons learned from the Fernald site can be invaluable in the resolution of difficult environmental issues and should be considered as DOE seeks increased collaboration and consensus with stakeholders to solve other environmental remediation challenges. (authors)

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

A novel conditional formulation of the Vlasov–Ampère equations: a conservative, positivity, asymptotic and Gauss law preserving scheme

We propose a novel reformulation of the Vlasov–Ampère equations for plasmas that reveals discrete symmetries that enables simultaneous conservation of mass, momentum and energy; preservation of Gauss’s law; positivity of the distribution function; and consistency with quasi-neutral asymptotics. The approach employs variable and coordinate transformations to yield a coupled system comprising a modified Vlasov equation and associated moment–field equations. The modified Vlasov equation advances a conditional distribution function that excludes mass, momentum and energy densities, which are instead evolved through moment equations enforcing the relevant symmetries, conservation laws and involution constraints. This reformulation aligns naturally with a recent slow-manifold reduction technique, which separates fast electron time scales and simplifies the treatment of the quasi-neutral limit within the reduced moment–field subsystem. Using this framework, we develop a numerical method for the reduced 1D1V subsystem that, for the first time in the literature, satisfies all key physical constraints while maintaining a quasi-neutral asymptotic behaviour. The advantages of the method are demonstrated on canonical electrostatic test problems, including the multiscale ion acoustic shock wave.

1D1V↗
DOE OSTI2020

On differentiable local bounds preserving stabilization for Euler equations

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. Furthermore, the importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. Additionally, in the case of transient problem, we also observe a reduction in the computational cost.

42 ENGINEERING↗
DOE OSTI2015

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution of a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Selective preservation of pyrogenic carbon across soil organic matter fractions and its influence on calculations of carbon mean residence times

The long-standing perspective that recalcitrance of soil organic carbon (SOC) controls its stability and persistence has shifted to one in which physical inaccessibility of SOC to microorganisms plays a predominant role. This paradigm shift has been facilitated by analytical techniques that isolate SOC into physical fractions protected from decomposers by different mechanisms. The correlation between these fractions and SOC age has reinforced the emphasis of SOC inaccessibility. Pyrogenic C (PyC; also called charcoal or black carbon), which has been thermally altered by fire, is known to contain highly recalcitrant components that decompose very slowly and could represent an exception to this paradigm shift. We employed hydrogen pyrolysis to quantify the contribution of PyC to total SOC across soil fractions from three long-term agricultural experiments with land use conversions that caused reductions in SOC. We show that all soil fractions contain PyC and up to one-fifth of SOC in soil fractions considered to have low accessibility is comprised of PyC. Regardless of the soil fraction in which it was located, PyC was relatively unaffected by land use conversion compared to biogenic C (organic C not altered by fire), which suggests that selective preservation, rather than physical protection, is the dominant mechanism limiting PyC decomposition in these sites. We accounted for PyC in calculations of C mean residence times (MRTs) using differences in stable C isotope ratios between PyC and SOC. Though results varied by site and soil fraction, MRTs for biogenic C were generally shorter than for total SOC. Based on these results, PyC decomposition is controlled by a different mechanism than biogenic C, and this should be considered in studies of soil C dynamics. In addition, methods based on physical fractionation alone may place too great an emphasis on the role of inaccessibility for long-term SOC persistence.

58 GEOSCIENCES↗
DOE OSTI2015

Total Laryngectomy Versus Larynx Preservation for T4a Larynx Cancer: Patterns of Care and Survival Outcomes

Purpose: To examine practice patterns and compare survival outcomes between total laryngectomy (TL) and larynx preservation chemoradiation (LP-CRT) in the setting of T4a larynx cancer, using a large national cancer registry. Methods and Materials: Using the National Cancer Database, we identified 969 patients from 2003 to 2006 with T4a squamous cell larynx cancer receiving definitive treatment with either initial TL plus adjuvant therapy or LP-CRT. Univariate and multivariable logistic regression were used to assess predictors of undergoing surgery. Survival outcomes were compared using Kaplan-Meier and propensity score–adjusted and inverse probability of treatment–weighted Cox proportional hazards methods. Sensitivity analyses were performed to account for unmeasured confounders. Results: A total of 616 patients (64%) received LP-CRT, and 353 (36%) received TL. On multivariable logistic regression, patients with advanced nodal disease were less likely to receive TL (N2 vs N0, 26.6% vs 43.4%, odds ratio [OR] 0.52, 95% confidence interval [CI] 0.37-0.73; N3 vs N0, 19.1% vs 43.4%, OR 0.23, 95% CI 0.07-0.77), whereas patients treated in high case-volume facilities were more likely to receive TL (46.1% vs 31.5%, OR 1.78, 95% CI 1.27-2.48). Median survival for TL versus LP was 61 versus 39 months (P<.001). After controlling for potential confounders, LP-CRT had inferior overall survival compared with TL (hazard ratio 1.31, 95% CI 1.10-1.57), and with the inverse probability of treatment–weighted model (hazard ratio 1.25, 95% CI 1.05-1.49). This survival difference was shown to be robust on additional sensitivity analyses. Conclusions: Most patients with T4a larynx cancer receive LP-CRT, despite guidelines suggesting TL as the preferred initial approach. Patients receiving LP-CRT had more advanced nodal disease and worse overall survival. Previous studies of (non-T4a) locally advanced larynx cancer showing no difference in survival between LP-CRT and TL may not apply to T4a disease, and patients should be counseled accordingly.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Early Radiosurgery Improves Hearing Preservation in Vestibular Schwannoma Patients With Normal Hearing at the Time of Diagnosis

Purpose: Vestibular schwannomas (VS) are increasingly diagnosed in patients with normal hearing because of advances in magnetic resonance imaging. We sought to evaluate whether stereotactic radiosurgery (SRS) performed earlier after diagnosis improved long-term hearing preservation in this population. Methods and Materials: We queried our quality assessment registry and found the records of 1134 acoustic neuroma patients who underwent SRS during a 15-year period (1997-2011). We identified 88 patients who had VS but normal hearing with no subjective hearing loss at the time of diagnosis. All patients were Gardner-Robertson (GR) class I at the time of SRS. Fifty-seven patients underwent early (≤2 years from diagnosis) SRS and 31 patients underwent late (>2 years after diagnosis) SRS. At a median follow-up time of 75 months, we evaluated patient outcomes. Results: Tumor control rates (decreased or stable in size) were similar in the early (95%) and late (90%) treatment groups (P=.73). Patients in the early treatment group retained serviceable (GR class I/II) hearing and normal (GR class I) hearing longer than did patients in the late treatment group (serviceable hearing, P=.006; normal hearing, P<.0001, respectively). At 5 years after SRS, an estimated 88% of the early treatment group retained serviceable hearing and 77% retained normal hearing, compared with 55% with serviceable hearing and 33% with normal hearing in the late treatment group. Conclusions: SRS within 2 years after diagnosis of VS in normal hearing patients resulted in improved retention of all hearing measures compared with later SRS.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

A diffuse interface model with immiscibility preservation

A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical-bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results.

42 ENGINEERING↗
DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

An energy-conserving and asymptotic-preserving charged-particle orbit implicit time integrator for arbitrary electromagnetic fields

Here we present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit motion in the small time-step limit, but also recovers all the first-order guiding center drifts as well as the correct gyroradius when stepping over the gyration time-scale. In contrast to previous efforts in this direction, the new scheme also features exact energy conservation. In the derivation of the scheme, we find that a new numerical time-scale is introduced. This scale is analyzed and the resulting restrictions on time-step are derived. Based on this analysis, we develop an adaptive time-stepping strategy the respects these constraints while stepping over the gyration scale when physically justified. It is shown through numerical tests on single-particle motion that the scheme's energy conservation property results in tremendous improvements in accuracy, and that the scheme is able to transition smoothly between magnetized and unmagnetized regimes as a result of the adaptive time-stepping.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Fast nonlinear iterative solver for an implicit, energy-conserving, asymptotic-preserving charged-particle orbit integrator

Here recently, an asymptotic-preserving (AP) particle orbit integrator has been proposed with remarkable properties including exact energy conservation, the ability to capture of all first-order drifts (including the ∇B-drift), the ability to capture trapped-passing boundaries with parallel velocity extremely close to the critical velocity, and the ability to transition from strongly to weakly magnetized spatial regions. The new AP orbit integrator is implicit, employing a Crank-Nicolson (CN) temporal discretization to ensure exact energy conservation. This, in turn, requires a local nonlinear iteration involving particle velocities and positions, and the local electromagnetic fields, to obtain the new-time solution. Ref. [1] did not attempt to provide an efficient solver for this system, and employed a brute-force GMRES-driven Jacobian-free Newton-Krylov (JFNK) solver to invert the particle orbit equations at every timestep for expediency. While JFNK is robust and reliable, it is also expensive and very intrusive for practical implementations of the method (it requires having the JFNK machinery available and solving a 6 x 6 Jacobian system iteratively once per iteration per particle).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ $\ggg$ 1 (with $\mathcal{X}$∥, $ \mathcal{X}$⟂ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. Further, the implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ~ (NΔt) 1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ = 10 10 ) .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗