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At least 1,459 records · Page 81

Evaluation of Nuclear Spent Fuel Disposal in Clay-Bearing Rock - Process Model Development and Experimental Studies

The DOE R&D program under the Spent Fuel Waste Science Technology (SFWST) campaign has made key progress in modeling and experimental approaches towards the characterization of chemical and physical phenomena that could impact the long-term safety assessment of heat-generating nuclear waste disposition in deep clay/shale/argillaceous rock. International collaboration activities such as heater tests and postmortem analysis of samples recovered from these have elucidated key information regarding changes in the engineered barrier system (EBS) material exposed to years of thermal loads. Chemical and structural analyses of sampled bentonite material from such tests has as well as experiments conducted on these are key to the characterization of thermal effects affecting bentonite clay barrier performance and the extent of sacrificial zones in the EBS during the thermal period. Thermal, hydrologic, and chemical data collected from heater tests and laboratory experiments has been used in the development, validation, and calibration of THMC simulators to model near-field coupled processes. This information leads to the development of simulation approaches (e.g., continuum vs. discrete) to tackle issues related to flow and transport at various scales of the host-rock and EBS design concept. Consideration of direct disposal of large capacity dual-purpose canisters (DPCs) as part of the back-end SNF waste disposition strategy has generated interest in improving our understanding of the effects of elevated temperatures on the EBS design. This is particularly important for backfilled repository concepts where temperature plays a key role in the EBS behavior and long-term performance. This report describes multiple R&D efforts on disposal in argillaceous geologic media through development and application of coupled THMC process models, experimental studies on clay/metal/cement barrier and host-rock (argillite) material interactions, molecular dynamic (MD) simulations of water transport during (swelling) clay dehydration, first-principles studies of metaschoepite (UO 2 corrosion product) stability, and advances in thermodynamic plus surface complexation database development. Drift-scale URL experiments provides key data for testing hydrological-chemical (HC) model involving strong couplings of fluid mixing and barrier material chemical interactions. The THM modeling focuses on heater test experiments in argillite rock and gas migration in bentonite as part of international collaboration activities at underground research laboratories (URLs). In addition, field testing at an URL involves in situ analysis of fault slip behavior and fault permeability. Pore-scale modeling of gas bubble migration is also being investigated within the gas migration modeling effort. Interaction experiments on bentonite samples from heater test under ambient and elevated temperatures permit the evaluation of ion exchange, phase stability, and mineral transformation changes that could impact clay swelling. Advances in the development, testing, and implementation of a spent nuclear fuel (SNF) degradation model coupled with canister corrosion focus on the effects of hydrogen gas generation and its integration with Geologic Disposal Safety Assessment (GDSA). GDSA integration activities includes evaluation of groundwater chemistries in shale formations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Mid- and low-latitude model of thermospheric emissions. I - O(+) (2P) 7320 A and N2 (2P) 3371 A

This paper presents an interhemispherically coupled model of airglow emissions of the O(+) (2P) metastable state (7320 A) and the 0-0 band of the N2 second positive system (3371 A), covering mid- and low-latitudes. The model produces volume emission rates as a function of altitude, latitude, longitude, and local time for any selected data and solar and magnetic conditions, and, thus, can be used to provide three-dimensional maps of the selected emission for comparison with data obtained from orbiting vehicles. The semiglobal graphical maps of the 7320 A and 3371 A emissions illustrate the seasonal, diurnal, and solar cyclic variations on a scale that covers mid- and low-latitudes, as well as the effects of interhemispheric coupling (conjugate photoelectrons). It is shown that, in both cases, conjugate photoelectrons result in excitation at mid- to high- nighttime-latitudes in the winter hemisphere.

Torr, Marsha R.↗

Getting a THUMP from a WIMP

Producing an acceptable thermal relic abundance of dark matter with masses >> 10 2 TeV is a challenge. We propose a novel mechanism where GeV-scale states establish a tiny thermal relic abundance for dark matter, which is later promoted to ultra massive status by a very light scalar. We refer to this dark matter as a THermal Ultra Massive Particle (THUMP). Direct detection of THUMPs can be naturally expected due to large scattering cross sections mediated by low mass states that couple THUMPs to the Standard Model. Our model generically leads to signals for the associated GeV-scale states at accelerator experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Accelerating the Lagrangian Particle Tracking in Hydrologic Modeling to Continental-Scale

Unprecedented climate change and anthropogenic activities have induced increasing ecohydrological problems, which have motivated the development of large-scale modeling for solutions. Water age/quality is as important as water quantity for understanding the water cycle. However, current scientific progress in tracking water parcels at large-scale with high spatiotemporal resolutions is far behind that in water balance/quantity owing to the lack of powerful tools. EcoSLIM is a particle tracking model that works with the hydrologic model ParFlow-CLM, which couples surface-subsurface hydrology with land surface processes. Here, we demonstrate a parallel framework to accelerate EcoSLIM to continental-scale on a distributed, multi-GPU platform with CUDA-Aware MPI. In tests from catchment-, to regional-, and then to continental-scale using 25-million to 1.6-billion particles, EcoSLIM shows significant speedup and excellent parallel performance. The parallel framework is portable to atmospheric and oceanic particle tracking models, where parallelization is inadequate and a standard parallel framework is absent. Parallelized EcoSLIM is a promising tool to accelerate our understanding of the terrestrial water cycle and the upscaling of subsurface hydrology to Earth system models.

54 ENVIRONMENTAL SCIENCES↗

Atacama Cosmology Telescope: Constraints on cosmic birefringence

We present new constraints on anisotropic birefringence of the cosmic microwave background polarization using two seasons of data from the Atacama Cosmology Telescope covering 456 square degrees of sky. The birefringence power spectrum, measured using a curved-sky quadratic estimator, is consistent with zero. Our results provide the tightest current constraint on birefringence over a range of angular scales between 5 arc minutes and 9°. Here, we improve previous upper limits on the amplitude of a scale-invariant birefringence power spectrum by a factor of between 2 and 3. Assuming a nearly massless axion field during inflation, our result is equivalent to a 2σ upper limit on the Chern-Simons coupling constant between axions and photons of g αγ < 4.0 × 10 –2 /H I , where H I is the inflationary Hubble scale.

79 ASTRONOMY AND ASTROPHYSICS↗

Regional inertia dynamics of U.S. interconnections: An event-based measurement approach

Power grid inertia plays a vital role in frequency stability following large disturbances, yet its distribution across the U.S. grid is highly uneven. While interconnection-wide inertia benchmarks are useful, they can mask regional variability driven by resource mix, network coupling, and geographic separation. This paper extends event-driven inertia estimation to the regional scale using field measurements from the Frequency Monitoring Network (FNET/GridEye). Starting from balancing authority and independent system operator footprints, candidate regions are refined using a composite coherency score that combines frequency-trajectory shape similarity, timing spread, and lead/lag behavior to ensure dynamic consistency. A filtered sliding difference method (FSDM) is then used to construct regional frequency trajectories, detect disturbance onset, and compute robust regional rate-of-change of frequency (RoCoF). Regional, local, and interconnection inertia are estimated by combining RoCoF with event power imbalance, and additional indicators (regional-to-system inertia ratio and inertial-support arrival time) quantify regional-to-interconnection coupling and relative regional contributions. The method is demonstrated on eleven regions across the Eastern Interconnection (EI) and the Western Electricity Coordinating Council (WECC), with the Electric Reliability Council of Texas (ERCOT) used for validation. In ERCOT, estimates compared against energy management system (EMS) values achieve a mean absolute percentage error of 17.94%. WECC exhibits consistently shorter inertial-support arrival times (0.15–0.3 s) than EI (0.7–1.1 s), highlighting contrasting coupling and disturbance-propagation behavior. Overall, the results reveal pronounced spatial heterogeneity in inertia and coupling, underscoring the value of regional monitoring for both operational decision-making and long-term system planning.

Disturbance events↗

Data transfers for full core heterogeneous reactor high- fidelity multiphysics studies

Multiphysics simulations for nuclear reactor analysis are usually performed by resorting to operator splitting and fixed point iterations between single-physics solvers. This enables the separate solution of each physics, such as neutronics, fuel performance, and thermal hydraulics, on meshes tailored to the requirements of the respective numerical discretizations of the equations. As the equations are coupled, several fields must be transferred between single-physics solves. Projecting fields between meshes while preserving order of accuracy, conservation properties, and mapping non-overlapping geometries is a complex endeavor. This conference paper will present the transfers as implemented in MOOSE, which can handle arbitrary meshes, arbitrary mappings, conservation of integral quantities, and are made to scale with distributed simulations on both ends of the transfers. Their adequacy for advanced nuclear reactor multiphysics coupling is shown through examples and numerical studies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Large-scale Genetic Characterization of a Model Sulfate-Reducing Bacterium

ABSTRACTSulfate-reducing bacteria (SRB) are obligate anaerobes that can couple their growth to the reduction of sulfate. Despite the importance of SRB to global nutrient cycles and their damage to the petroleum industry, our molecular understanding of their physiology remains limited. To systematically provide new insights into SRB biology, we generated a randomly barcoded transposon mutant library in the model SRB Desulfovibrio vulgaris Hildenborough (DvH) and used this genome-wide resource to assay the importance of its genes under a range of metabolic and stress conditions. In addition to defining the essential gene set of DvH, we identified a conditional phenotype for 1,137 non-essential genes. Through examination of these conditional phenotypes, we were able to make a number of novel insights into our molecular understanding of DvH, including how this bacterium synthesizes vitamins. For example, we identified DVU0867 as an atypical L-aspartate decarboxylase required for the synthesis of pantothenic acid, provided the first experimental evidence that biotin synthesis in DvH occurs via a specialized acyl carrier protein and without methyl esters, and demonstrated that the uncharacterized dehydrogenase DVU0826:DVU0827 is necessary for the synthesis of pyridoxal phosphate. In addition, we used the mutant fitness data to identify genes involved in the assimilation of diverse nitrogen sources, and gained insights into the mechanism of inhibition of chlorate and molybdate. Our large-scale fitness dataset and RB-TnSeq mutant library are community-wide resources that can be used to generate further testable hypotheses into the gene functions of this environmentally and industrially important group of bacteria.

Trotter, Valentine V↗

Polymer Macrocycles: A novel topology to control dynamics of rubbery materials (Final Report)

One of the current challenges in polymer physics and engineering is to understand the behavior of circular macromolecules. Though such molecules have been made by dilute solution ring closure methods in the past, such procedures have been limited to relatively small, unentangled rings as well as to small sample quantities. Initial studies were also hampered by issues surrounding purity of the rings, though this problem has been somewhat overcome by the use of liquid chromatography at critical conditions (LCCC) methods that separate rings and linear chains. Furthermore, in spite of the continued progress a full understanding of ring dynamics remains elusive. The present work has addressed multiple aspects of the behavior of ring molecules by using a novel synthetic route: reversible radical recombination redox polymerization (R3P) to produce poly(3,6-dioxa-1,8-octanedithiol) (PolyDODT) molecules. The synthesis conditions were chosen to produce linear (LDODT), cyclic (RDODT) and linear-cyclic mixtures (LRDODT) in order to investigate dilute solution and rheological responses of the materials. Importantly, the R3P synthesis makes larger quantities and higher molecular weights than do the dilute solution ring closure methods and also has the potential to be scaled to industrial quantities, thus becoming commercializable. We emphasize two important outcomes of the work. The first is that the rheological investigation shows that very large molecular weight the PolyDODT rings permitted the investigation of ring dynamics from glassy towards terminal flow for molecular sizes corresponding to approximately 300 entanglements of the linear counterpart. At the same time, these very large sized rings could be diluted in a solvent in order to reduce the molecular entanglement density to less than unity. The results demonstrate that ring viscosity follows a Rouse-like linear dependence on molecular weight or entanglement number to approximately 15 entanglements. This range of "Rouse-like" response is greater than what was achieved in all prior works where synthesis conditions have limited the molecular sizes achievable. After the entanglement number $Z_w$ increases beyond approximately 15, we find that the viscosity-molecular weight scaling undergoes a rapid change from the Rouse-like $η\sim{Z}^1_w$ to a very strong power-law scaling that is approximately $η\sim{Z}^{5.8}_w$. This aspect of the work strongly suggests that prior investigations on highly pure rings have invariably been performed on unentangled systems simply because ring molecules have very high entanglement thresholds. The results are further supported by plateau modulus measurements that show that in the "Rouse-like" viscosity regime, for the RDODT samples there is a corresponding lack of a rubbery entanglement plateau and once entanglement coupling is seen, the rubbery plateau also appears in the dynamic modulus data. Furthermore, upon appropriate scaling, we show that the unentangled polyDODT rings (i.e., the diluted high molecular weight rings) show virtually identical dynamics (upon appropriate scaling to account for the chain dilutions) to the dynamics of similarly unentangled LCCC fractionated polystyrene rings.

36 MATERIALS SCIENCE↗

CompLaB v1.0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism, and biofilm dynamics

Abstract. Microbial activity and chemical reactions in porous media depend on the local conditions at the pore scale and can involve complex feedback with fluid flow and mass transport. We present a modeling framework that quantitatively accounts for the interactions between the bio(geo)chemical and physical processes and that can integrate genome-scale microbial metabolic information into a dynamically changing, spatially explicit representation of environmental conditions. The model couples a lattice Boltzmann implementation of Navier–Stokes (flow) and advection–diffusion-reaction (mass conservation) equations. Reaction formulations can include both kinetic rate expressions and flux balance analysis, thereby integrating reactive transport modeling and systems biology. We also show that the use of surrogate models such as neural network representations of in silico cell models can speed up computations significantly, facilitating applications to complex environmental systems. Parallelization enables simulations that resolve heterogeneity at multiple scales, and a cellular automaton module provides additional capabilities to simulate biofilm dynamics. The code thus constitutes a platform suitable for a range of environmental, engineering and – potentially – medical applications, in particular ones that involve the simulation of microbial dynamics.

58 GEOSCIENCES↗

Reusable Launch Vehicle Control In Multiple Time Scale Sliding Modes

A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.

Shtessel, Yuri↗

Pore-scale simulation of drying in porous media using a hybrid lattice Boltzmann: pore network model

In this work, a hybrid method coupling a pseudo-potential lattice Boltzmann model (LBM) and a pore network model (PNM) to simulate drying in porous media is proposed. Based on the watershed method, the porous medium is firstly decomposed into pore regions. According to the liquid–vapor phase distribution at a given time, the pore regions are further divided into four pore types, namely two-phase pores where a liquid–vapor interface exists, buffer pores next to the two-phase pores, single-liquid and single-vapor phase pores. The pseudo-potential LBM is used in the two-phase and buffer pores to simulate liquid drying and track the movement of the interfaces, while the single-phase PNM simulations are conducted in the buffer and single-phase pores to simulate vapor or liquid flow. LBM and PNM are coupled in the buffer pores through exchange of boundary information. The hybrid method is applied to simulate liquid drying in a porous medium. The whole-domain LBM simulation is considered as the reference solution to validate the hybrid method. Liquid saturation variation during the drying process and detailed phase and pressure distributions obtained by the two methods match quite well, demonstrating the accuracy of the hybrid method. For the specific case studied, the hybrid method saves more than 60% computational time compared to the whole-domain LBM simulation. In addition, the speedup of the hybrid method becomes more significant for a larger computational domain. In summary, the hybrid method developed in this work combines the accuracy of LBM and the efficiency of PNM to simulate drying in porous media at pore scale and can lead to significant reduction of computation time, thus allowing the pore-scale consideration of drying in larger porous systems.

36 MATERIALS SCIENCE↗

Spatial Microbial Respiration Variations in the Hyporheic Zones Within the Columbia River Basin

Abstract While the hyporheic zone (HZ) accounts for a significant portion of whole stream CO 2 concentrations, HZ respiration modeling studies are lacking in quantifying their contributions to the total CO 2 at large watershed/basin scales. Quantifying the contribution of anaerobic respiration is also underappreciated. This study used a carbon‐nitrogen‐coupled river corridor model to quantify HZ aerobic and anaerobic respiration and determined the key factors controlling their spatial variability within the Columbia River Basin (CRB). The modeled respiration patterns showed high spatial variability. Among the nine sub‐basins composing the CRB, the Lower Columbia and the Willamette, which receive higher precipitation, had higher respiration. Medium‐sized rivers (fourth to sixth orders) produced the highest aerobic and anaerobic respiration among reaches of different sizes. At the basin scale, aerobic respiration is dominant, representing approximately 98.7% of the total respiration across the CRB. While most of the reaches were dominant with aerobic respiration, reaches in agricultural land showed a relatively higher anaerobic respiration (18%) ratio. A variable importance analysis showed that hyporheic exchange flux controlled most of the spatial variability of HZ respiration, dominating over other physical variables such as residence time, stream dissolved organic carbon (DOC), nitrate, and dissolved oxygen (DO). The influence of substrate concentration (DOC and DO) is larger in modeling anaerobic respiration than aerobic respiration. Future efforts will focus on improving the estimation of the HZ exchange flux and the implementation of spatially explicit parameterizations for the reactions of interest to reduce model uncertainty.

54 ENVIRONMENTAL SCIENCES↗

Hawaii Solar Desalination Project

This project built the world’s largest Forward Osmosis (FO) solar thermal desalination plant at the NELHA Hawaii Ocean Science and Technology Park for a high visibility “on sun” demonstration of seawater desalination for agricultural applications. The project included re-commissioning an existing 2MW micro-dish solar thermal array and coupling it to a next-generation 500m3/day FO system. The purpose of the project was to validate FO at commercial scale; to verify that the water produced is safe for potential downstream agricultural users; to gather data on capital cost, energy consumption and operating expense for the technology; and to demonstrate that FO can be successfully coupled to low-grade thermal resources. The plant implemented advancements in FO component technology, including hot nano-filtration, polymeric heat exchangers, draw solutions, and improved FO membranes, and operated from June 2022 to September 2023 - producing 30gpm of permeate water. Thermal energy was below 30kWh/m 3 during operation, establishing a new benchmark in thermal desalination technology, with recovery rates at times exceeding 65%, well above what commercial RO systems can achieve. Combining the plant capital cost (CAPEX) and the operating expenses (OPEX) yields a Levelized Cost of Water (LCOW) that is competitive with existing carbon-intensive technologies such as RO. The ability of the plant to operate from a renewable resource paves the way toward a low-carbon desalination future using low-grade thermal resources.

14 SOLAR ENERGY↗

Techno-Economic Implications of Electrical Machine Scaling for Wave Energy Converters

The sizing of an electrical machine for a Wave Energy Converter (WEC) can have a substantial impact on the overall sizing, cost, and rating of the device. An electrical generator is typically part of the power take-off system, which is the mechanism by which the energy absorbed by the prime mover is transformed into usable electrical energy. For practically all WECs, the rate of change of actuation is predominantly determined by the wave resource (i.e., the wave height and frequency), and devices will see a sinusoidal varying velocity according to the wave conditions. The same can then be said for both directly and indirectly coupled power take-offs with electrical generators. This techno-economic study investigates electrical machine scaling and associated cost implications through core machine design theory, manufacturer data, supporting literature, and the Reference Model Project sponsored by the U.S. Department of Energy. The Reference Model Project was a partnered effort to develop open-source marine energy point designs as reference models to benchmark marine energy technology performance and costs, methods for design and analysis of marine energy technologies, estimations for capital costs, operational costs, and levelized cost of energy. The results from this study show torque is directly related to (1) the physical size of the machine required to increase the air-gap sheer stresses, (2)the amount of active material, (3) the support structure, (4) bearing size and rating, and (5) offshore cable rating, all of which have a significant effect on overall system costs in terms of both capital and operational expenditures. This paper aims to be a critical benchmark in helping determine an "optimal" nameplate rating for wave energy devices and their associated power take-offs. With an optimized rating and sizing process, WEC costs can be reduced and overall performance can be improved.

cables↗

Reduced global plant respiration due to the acclimation of leaf dark respiration coupled with photosynthesis

Summary Leaf dark respiration ( R d ) acclimates to environmental changes. However, the magnitude, controls and time scales of acclimation remain unclear and are inconsistently treated in ecosystem models. We hypothesized that R d and Rubisco carboxylation capacity ( V cmax ) at 25°C ( R d,25 , V cmax,25 ) are coordinated so that R d,25 variations support V cmax,25 at a level allowing full light use, with V cmax,25 reflecting daytime conditions (for photosynthesis), and R d,25 / V cmax,25 reflecting night‐time conditions (for starch degradation and sucrose export). We tested this hypothesis temporally using a 5‐yr warming experiment, and spatially using an extensive field‐measurement data set. We compared the results to three published alternatives: R d,25 declines linearly with daily average prior temperature; R d at average prior night temperatures tends towards a constant value; and R d,25 / V cmax,25 is constant. Our hypothesis accounted for more variation in observed R d,25 over time ( R 2 = 0.74) and space ( R 2 = 0.68) than the alternatives. Night‐time temperature dominated the seasonal time‐course of R d , with an apparent response time scale of c. 2 wk. V cmax dominated the spatial patterns. Our acclimation hypothesis results in a smaller increase in global R d in response to rising CO 2 and warming than is projected by the two of three alternative hypotheses, and by current models.

Plant Sciences↗

Axion-like particle at the 10 GeV scale: Higgs decays to wide jets and photons

If axion-like particles (ALPs) exist, they may have renormalizable couplings only to the Higgs boson ($h^0$) or to fields beyond the Standard Model. An ALP $A_h$ lighter than about 60 GeV would allow the $h^0 \to A_h A_h$ decay, with a branching fraction determined by the explicit global symmetry breaking responsible for the main contributions to the $A_h$ mass ($M_A$). New heavy fields that carry color and electric charge, such as squarks, can mediate $A_h$ decays at one loop mostly into gluons, but also into photons. Exploring LHC sensitivity to $A_h$, we show that the $h^0 \to A_h A_h \to (gg)(γγ)$ channel leads to a diphoton resonance at $M_A$ whose production rate is consistent with a $3.5σ$ excess reported by a CMS search at $M_A \approx 13.6$ GeV. For $M_A$ of order 10 GeV, the $h^0 \to A_h A_h \to 4g$ cascade decay leads to two wide jets (each with 2-prong substructure) that form a resonance at 125 GeV.

Dobrescu, Bogdan A. [Fermilab] (ORCID:000000034291↗

Performance and Accuracy Implications of Parallel Split Physics-Dynamics Coupling in the Energy Exascale Earth System Atmosphere Model

Simultaneous calculation of atmospheric processes is faster than calculating processes one at a time. This type of parallelism is beneficial or perhaps even necessary to provide good performance on modern supercomputers, which achieve faster performance through increased processor count rather than improved clock speed. The scalability of the Energy Exascale Earth System Model (E3SM) Atmosphere Model (EAM) is limited by the fluid dynamics which scales up to the number of mesh cells in the global mesh. In contrast, the suite of physics parameterizations in EAM is scalable up to the total number of physics columns, which is an order of magnitude greater than the number of mesh cells. A proposed solution to unlocking the greater potential performance from the physics suite is to solve the physics and dynamics in parallel. This work represents a first attempt at parallel splitting of the grid-scale fluid dynamics model and the subgrid-scale physics parameterizations in a global atmosphere model. We will demonstrate that switching to parallel physics-dynamics coupling extends the scalability of the EAM to up to 3 times the previous peak scalability limit and is up to 20% faster than the sequentially split coupling at the highest core counts and the same time step. Decadal simulations of both coupling approaches show very little impact to the model climate. This improved performance does not come without drawbacks, however. Parallel splitting requires a shorter time step and other modifications which largely offset performance gains. A mass fixer is required for conservation. Techniques for mitigating these issues are also discussed.

97 MATHEMATICS AND COMPUTING↗