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DOE OSTI2024

Coupled modeling of wake steering and platform offsets for floating wind arrays

Wake effects are a key challenge in the design and analysis of wind farms. For floating wind farms, the platforms offset under the aerodynamic loading of the turbine and are constrained by mooring systems that can vary significantly in allowable offsets. When considering wake steering, the crosswind offset of the turbine can counteract the lateral deflection of the wake. This work presents a tool to efficiently model the coupled impacts of wake steering and platform offsets for floating wind farms. The tool relies on the frequency-domain wind farm model RAFT and the steady-state wake model FLORIS. A verification with FAST.Farm is presented, then the tool is applied to a simple two-turbine case study. A range of mooring systems with increasing platform offsets and varied yaw misalignment angles are considered while comparing the impact on turbine power. Additional sensitivities to turbine spacing and mooring system orientation are explored. The results show that there is a least-optimal watch circle width for downwind turbine power production that varies with yaw misalignment angle and turbine spacing. Additionally, the turbine offsets under yaw-misaligned conditions vary significantly depending on mooring system orientation relative to the rotor plane, which in turn impacts the optimal misalignment angle. These results highlight the importance of including floating platform offsets and mooring systems in the evaluation of wake steering strategies for floating wind arrays.

17 WIND ENERGY↗

DOE OSTI2026

Critical structural parameter determining magnetic phases in the F⁡e 2 ⁢M⁢o 3 ⁢O 8 altermagnet system

A systematic structural investigation of F⁡e 2 ⁢M⁢o 3⁢ O 8 as a function of pressure, temperature, and magnetic field reveals that the 𝑃⁢6 3 ⁢𝑚⁢𝑐 space group remains robust over a wide range of conditions. No changes in the long-range crystal structure are observed for pressures up to 10 GPa, temperatures between 11 K and 300 K, and magnetic fields up to 9 T. The magnetostructural response, quantified by Δ⁢𝑐/𝑐, is determined for magnetic fields applied transverse to the crystallographic 𝑐 axis, demonstrating strong magnetoelastic coupling. The well-known magnetic-field-induced transition is confirmed to be first order and isostructural, occurring between two distinct altermagnetic states. Importantly, this transition can also be accessed using magnetic fields applied within the 𝑎𝑏 plane. When expressed in terms of the 𝑐/𝑎 ratio, the structural evolution under pressure (0–10 GPa) maps continuously onto that observed across the full Zn substitution range in (F⁡e 1−𝑦⁢ Z⁢n 𝑦 )2 M⁢o 3 ⁢O 8 ⁢(0 ≤ 𝑦 ≤ 1), indicating a common underlying structural control parameter. Furthermore, these results demonstrate that the 𝑐-axis lattice parameter is the primary structural degree of freedom governing magnetic behavior under external tuning parameters. More broadly, they indicate that magnetic order in this family of complex oxides (𝐴 2 ⁢M⁢o 3 ⁢O 8 , 𝐴 = Co,Mn,Ni) can be systematically tuned via pressure. This tunability highlights these materials as promising platforms for controllable magnetic switching, particularly in thin films integrated with piezoelectric substrates.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Neural Lyapunov Differentiable Predictive Control

We present a learning-based predictive control methodology using the differentiable programming framework with sufficient Lyapunov-based guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state, and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide an initial condition sampling-based statistical guarantee for the training of NLDPC. Our offline training approach provides a computationally efficient and scalable alternative to classical model predictive control solutions, which now directly comes with Lyapunov based guarantees as shown in this paper. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.

Mukherjee, Sayak↗

DOE OSTI2021

Microcoleus (Cyanobacteria) form watershed-wide populations without strong gradients in population structure

The relative importance of separation by distance and by environment to population genetic diversity can be conveniently tested in river networks, where these two drivers are often independently distributed over space. To evaluate the importance of dispersal and environmental conditions in shaping microbial population structures, we performed genome-resolved metagenomic analyses of benthic Microcoleus -dominated cyanobacterial mats collected in the Eel and Russian River networks (California, USA). The 64 Microcoleus genomes were clustered into three species that shared >96.5% average nucleotide identity (ANI). Most mats were dominated by one strain, but minor alleles within mats were often shared, even over large spatial distances (>300 km). Within the most common Microcoleus species, the ANI between the dominant strains within mats decreased with increasing spatial separation. However, over shorter spatial distances (tens of kilometres), mats from different subwatersheds had lower ANI than mats from the same subwatershed, suggesting that at shorter spatial distances environmental differences between subwatersheds in factors like canopy cover, conductivity, and mean annual temperature decreases ANI. Since mats in smaller creeks had similar levels of nucleotide diversity (π) as mats in larger downstream subwatersheds, within-mat genetic diversity does not appear to depend on the downstream accumulation of upstream-derived strains. The four-gamete test and sequence length bias suggest recombination occurs between almost all strains within each species, even between populations separated by large distances or living in different habitats. Overall, our results show that, despite some isolation by distance and environmental conditions, sufficient gene-flow occurs among cyanobacterial strains to prevent either driver from producing distinctive population structures across the watershed.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Diffusion bonding of tungsten-vanadium-zirconium using vacuum hot pressing for the development of a low decay heat cladding solution for tungsten spallation targets

Tantalum has been used as cladding material for water-cooled solid tungsten targets at many leading spallation neutron production facilities thanks to its high neutron yield, manageable radiation damage behavior, and excellent corrosion/erosion resistance in radiation environments. However, from a safety hazard perspective, thermal neutron capture of tantalum in spallation environments causes a high specific decay heat in the target volume, which often becomes a limiting factor in increasing the beam power on the target. In this paper, we studied vacuum hot pressing (VHP) parameters to diffusion bond zirconium to tungsten to explore the feasibility of using zirconium alloys as an alternative cladding material to tantalum. Zirconium alloys have long been used as cladding material for early generation solid spallation targets, and nuclear fuel rods. In spallation environments zirconium has significantly lower decay heat with shorter decay time compared to tantalum. The hot isostatic pressing (HIP) of zirconium and tungsten is known to produce limited bonding quality due to the formation of the brittle ZrW2 intermetallic layer. To overcome this problem, placing a vanadium interlayer between tungsten and zirconium has been proposed by exploring parameter space in binary alloy phase diagrams. Under the VHP conditions, 860 ◦C at 70 MPa for 4 hours, Zr-V and V-W showed good diffusion bonding, which demonstrates the feasibility of a single step HIP process to make the zirconium alloy clad tungsten spallation volumes.

Lee, Yong Joong↗

DOE OSTI2022

Vitrification of Hanford Tank 241-AP-101 Waste and Simulant

Hanford tank 241-AP-101 (referred to herein as AP-101) is the second Hanford radioactive tank waste planned to be processed and vitrified. A simulant version of AP 101 waste was formulated from the best-basis inventory (BBI) for the Hanford Tank 241-AP-101 liquid with an assumed target dilution of the waste from the BBI sodium molarity of 8.61 M to the desired 5.5 M Na. After the addition of glass-forming chemicals (GFCs), the simulant melter feed was processed in a non-radioactive, continuous laboratory-scale melter (CLSM) system. The AP-101 simulant melter feed was charged into the CLSM for 6.11 h of processing, which produced 6.55 kg of glass, for an average glass production rate of 2275 kg m 2 d -1 . Since there were no processing issues with the AP-101 simulant melter feed, AP-101 melter feed made with actual waste was then processed in a CLSM system built into a contamination area in a radioactive environment. The melting behavior characteristics appeared similar for both the simulant and waste melter feeds. The AP-101 waste melter feed was charged into the CLSM for 12.14 h of processing, which produced 8.75 kg of glass, for an average glass production rate of 1530 kg m 2 d -1 . During the AP-101 waste melter feed charging, the pump used to move the feed reached a maximum and it is believed that if the pump had a greater capacity, a greater average glass production rate could have been achieved. A constituent of interest present in low quantities in the AP-101 waste is 99 Tc or its non-radioactive surrogate, Re, added to the AP-101 simulant. Analysis for the quantities of 99 Tc and Re in the AP-101 glass product resulted in an average single-pass retention from the melter feed during relative chemical steady state of 55 ± 2 % for 99 Tc and 45 ± 2 % for Re. Compared to the processing of other melter feeds, the retention of 99 Tc in the AP-101 glass was greater than in both AP-107 and AP-105 glass, while the retention of Re in the AP-101 was less than in the AP-107 glass, but greater than in the AP-105 glass. A spike of I was added into the AP-101 melter feed that could be detected above the analysis detection limits. However, the iodine was only detectable above the ~6 ppm limit in one glass pour: the pour immediately following the burn off of the cold cap, where the I level reached ~30 ppm. This event was significant because the glass was poured immediately after burn off and thus it is presumed that the iodine had yet to volatilize from the glass melt while idling. It is recommended to perform future tests with I spikes at greater levels so that it can be detected in additional glass pours to determine if the expected 50 % retention of I used in the Kim et al. glass models can be confirmed. Offgas liquid samples were analyzed for acetonitrile, which was present at greater concentrations in CLSM liquids than in other scaled melter systems. This result was expected based on unique conditions with the CLSM system including a small plenum space leading to low residence time for offgas and the rapidity of offgas cooling upon exiting the CLSM vessel due to the location and environment. About 90 % of the total acetonitrile captured during both the AP-101 simulant and waste CLSM runs was found in the offgas condensate and demister liquids, thus it is recommended that only those liquids be sent for analysis if future testing to study the presence of acetonitrile in offgas products is desired.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2026

Virtual Growth of SRF Materials

Niobium's native surface oxide affects SRF cavity and superconducting qubit performance, motivating interest in controlling its crystalline structure. We combine a literature-derived machine-learning analysis with temperature-dependent XRD to study crystalline ordering in Nb2O5. Random Forest models, trained on 74 processing conditions from 17 papers and validated by leave-one-group-out cross-validation, predicted broad crystallinity outcomes well (balanced accuracy 0.809), but struggled with specific polymorph identity (0.577). Annealing temperature was the dominant predictor across all targets; oxygen partial pressure showed negligible importance, reflecting narrow literature coverage rather than physical irrelevance. Temperature-dependent XRD on anodized and H2O2-treated Niobium showed structural evolution consistent with the machine learning predictions. Our model and overall approach provide a data-driven framework for identifying and optimizing conditions that promote crystallization in initially amorphous oxides. This framework can guide the selection of growth and post-annealing conditions for Nb surfaces by narrowing the experimental parameter space, thereby reducing trial-and-error efforts in developing oxide structures relevant to SRF applications.

Tilkin, Anthony [Fermilab]↗

DOE OSTI2021

An Acoustic Quench Detection Method for CICC Conductor Operating in Gas or Liquid

A method using micro-electro-mechanical system (MEMS) acoustic sensor technology to detect a quench and abnormal behavior of a superconductor is discussed. MEMS of microphone chips are installed along the coolant space of a superconducting conductor to monitor the coolant condition. By arranging the acoustic sensor array in a coolant flow channel, it is possible to quickly detect a change in the local condition of the coolant with precise spatial resolution. This method is useful for monitoring superconducting magnets and power cables, especially those made with a cable-in-conduit-conductor (CICC) configuration. The methodology described in this work will also be very useful for a high temperature superconducting (HTS) conductor, such as REBCO tape conductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Majorana pair based qubits for fault tolerant quantum computing architecture using superconducting gold surface states

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Here we disclose a metal-based heterostructure platform to produce these Majorana zero modes which utilizes the surface states of certain metals in combination with a ferromagnetic insulator and a superconductor. This platform has the advantage of having a robust energy scale and the possibility of realizing complex circuit designs using lithographic methods. The Majorana zero modes are interrogated using planar tunnel junctions and electrostatic gates to selectively tunnel into designated pairs of Majorana zero modes. We give example of qubit designs and circuits that are particularly suitable for the metal-based heterostructures.

Moodera, Jagadeesh S.↗

DOE OSTI2026

Virtual Growth of SRF Materials: A Machine Learning Approach to Predict the Crystalline Structural Ordering in Nb Surface Oxides

Tilkin, Anthony [Unlisted, US, IL; Fermilab]↗

DOE OSTI2026

Theoretical assessment of the transition between electron emission mechanisms in a collisional crossed-field gap

Understanding the transition to the limiting current under vacuum and collisional conditions for thermal-field emission in a crossed-field gap is critical for characterizing the operating regime for numerous applications, such as high-power microwaves and Hall thrusters. By deriving the exact solution for the current density as a function of cathode temperature (and, by extension, initial velocity), cathode electric field, applied voltage, collision frequency, and magnetic field, we determine the transition from the canonical current source (thermal-field emission) to the vacuum and collisional limiting currents under different operating conditions. Here, we further show that the exact solution recovers the asymptotic solutions for the canonical and limiting currents for vacuum and collisional crossed-field gaps under appropriate limits. The exact solution demonstrates that the critical current decreases with both increasing magnetic field strength and increasing collisionality. Nexus phase space plots constructed by matching the individual asymptotic solutions provide the conditions for the transitions between mechanisms, elucidating when a single mechanistic equation would suffice and when theories combining multiple mechanisms are necessary.

Breen, Lorin I. [Purdue Univ., West Lafayette, IN ↗

DOE OSTI2021

Sensitivity of organized convective storms to model grid spacing in current and future climates

Mesoscale convective systems (MCSs) are complexes of thunderstorms that become organized and cover hundreds of kilometres over several hours. MCSs are prolific rain producers in the tropics and mid-latitudes and are the major cause of warm-season flooding. Traditionally, climate models have difficulties in simulating MCSs partly due to the misrepresentation of complex process interactions that operate across a large range of scales. Significant improvements in simulating MCSs have been found in kilometre-scale models that explicitly simulate deep convection. However, these models operate in the grey zone of turbulent motion and have known deficiencies in simulating small-scale processes (e.g. entrainment, vertical mass transport). Here, we perform mid-latitude idealized ensemble MCS simulations under current and future climate conditions in three atmospheric regimes: hydrostatic (12 km horizontal grid spacing; Δx), non-hydrostatic (Δx = 4, 2 and 1 km) and large eddy scale (Δx = 500 m and 250 m). Our results show a dramatic improvement in simulating MCS precipitation, movement, cold pools, and cloud properties when transitioning from 12 km to 4 km Δx. Decreasing Δx beyond 4 km results in modest improvements except for up- and downdraft sizes, average vertical mass fluxes, and cloud top height and temperature, which continue to change. Most important for climate modelling is that Δx = 4 km simulations reliably capture most MCS climate change signals compared to those of the Δx = 250 m runs. Significantly different climate change signals are found in Δx = 12 km runs that overestimate extreme precipitation changes by up to 100%.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Blockage and speedup in the proximity of an onshore wind farm: A scanning wind LiDAR experiment

To maximize the profitability of wind power plants, wind farms are often characterized by high wind turbine density leading to operations with reduced turbine spacing. As a consequence, the overall wind farm power capture is hindered by complex flow features associated with flow modifications induced by the various wind turbine rotors. In addition to the generation of wakes, the velocity of the incoming wind field can reduce due to the increased pressure in the proximity of a single turbine rotor (named induction); a similar effect occurs at the wind-farm level (global blockage), which can have a noticeable impact on power production. On the other hand, intra-wind-farm regions featuring increased velocity compared to the freestream (speedups) have also been observed, which can be a source for a potential power boost. To quantify these rotor-induced effects on the incoming wind velocity field, three profiling LiDARs and one scanning wind LiDAR were deployed both before and after the construction of an onshore wind turbine array. The different wind conditions are classified according to the ambient turbulence intensity and streamwise/spanwise spacing among wind turbines. The analysis of the mean velocity field reveals enhanced induction and speedup under stably stratified atmospheric conditions. Additionally, a reduced horizontal area between adjacent turbines has a small impact on the induction zone but increases significantly the speedup between adjacent rotors.

17 WIND ENERGY↗

DOE OSTI2026

CTGAN-TVAE

SAND2026-18914O CTGAN-TVAE (Conditional Tabular Generative Adversarial Networks-Tabular Variational Autoencoders) generates extensive sets of variable generation data through a hybrid framework. It enhances latent space representation by combining TVAE's robust feature-embedding with CTGAN's ability to condition categorical variables such as time. CTGAN-TVAE employs a fully connected neural network within a conditional generative adversarial network framework to manage continuous and categorical data effectively, capturing complex feature interactions without needing sequential modeling. This was developed as part of NNSA-MSIPP: Minority Serving Institution Partnership Program, Grant Number DE-NA0004016. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

Newlun, Cody [Sandia National Lab. (SNL-CA), Liver↗

DOE OSTI2022

FY22 Progress on Computational Modeling of the Water-Based NSTF

This report summarizes the system-level modeling effort by Argonne National Laboratory (Argonne) of the Natural convection Shutdown heat removal Test Facility (NSTF) in FY22. As an extension of the effort from FY21, this year’s work focuses primarily on the two-phase modeling of the NSTF using RELAP5-3D, particularly with the inclusion of the cavity model. The results from simulations were used to compare against experimental data for benchmarking purposes of the RELAP5 deck. Additionally, RELAP5 was used as a predictive tool to guide planned test operations and identify expected system behaviors. In the first part of this report, details are provided of the cavity omitted model where heat flux is applied directly as a boundary condition to the risers. The general trend predicted by the RELAP5 model matches that from the experimental data when a single-phase natural circulation flow is first established, followed by an oscillatory two-phase period and finally a stable two-phase flow. However, the onset of oscillations is predicted early by the model due to the smaller thermal mixing region in the tank. However, by expanding the simulated thermal mixing region in the tank, the onset of oscillations predicted by the model is able to match that from the experiment. These oscillations where studied in depth and are deduced to be flashing-induced instability. The model was then modified to simulate an accident scenario case where a representative heat load based on the full-scale Framatome’s 625 MW t SC-HTGR was applied directly to the riser channels. The simulated initial and boundary conditions were identical to those performed experimentally, facilitating direct comparisons between the predicted and experimental results. It was determined that the results showed some discrepancies remain, likely due to the overprediction of vapor generation rate by the computer model. In the second part of this report, the cavity model is re-introduced where it is observed that the RELAP5 prediction is now able to capture the major trends of the observed flow commonly observed during two-phase conditions. However, the onset of oscillations is once again predicted early by the model, possibly caused by the underprediction of heat loss from the heater and cavity. This is likely due to the omission of support structures in the cavity that can act as additional pathways for heat to escape to the environment. To overcome the underprediction of heat loss, part of the insulation surrounding the cavity side panels and the back of the heaters are removed to allow heat to escape directly to the environment, which then improves the RELAP5 prediction. Parametric studies are also performed to investigate the effects of heater power, tank inventory level, and tank gas space pressure on flow behaviors, also in direct comparison to conditions tested experimentally. User option-61 in the RELAP5-3D input deck, which changes the heat transfer coefficient correlations used for calculating the vapor generation, is also investigated where it is found that by enabling the option, the overall duration of oscillations is increased and matches that from the experiment better. The RELAP5 model is further benchmarked with a header inlet- throttling case where it is observed that the prediction from the model fails to capture some major features observed in the experiment. By using a modified loss coefficient curve for the valve, the accuracy of the prediction is improved where most of the major features observed in the experiment are predicted by the model. Lastly, the model is benchmarked with an inventory depletion scenario where it is observed that despite the modeling limitation of RELAP5, the prediction shows good agreement with the experimental data where major trends and features are captured by the model. Future work will see continued development of the current RELAP5-3D input deck of the NSTF to both improve the accuracy of the model’s predictive capability and continuing serving the experimental program. The mutually beneficial relationship between analysis and experimental efforts has become integral to the parent NSTF program, and the greater objective to fully understand and accurately predict the heat removal performance of a full scale RCCS concept.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Conformal conserved currents in embedding space

We study conformal conserved currents in arbitrary irreducible representations of the Lorentz group using the embedding space formalism. With the help of the operator product expansion, we first show that conservation conditions can be fully investigated by considering only two- and three-point correlation functions. We then find an explicitly conformally-covariant differential operator in embedding space that implements conservation based on the standard position space operator product expansion differential operator ∂μ, although the latter does not uplift to embedding space covariantly. The differential operator in embedding space that imposes conservation is the same differential operator $D_{ijA}$ used in the operator product expansion in embedding space. We provide several examples including conserved currents in irreducible representations that are not symmetric and traceless. With an eye on four-point conformal bootstrap equations for four conserved vector currents $\langle JJJJ\rangle$ and four energy-momentum tensors $\langle TTTT\rangle$, we mostly focus on conservation conditions for $\langle JJ\mathcal{O}\rangle$ and $\langle TT\mathcal{O}\rangle$. Finally, we reproduce and extend the consequences of conformal Ward identities at coincident points by determining three-point coefficients in terms of charges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Investigating the interactions between wakes and floating wind turbines using FAST.Farm

As floating offshore wind progresses to commercial maturity, wake and array effects across a farm of floating offshore wind turbines (FOWTs) will become increasingly important. While wakes of land-based and bottom-fixed offshore wind turbines have been extensively studied, only recently has this topic become relevant for floating turbines. This work presents an investigation of the mutual interaction between the motions of floating wind turbines and wakes using FAST.Farm. While FAST.Farm has been extensively validated across a wide range of conditions, it has never been validated for FOWT applications. Hence, in the first part of this work, we validate FAST.Farm by comparing simulations of a single FOWT against high-fidelity results from large-eddy simulations available in the literature. The validation is based on wake meandering, mean wake deflection, and velocity deficit at different downstream locations. This validation showed that the original axisymmetric (polar) wake model of FAST.Farm overpredicts the vertical wake deflection induced by shaft tilt and floater pitch, while the new curled wake model is capable of properly capturing the vertical wake deflection. In the second part, we use FAST.Farm to analyze a small three-unit array of FOWTs with a spacing of 7 diameters across a wide range of environmental conditions. The same National Renewable Energy Laboratory 5 MW reference wind turbine atop the OC4-DeepCwind semisubmersible is adopted for the three FOWTs and for the validation against high-fidelity simulations. To assess the effect of the floating substructure, we compare the power production, tower-base moments, and blade-root moments obtained for the floating turbines with the results obtained in a fixed-bottom configuration. The main differences introduced by the floating substructure are the motions induced by the waves, the change in the natural frequencies of the tower caused by differences in the boundary condition at its base, and the larger vertical deflection of the wake deficit due to the mean pitch of the platform. The impact of these differences, as well as other minor effects, are analyzed in detail.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗