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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Determination of a suitable molar absorption coefficient (ε) for lignin analysis of fibrous plants using the CASA method

In this study, the benchmarking and applicability of the CASA method for the analysis of fibrous plants, such as flax, hemp, and jute, is evaluated. Lignin is a phenolic biopolymer present in plant cell walls and is composed of three primary monomeric units, designated G, S, and H. Various factors, such as the genetic variability, influence the relative proportions of these units in plant samples. Recently, the cysteine-assisted sulfuric acid (CASA) method has been introduced as a rapid method for the quantification of lignin in wood samples. The aim of this study is to establish a suitable molar absorption coefficient (ε, L·g –1 ·cm –1 ) to adapt the CASA method for use with annual plant fibers. This investigation was motivated by the technical advantages of the CASA method, including higher throughput, lower reaction temperatures, and ecological benefits due to the absence of carcinogenic, mutagenic, or reprotoxic (CMR) substances and the need for minimal sample quantities. In this method, lignin solubilization is facilitated by cysteine, which is an amino acid that enhances the reaction kinetics, using a one-hour incubation period. However, as with any spectrophotometric technique, the CASA method depends on a molar absorption coefficient (ε) that varies according to the ratio of the aromatic units within the polymer. To evaluate the suitability of CASA for quantifying lignin in economically significant plant fibers, we investigate the impact of the unit ratios on the accuracy of ε. The results are compared with those of two widely recognized lignin analytical methods: the Klason method, which is a gravimetric reference method, and the acetyl bromide soluble lignin method, which is the most commonly used spectrophotometric approach. The final ε obtained in this study reveals a relative difference in lignin content ranging from –8 % to +9 % based on a comparison between the CASA and Klason methods across different industrial hemp varieties. As a result, using known G:S ratios in annual fibrous plants, ε can be estimated from our results.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

A physical method for downscaling land surface temperatures using surface energy balance theory

Fine-resolution land surface temperature (LST) derived from thermal infrared remote sensing images is a good indicator of surface water status and plays an essential role in the exchange of energy and water between land and atmosphere. A physical surface energy balance (SEB)-based LST downscaling method (DTsEB) is developed to downscale coarse remotely sensed thermal infrared LST products with fine-resolution visible and near-infrared data. Here, the DTsEB method is advantageous for its ability to mechanically interrelate surface variables contributing to the spatial variation of LST, to quantitatively weigh the contributions of each related variable within a physical framework, and to efficaciously avoid the subjective selection of scaling factors and the establishment of statistical regression relationships. The applicability of the DTsEB method was tested by downscaling 12 scenes of 990 m Moderate Resolution Imaging Spectroradiometer (MODIS) and aggregated Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) LST products to 90 m resolution at six overpass times between 2005 and 2015 over three 9.9 km by 9.9 km cropland (mixed by grass, tree, and built-up land) study areas. Three typical LST downscaling methods, namely the widely applied TsHARP, the later developed least median square regression downscaling (LMS) and the geographically weighted regression (GWR), were introduced for intercomparison. The results showed that the DTsEB method could more effectively reconstruct the subpixel spatial variations in LST within the coarse-resolution pixels and achieve a better downscaling accuracy than the TsHARP, LMS and GWR methods. The DTsEB method yielded, on average, root mean square errors (RMSEs) of 2.01 K and 1.42 K when applied to the MODIS datasets and aggregated ASTER datasets, respectively, which were lower than those obtained with the TsHARP method, with average RMSEs of 2.41 K and 1.71 K, the LMS method, with average RMSEs of 2.35 K and 1.63 K, and the GWR method, with average RMSEs of 2.38 K and 1.64 K, respectively. The contributions of the related surface variables to the subpixel spatial variation in the LST varied both spatially and temporally and were different from each other. In summary, the DTsEB method was demonstrated to outperform the TsHARP, LMS, and GWR methods and could be used as a good alternative for downscaling LST products from coarse to fine resolution with high robustness and accuracy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Involute Working Group – FSI Analysis of Fuel Plates Using Finite Volume and Finite Element Methods

The three involute plate research reactors RHF, HFIR, and FRM II have expressed an interest in using computational software to carry their steady-state safety analysis. Since these tools represent a significant departure from the methods used currently (one-dimensional), the acceptability of the new approach by regulators requires thorough verification and validation of these tools. Therefore, Argonne National Laboratory and the three involute-plate reactors formed an informal group called the Involute Working Group aiming at qualifying computational tools to perform steady-state safety analysis. The present report focuses on a comparison of finite volume and finite element methods to model solids in fluid-structure interaction problems with the goal to estimate the coolant flow-induced fuel plate deflections obtained with the two methods. The finite volume method will be obsoleted in STARCCM+ by the end of 2021, nevertheless, this evaluation is important because the method was used by ANL researchers to model the response of the fuel plates, despite its drawbacks, which are discussed in the report. It was essential to check how those estimates compare to the results obtained with the finite element method that is considered superior for structural analysis. Various geometries, i.e., flat, cylindrical and circle-involute fuel plates, as well as coolant flow speed, were considered. The comparison shows that, independently of the plate geometry, the finite volume method significantly underestimates the deflection as compared to finite element method for coarser meshes. When the discretization is developed as a result of a mesh sensitivity study using finite element method, the result obtained using finite volume method can be a few times smaller than the corresponding finite element method solution. A code-to-code comparison , between STAR-CCM+ and LS-DYNA was included in the analysis. Within the LS-DYNA models, two types of finite element formulations were used: solid and shell finite elements. Mesh sensitivity study showed that both approaches converge to a similar value that was obtained with STAR-CCM+ finite element solver. The evaluation of the computational solvers was extended by adding two benchmark cases from the STAR-CCM+ Verification Suite and presented in the Appendix A. The selected cases are: (1) bending of a cantilever beam under external load, and (2) cylindrical shell deformation analysis, known in the literature as ‘Scordelis-Lo roof’. The problems were solved with finite volume, and finite element methods, and the results confirmed the previously discussed findings. The analysis shows that the finite element solver is superior to the finite volume solver in terms of representation of model geometry and estimating the structural behavior of fuel plates. Depending on the ratio of the load to the flexibility of the plate, the finite volume solver can greatly under- or overestimate the structural response if a very carefully selected mesh is not used.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

An extension of the localized artificial diffusivity method for immiscible and high density ratio flows

The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a wide range of multi-material problems. However, traditional LAD methods face significant challenges when applied to flows with large density ratios and when maintaining thermodynamic equilibrium across material interfaces. These limitations arise from the formulation of the artificial diffusivity flux and the reliance on enthalpy diffusion for interface regularization. Additionally, traditional LAD methods struggle to ensure stability under large density ratio conditions, fail to maintain a finite interface thickness, and are therefore unsuitable for modeling immiscible interfaces. Here, in this work, we discuss the origins of these issues in traditional LAD methods and propose modifications which enable the simulation of large density ratio and immiscible flows. The proposed method targets the artificial diffusion fluxes at gradients and ringing in the volume fraction, rather than the mass fraction in traditional methods, to consistently regularize large density ratio interfaces. Furthermore, the proposed method introduces an artificial bulk density diffusion term to enforce equilibrium conditions across interfaces. To address the challenge of modeling immiscible flows, a conservative diffuse interface term is incorporated into the formulation to ensure a finite interface thickness. Specific consideration is taken in the design of the method to ensure that these crucial properties are maintained for N -material flows. The effectiveness of the proposed method is demonstrated through a series of canonical test cases, and its accuracy is validated by comparison with experimental data on micro-bubble collapse in water. These results highlight the method’s robustness and its ability to overcome the limitations of traditional LAD approaches.

Artificial diffusivity↗
DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Comparison of Infiltration Test Methods for Soil Health Assessment

Infiltration rate (IR) has been commonly used as a metric to evaluate soil quality and health. For the USDA Soil Quality Test Kit, a 15-cm (6-in) diameter (ID) cylinder is used to measure IR with 444 cm 3 (equivalent to 2.54 cm or 1 in) of water while other standard IR procedures require substantially larger volumes of water. The general objective of this study was to compare different methods for IR measurement. Using three replications, IR measurements were conducted along a 9-m (27-ft) long transect in two different soil types by the double-ring infiltrometer (DRI) using 25- and 50-cm (10-and 20-in, respectively) cylinders, single-ring infiltrometer (SRI) using 25- and 50-cm cylinders, Cornell sprinkle infiltrometer (CSI) using a 24.1-cm (9.5-in) cylinder, the USDA recommended procedure using a 15-cm diameter cylinder (hereafter referred to as USDA-15 method), and a modified USDA method using a 24.1-cm diameter cylinder. Although the USDA-15 method is simple and requires a small amount of water, based on high variability among replications and significant reduction in IR during early stages of water entry into the soil, the procedure does not offer an accurate estimate of the soil infiltration potential. The CSI procedure was reproducible, but it is more cumbersome to perform than other methods. The DRI, SRI, and CSI methods required a much greater volume of water than the USDA-15 method but produced results that are more consistent. The most consistent results were obtained by the CSI and DRI methods. The modified USDA method results were similar to the SRI method and were an improvement over the original USDA-15 method. For assessing soil health, additional investigations should be conducted to evaluate a modified version of the USDA procedure using a larger cylinder.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The strip method for shape derivatives

Abstract A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches to computing shape derivatives. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. We introduce the strip method , which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. As an added benefit, its computational complexity is comparable to that of the boundary method, that is, it is faster than the volume method. We illustrate the benefits of the strip method with numerical examples.

Hardesty, Sean↗
DOE OSTI2023

Synthesis and characteristics of porous ceramic tubes: a comparison of centrifugal casting and cold isostatic pressing methods

Short porous ceramic tubes in small quantities are needed for membrane-related research and development efforts and can be synthesized by centrifugal casting (CC) or cold isostatic pressing (CIP) methods. Here, this work evaluates the characteristics of porous ceramic tubes prepared by both methods and provides a strategy for selecting the proper method for ceramic tube fabrication, depending on its application. Samarium-doped ceria (SDC) with an average crystallite size of 10 nm was synthesized by a citrate method and used to make porous SDC tubes by the CC and CIP methods under different conditions. Porous SDC tubes were prepared from an aqueous suspension of the SDC powder with polyvinyl alcohol (PVA) using a cylindrical metallic mold, centrifugated at 4000–6000 rpm, followed by sintering in 1200–1500 °C. SDC tubes were also made by the CIP method from the SDC powder placed inside a cylindrical rubber bag followed by isostatic compression at 1379 bar. The pore structure of the SDC tubes was characterized by helium permeation and liquid nitrogen Archimedes method. Due to high compression pressure giving a low porosity green tube, the CIP method with lower sintering temperature produces SDC tubes with much lower porosity and average pore size and similar tortuosity compared to the CC methods. The CIP method should be used to prepare low porosity or dense ceramic tubes, and the CC method should be used for preparing high-porosity ceramic tubes or tubes with pore gradient tube wall.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Assessing methods in fusion and fitting for time series construction in remote sensing-based earth observations

This study evaluates the comparative performance of spatiotemporal fusion and time-series fitting methods for constructing high-spatiotemporal-resolution remote sensing time-series data. Due to in-class similarity of fusion methods and fitting methods, we employ the Fit-FC (Fitting, spatial Filtering, and residual Compensation) model as a representative fusion method and the linear harmonic fitting model as a representative fitting method. Both Fit-FC and the linear harmonic fitting are widely used for high-spatiotemporal-resolution time-series data construction, and we modify the original Fit-FC model to enable automatic time-series fusion. To ensure data representativeness, we use 3 years (2019–2021) of Harmonized Landsat and Sentinel-2 surface reflectance datasets and Terra MCD43A4 products. Eight experimental regions are selected worldwide to guarantee generalization of the comparative performance between fusion and fitting methods, covering diverse land-use types (cropland, developed land, forest, and grassland) and varying climatological conditions. Time-series of NDVI and surface reflectance are analyzed under both actual observations and simulated data-missing scenarios. The constructed time-series data reveals that (1) the modified Fit-FC and linear harmonic fitting model achieve excellent performance in constructing high-resolution time-series images; (2) the fusion method outperforms the fitting method in constructing time-series of NDVI and surface reflectance images in cropland-, forest-, and grassland-dominated regions; (3) both methods achieve comparable performance in developed-dominated regions; (4) the fusion method is more robust to missing data, and better captures abrupt phenological transitions under conditions of continuous missing data; (5) the fitting method is computationally more efficient, making it suitable for large-scale time-series image reconstruction. This study provides valuable insights for selecting optimal strategies to generate high-resolution time-series images across diverse application scenarios and lays a foundation for extensions to other vegetation indices or land surface variables.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Mitigating contamination in LSS surveys: a comparison of methods

ABSTRACT Future large-scale structure surveys will measure the locations and shapes of billions of galaxies. The precision of such catalogues will require meticulous treatment of systematic contamination of the observed fields. We compare several existing methods for removing such systematics from galaxy clustering measurements. We show how all the methods, including the popular pseudo-Cℓ Mode Projection and Template Subtraction methods, can be interpreted under a common regression framework and use this to suggest improved estimators. We show how methods designed to mitigate systematics in the power spectrum can be used to produce clean maps, which are necessary for cosmological analyses beyond the power spectrum, and we extend current methods to treat the next-order multiplicative contamination in observed maps and power spectra, which reduced power spectrum errors from $\Delta \chi ^2_{\rm C_\ell }\simeq 10$ to ≃ 1 in simulated analyses. Two new mitigation methods are proposed, which incorporate desirable features of current state-of-the-art methods while being simpler to implement. Investigating the performance of all the methods on a common set of simulated measurements from Year 5 of the Dark Energy Survey, we test their robustness to various analysis cases. Our proposed methods produce improved maps and power spectra when compared to current methods, while requiring almost no user tuning. We end with recommendations for systematics mitigation in future surveys, and note that the methods presented are generally applicable beyond the galaxy distribution to any field with spatial systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases

Abstract Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.

Zhang, Shuaifang↗
DOE OSTI2024

Detectability of Varied Hybridization Scenarios Using Genome-Scale Hybrid Detection Methods

Hybridization events complicate the accurate reconstruction of phylogenies, as they lead to patterns of genetic heritability that are unexpected under traditional, bifurcating models of species trees. This phenomenon has led to the development of methods to infer these varied hybridization events, both methods that reconstruct networks directly, as well as summary methods that predict individual hybridization events from a subset of taxa. However, a lack of empirical comparisons between methods – especially those pertaining to large networks with varied hybridization scenarios – hinders their practical use. Here, we provide a comprehensive review of popular summary methods: TICR, MSCquartets, HyDe, Patterson’s D-Statistic (ABBA-BABA), D3, and Dp. TICR and MSCquartets are based on quartet concordance factors gathered from gene tree topologies and HyDe, Patterson’s D-Statistic, D3, and Dp use site pattern frequencies to identify hybridization events between sets of three taxa. We then use simulated data to address questions of method accuracy and ideal use scenarios by testing methods against complex networks which depict gene flow events that differ in depth (timing), quantity (single vs. multiple, overlapping hybridizations), and rate of gene flow (γ). We find that deeper or multiple hybridization events may introduce noise and weaken the signal of hybridization, leading to higher relative false negative rates across all methods. Despite some forms of hybridization eluding quartet-based detection methods, MSCquartets displays high precision in most scenarios. While HyDe results in high false negative rates when tested on hybridizations involving extinct or unsampled ghost lineages, HyDe is the only method able to identify the direction of hybridization, distinguishing the source parental lineages from recipient hybrid lineages. Lastly, we test the methods on a dataset of ultraconserved elements from the bee subfamily Nomiinae, finding possible hybridization events between clades which correspond to regions of poor support in the species tree estimated in a previous study.

Bjorner, Marianne B.↗
DOE OSTI2026

Refining a Novel Process Monitoring Method to Safeguard Continuously Cycling Designs Using Isotopic Ratios

In advanced reactor (AR) designs, a common feature is continuous chemical processing and circulation of the nuclear material. This work bridges a significant measurement gap in safeguarding reactors with circulating fuel or continuous refueling by leveraging and building on the isotope ratio method first developed by our team under an FY21 Advanced Reactors International Safeguards Engagement (ARISE) project (Uribe et al. 2021). In circulating fuel designs, the radioisotope inventory changes from traditional effects (e.g., radioactive decay, fission) but also includes material transport due to pressure and temperature gradients. Such designs may also require regular or continuous additions or removals during operation, which significantly increases the rate of inventory change compared to traditional pressurized water reactor (PWR)s. Thus, directly tracking the nuclear inventory is ineffective since the isotopes are continuously added and removed. The isotope ratio method instead focuses on detecting changes to the input and output flows of radioisotopes. Previous work showed that for well-chosen pairs of isotopes, the isotopic ratio provides a sensitive and lasting indicator of deviation from normal conditions (e.g., startup, shutdown, diversion). The isotope ratio method is a process monitoring method with potential for application in for forward-looking approaches to International Atomic Energy Agency (IAEA) safeguards. The original process monitoring method was developed for a specific case—the decay tank of a thorium-fueled molten salt breeder reactor. In this expanded work, we explored other types of reactors and processes with nonstationary (e.g., flowing) nuclear material, which are difficult to safeguard with traditional methods because of the transient nature of the systems. The goal of the present work is to generalize the isotope ratio method for use in processes with continuously flowing nuclear material. All continuous processes have an average time for isotopes to be replaced in the system. The isotope ratio method works by choosing radioisotopes with half-lives both above and below the processing time. The present work seeks to explore which isotopes are suitable for the method by simulating the nuclear inventory, radioisotope emissions, and detector responses for several classes of advanced reactors. While the method can in principle be applied to other processes (e.g., enrichment or reprocessing facilities), the present work limits scope to ARs with continuously flowing fuel. Section 2 details the mathematics supporting the isotope ratio method, and Section 3 introduces the representative ARs selected for this work. Section 4 discusses how each reactor was analyzed, and Section 5 showcases the results for each representative reactor. Finally, Section 6 provides concluding remarks and suggests pathways for further analysis.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗
DOE OSTI2021

Implicit-Explicit Multirate Infinitesimal GARK Methods

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified “fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge--Kutta (IMEX-MRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A unified framework of stabilized finite element method for solving the Boltzmann transport equation

This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modifies the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embeds it in the Galerkin weak form to yield a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods area similar with the same stabilization parameter, and all these stabilized techniques can obtain a correct and stable solution. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model

This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Implicit–explicit multirate infinitesimal stage-restart methods

Implicit–Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is split into stiff and nonstiff processes with the goal of lower computational costs than a purely implicit or explicit approach. A complementary form of flexible IVP solvers are multirate infinitesimal methods for problems split into fast- and slow-changing dynamics, that solve a multirate IVP by evolving a sequence of “fast” IVPs using any suitably accurate algorithm. This article introduces a new class of high-order implicit–explicit multirate methods that are designed for multirate IVPs in which the slow-changing dynamics are further split in an IMEX fashion. This new class, which we call implicit–explicit multirate infinitesimal stage-restart (IMEX-MRI-SR), both improves upon the previous implicit–explicit multirate infinitesimal generalized-structure additive Runge Kutta (IMEX-MRI-GARK) methods by allowing for far easier creation of new embedded methods, and extends multirate exponential Runge Kutta (MERK) methods by allowing the fast-changing dynamics to be nonlinear and the methods to be implicit. We leverage GARK theory to derive conditions for orders of accuracy up to four, and we provide second- and third-order accurate example methods, which are the first known embedded MRI methods with IMEX structure. We then perform numerical simulations demonstrating convergence rates and computational performance in both fixed-step and adaptive-step settings.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗