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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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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Coupled CFD and chemical-kinetics simulations of cellulosic-biomass enzymatic hydrolysis: Mathematical-model development and validation

Computational simulations of cellulosic-biomass enzymatic hydrolysis using a computational-fluid-dynamics (CFD) model coupled to a chemical-kinetics model are presented in this work. A time-step sub-cycling strategy was used to circumvent large disparities in time scales with respect to transport physics and chemical kinetics. The unknown reaction and transport parameters in the mathematical model were first fit to two canonical experiments: a well-mixed case that was limited by reaction kinetics and a settled-solids case that was limited by transport. Here, the model was then validated against a benchtop experiment for an intermediate-mixing scenario, for which simulation results were in reasonable agreement with experimentally measured cellulose conversions. Settling of cellulose particles and diffusion of enzymes determine overall conversion rates for lower mixing rates, while reaction rates dominate conversion at higher mixing rates for which greater homogenization of substrates is achieved.

09 BIOMASS FUELS↗
DOE OSTI2018

Hydrogen shift isomerizations in the kinetics of the second oxidation mechanism of alkane combustion. Reactions of the hydroperoxypentylperoxy OOQOOH radical

Hydroperoxyalkylperoxy species are important intermediates that are generated during the autoignition of transport fuels. In combustion, the fate of hydroperoxyalkylperoxy is important for the performance of advanced combustion engines, especially for autoignition. A key fate of the hydroperoxyalkylperoxy is a 1,5 H-shift, for which kinetics data are experimentally unavailable. In the present work, we study 1-hydroperoxypentan-3-yl)dioxidanyl (CH 3 CH 2 CH(OO)CH 2 CH 2 OOH) as a model compound to clarify the kinetics of 1,5 H-shift of hydroperoxyalkylperoxy species, in particular α-H isomerization and alternative competitive pathways. With a combination of electronic structure calculations, we determine previously missing thermochemical data, and with multipath variational transition state theory (MP-VTST), a multidimensional tunneling (MT) approximation, multiple-structure anharmonicity, and torsional potential anharmonicity, we obtained much more accurate rate constants than the ones that can computed by conventional single-structure harmonic transition state theory (TST) and than the empirically estimated rate constants that are currently used in combustion modeling. The roles of various factors in determining the rates are elucidated. The pressure-dependent rate constants for these competitive reactions are computed using system-specific quantum RRK theory. The calculated temperature range is 298–1500 K, and the pressure range is 0.01–100 atm. The accurate thermodynamic and kinetics data determined in this work are indispensable in the detailed understanding and prediction of ignition properties of hydrocarbons and alternative fuels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

An experimental and detailed kinetic modeling study of the pyrolysis and oxidation of allene and propyne over a wide range of conditions

Allene and propyne are important intermediates in the pyrolysis and oxidation of higher hydrocarbon fuels, and they are also a major source of propargyl radical formation, which can recombine into different C 6 H 6 isomers and finally produce soot. In a prior work (Panigrahy et al., “A comprehensive experimental and improved kinetic modeling study on the pyrolysis and oxidation of propyne”, Proc. Combust. Inst 38 (2021)), the pyrolysis, ignition , and laminar flame speed of propyne were investigated. To understand the kinetic features of initial fuel breakdown and oxidation of the two C 3 H 4 isomers, new measurements for allene pyrolysis and oxidation are conducted in the present paper at the same operating conditions as those studied previously for propyne. Ignition delay times of allene are measured using a high-pressure shock tube and a heated twin-opposed piston rapid compression machine in the temperature range 690– 1450 K at equivalence ratios of 0.5, 1.0 and 2.0 in ‘air’, and at pressures of 10 and 30 bar. Pyrolysis species measurements of allene and propyne are also performed using a gas chromatography integrated singlepulse shock tube in the temperature range 1000–1700 K at pressure of 2 and 5 bar. Furthermore, laminar flame speeds of allene are measured at elevated gas temperatures of 373 K at pressures of 1 and 2 bar for a wide range of equivalence ratios from 0.6 to 1.5. A newly updated kinetic mechanism developed for this study is the first model that can well reproduce all of the experimental results for both allene and propyne. It is observed that in the pyrolysis process, allene dissociates faster than propyne. Both isomers exhibit similar ignition delay times at high temperatures (>1000 K), while, at intermediate temperatures (770–1000 K) propyne is the faster to ignite, and at lower temperatures (< 770 K) allene becomes more reactive. Furthermore, laminar flame speeds for propyne are found to be slightly faster than those for allene under the conditions studied in this work

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

An experimental and kinetic modeling study of the pyrolysis of isoprene, a significant biogenic hydrocarbon in naturally occurring vegetation fires

Isoprene dominates the carbon flux emitted by vegetation and constitutes 40% of non-methane biogenic emissions worldwide. Despite pyrolysis experiments at temperatures above 1000 K showing a link between isoprene combustion and aromatic species formation, comprehensive mechanistic research on isoprene is scarce in the literature. Here, in this work, we carry out an experimental and theoretical study to build, for the first time, a chemical kinetic model describing isoprene pyrolysis. The formation of polycyclic aromatic hydrocarbon (PAH) precursor species, often observed in vegetation fire plumes, is partially explained by isoprene pyrolysis experiments and theoretical modeling. Molecular dynamics (MD) simulations unveil reaction pathways from allylic isoprenyl radicals to allene and cyclopentadiene (CPD) intermediates, two relevant species detected in the experiments. Rate constants for these identified pathways are calculated using variational transition state theory to update the kinetic model, which is validated against single-pulse shock tube (SPST), and jet-stirred reactor (JSR) experimental data in the temperature range of 850–1690 K. The kinetic model presents satisfactory agreement with the SPST experimental data, and a reaction pathway analysis shows that association of propargyl radicals results in benzene formation. The JSR pathway analysis also identifies the prominent reactions for CPD, benzene, styrene, and toluene formation. Our model does not reproduce the CPD experimental profiles, indicating that additional studies are necessary. Overall, our findings advance the understanding of isoprene pyrolysis and its related atmospheric pollutants in naturally occurring vegetation fires where smoldering and oxygen-deficient combustion processes are present.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A wide range experimental study and further development of a kinetic model describing propane oxidation

This work presents an experimental and kinetic modeling study of propane oxidation. Ignition delay times of propane were measured in a high-pressure shock tube and in rapid compression machines in the temperature range 689 - 1700 K at equivalence ratios of 0.5, 1.0 and 2.0 in 'air', for a wide range of pressures from 20 to 90 bar. CO and H 2 O mole fraction profiles for propane oxidation were measured in a shock tube behind reflected shock waves in the temperature range 1370-1840 K at equivalence ratios of 0.5, 1.0 and 2.0 and at a pressure of approximately 1.3 atm. Moreover, propane oxidation was studied using a jet-stirred reactor coupled to a synchrotron vacuum ultraviolet photoionization mass spectrometer at low temperatures in the range 565 - 690 K and at a pressure of 1 atm. Further, this wide range of experimental datasets for propane oxidation was used to reoptimize and update our previous kinetic mechanisms, AramcoMech3.0 and NUIGMech1.1. In the current mechanism, NUIGMech1.3, the thermo-chemical parameters of all species relevant to low-temperature propane oxidation chemistry, including propyl-peroxyl, hydroperoxyl-propyl, hydroperoxyl-propyl-peroxyl, and carbonyl-hydroperoxide radicals, are updated based on newly calculated values at the CCSD(T)-F12/TZ-F12//B2PLYPD3/TZ///B2PLYP-D3/TZ level of theory. The improvements made in the thermochemical values and in the kinetic parameters for the low-temperature propane oxidation reactions in NUIGMech1.3 result in better model agreement with the new IDTs and speciation data, including carbon monoxide, formaldehyde, propene, acetaldehyde and various minor products such as ethylene, acetic acid, acrolein as well as various hydroperoxide and cyclic ether species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Kinetic Monte Carlo simulations of structural evolution during anneal of additively manufactured materials

Our experiments indicated that upon a post-processing anneal, an additively manufactured 316L stainless steel exhibits cubic grains rather than the conventional equiaxed grains. In this work, we have used kinetic Monte Carlo simulations to explore the origin of these cubic grains. First, we implemented a new kinetic Monte Carlo model in parallel code SPPARKS to simulate grain growth and recrystallization under a residual energy distribution. Our model incorporates physical properties and real-time, as opposed to generic properties and relative time. We further validated that our SPPARKS simulations reproduced the expected kinetic behavior of single-grain evolution. We then used the validated approach to simulate the anneal of an additively manufactured material under the same conditions used in our experiments. We found that the cubic grains can origin from a periodically varying residual energy that may be present in additively manufactured materials.

36 MATERIALS SCIENCE↗
DOE OSTI2018

The F-t-Pj-RG method: An adjacent-rolling-windows based steady-state detection technique for application to kinetic Monte Carlo simulations

A window-based steady-state detection algorithm has been developed for application to kinetic Monte Carlo simulation data. The algorithm, termed F-t-Pj-RG sequentially applies an F-test, a t-test, and a projection test on adjacent windows of the data while rolling (or shifting) and growing the windows when any of the tests fail. In aggregate, the algorithm is able to (a) automatically reject the warm-up period as not being at steady-state, as well as (b) determine an appropriate window size for converged statistics when sampling the data, which is necessary for detection of steady-state, and (c) detect steady-state within a particular tolerance. The last step, the projection test, is actually an oscillating-slope projection test, and is performed on j sequential data windows (i.e., more than two adjacent windows). It requires more than simply being within the user defined tolerance: the oscillating-slope projection test includes a condition that the slope must oscillate around zero when 2, which is an additional indication of steady-state. When all three tests are passed, the F-t-Pj test is passed, indicating that the prerequisites of steady-state detection have been met and also that conditions consistent with the definition of steady-state have been realized. This algorithm is applied to a variety of data sets that correspond to the diverse type of data trends that can be produced by kinetic Monte Carlo simulations. The algorithm is shown to be robust in its ability to handle differing functional forms, and is able to detect steady-state with low computational cost. Finally, the low computational cost of this method and its robustness towards varied data trends make it suitable for on-the-fly use in kinetic Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Biomass char gasification kinetic rates compared to data, including ash effects

This investigation provides both experimental and theoretical analyses of biomass char gasification kinetics over 1150–1350 °C in the environment of CO 2 , H 2 O and combinations of these reactants. The experimental data include continuous measurements of particle mass, external and internal temperatures, shape, and size with periodic but not continuous measurements of char porosity, pore size distribution, and pore surface area. The model describes heterogeneous char gasification for poplar wood, corn stover and switchgrass in different shapes and industrially relevant sizes (12.5 mm and smaller). Nonlinear least-squares regression produces optimized power-law model parameters for global kinetics that describe biomass char gasification with respect to both CO 2 and H 2 O separately and in combination. A single set of kinetic parameters describes reaction rates for all three fuels. Model simulations agree with measured data at all stages of char conversion even though the observed mass loss rates change significantly with conversion. In conclusion, the change in rate with conversion depends strongly on ash content, and this investigation provides a simple and theoretically based reaction rate expression that includes the effect of inert ash occupying an increasing portion of the reactive surface with increased conversion.

09 BIOMASS FUELS↗
DOE OSTI2021

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Dual carbonate clumped isotopes (Δ 47 -Δ 48 ) constrains kinetic effects and timescales in peridotite-associated springs at the Cedars, Northern California

The Cedars is an area in Northern California with a chain of highly alkaline springs resulting from CO 2 -charged meteorological water interacting with a peridotite body. Serpentinization resulting from this interaction at depth leads to the sequestration of various carbonate minerals into veins accompanied by a release of Ca 2+ and OH – enriched water to the surface, creating an environment which promotes rapid precipitation of CaCO 3 at surface springs. This environment enables us to apply the recently developed Δ 47 -Δ 48 dual clumped isotope analysis to probe kinetic isotope effects (KIEs) and timescales of CO 2 transformation in a region with the potential for geological CO 2 sequestration. Here, we analyzed CaCO 3 recovered from various localities and identified significant kinetic fractionations associated with CO 2 absorption in a majority of samples, characterized by enrichment in Δ 47 values and depletion in Δ 48 values relative to equilibrium. Surface floes exhibited the largest KIEs (ΔΔ 47 : 0.163‰, ΔΔ 48 : -0.761‰). Surface floe samples begin to precipitate out of solution within the first hour of CO 2 absorption, and the dissolved inorganic carbon (DIC) pool requires a residence time of >100 h to achieve isotopic equilibria. The Δ 48 /Δ 47 slope of samples from the Cedars (-3.223 ± 0.519) is within the range of published theoretical values designed to constrain CO 2 hydrolysis-related kinetic fractionation (-1.724 to -8.330). The Δ 47 /δ 18 O slope (-0.009 ± 0.001) and Δ 47 /δ 13 C slope (-0.009 ± 0.001) are roughly consistent with literature values reported from a peridotite in Oman of -0.006 ± 0.002 and -0.005 ± 0.002, respectively. The consistency of slopes in the multi-isotope space suggests the Δ 47 -Δ 48 dual carbonate clumped isotope framework can be applied to study CO 2 -absorption processes in applied systems, including sites of interest for geological sequestration.

58 GEOSCIENCES↗
DOE OSTI2021

Temperature-responsive smart tracers for field-measurement of inter-well thermal evolution: Heterogeneous kinetics and field demonstration

Temperature-responsive smart tracers enable advanced warning of a “premature thermal breakthrough” and may therefore improve reservoir management and reduce financial risk. A successful calculation of inter-well fluid temperatures requires that temperature-dependent kinetics are known, which typically result from homogeneous batch reactor experiments. However, recent meso-scale field experiments at the Altona Field Laboratory involving fluid flow in a discretely-fractured reservoir suggest that silica-fluid interfaces may accelerate hydrolysis kinetics. Here, the Arrhenius parameters of phenyl acetate hydrolysis are investigated under heterogeneous reaction conditions in packed-bed column experiments. The breakthrough curve of the reaction product is compared to an inert reference tracer (carbon-cored nanoparticles). Temperatures experienced during field testing ranging from 10 to 40 °C were studied using a phosphate buffer solution to maintain a near-neutral pH, as found in the reservoir. The empirically-determined pre-exponential factor and activation energy values are subsequently used in a first-order kinetic model to improve calculations of effective reservoir temperatures for these meso-scale field tests. Here, the results suggest that hydrolysis reactions can directly monitor inter-well reservoir temperatures, but only if the influence of solid-fluid interactions are carefully accounted for.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Kinetic analysis of Cas12a and Cas13a RNA-Guided nucleases for development of improved CRISPR-Based diagnostics

Bacterial CRISPR systems provide acquired immunity against invading nucleic acids by activating RNA-programmable RNases and DNases. Cas13a and Cas12a enzymes bound to CRISPR RNA (crRNA) recognize specific nucleic acid targets, initiating cleavage of the targets as well as non-target (trans) nucleic acids. Here, we examine the kinetics of single-turnover target and multi-turnover trans-nuclease activities of both enzymes. High-turnover, non-specific Cas13a trans-RNase activity is coupled to rapid binding of target RNA. By contrast, low-turnover Cas12a trans-nuclease activity is coupled to relatively slow cleavage of target DNA, selective for DNA over RNA, indifferent to base identity, and preferential for single-stranded substrates. Combining multiple crRNA increases detection sensitivity of targets, an approach we use to quantify pathogen DNA in samples from patients suspected of Buruli ulcer disease. Results reveal that these enzymes are kinetically adapted to play distinct roles in bacterial adaptive immunity and show how kinetic analysis can be applied to CRISPR-based diagnostics.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Metastable formation and disordering kinetics of body-centered orthorhombic CrNi 2 laths in a Cr-Ni binary alloy

Chromium (Cr) alloys combine low density with high-temperature strength but suffer from brittleness and rapid softening. Body-centered orthorhombic (BCO) CrNi 2 laths have been shown to improve Cr-alloy high-temperature strength retention, yet their thermal stability and transformation behavior remain unclear. CrNi 2 conventionally forms through long-range ordering from a face-centered cubic (FCC) phase. Using multiscale microscopy and neutron diffraction, we show that CrNi 2 instead nucleates from a body-centered cubic (BCC) matrix, in a binary Cr 85 Ni 15 alloy. Despite aging above the equilibrium ordering temperature, CrNi 2 persists for ∼220 h at 760 °C before fully disordering, indicating sluggish transformation kinetics. The formation and decomposition follow differing transformation pathways (BCC → CrNi 2 → FCC), revealing kinetic asymmetry not captured by equilibrium Cr-Ni phase diagrams. In conclusion, these findings redefine the transformation behavior of CrNi 2 , establish its metastable kinetic window, and suggest alloying strategies to stabilize CrNi 2 for precipitation strengthening of high-temperature Cr-alloys.

CrNi2 transformation kinetics↗
DOE OSTI2020

Oxide-catalyzed self- and cross-condensation of cycloketones. Kinetically relevant steps that determine product distribution

Metal oxides with acid-base properties can be used to catalyze aldol condensation and potentially obtain valuable chemicals from biomass-derived oxygenates. Understanding the reaction mechanisms could enable the development of effective catalysts with controllable selectivity. In this work, we investigate the reaction parameters that affect the kinetics and product distribution of self- and cross-aldol condensation of cyclopentanone (CPO) and cyclohexanone (CHO) over CeO 2 and ZrO 2 catalysts by combining detailed analysis of experiments and DFT calculations. It is well-known that either the deprotonation of an α-C–H that generates an enolate or the C–C coupling that produces the dimers can be rate-limiting step. Indeed, the detailed kinetics analysis shows that the observed data can be fitted by unimolecular or bimolecular Langmuir-Hinshelwood models. Specifically, on the ZrO 2 catalyst, the unimolecular α-C–H activation is the rate limiting step for the CPO self-condensation, while the bimolecular C–C coupling limits the CHO self-condensation. By contrast, on CeO 2 , the bimolecular C–C coupling step seems to be rate-limiting for both CPO and CHO self-condensation reactions. The adsorption parameters derived from kinetics fitting indicate that when the two reactants are co-fed, the surface is preferentially covered by CHO. So, the condensation rate of [CPO]-activated products ([CPO]CPO + [CPO]CHO) decreases in the presence of CHO, due to the competitive adsorption. However, despite a higher surface coverage, CHO is not an effective electrophile because it imposes stronger steric constraints to the formation of the C–C bond than CPO. Therefore, for a given enolate, the product distribution shows that [CPO]CPO > [CPO]CHO and, similarly [CHO]CPO > [CHO]CHO. Likewise, the yields of [CPO]- and [CHO]-activated products in mixed CPO/CHO feeds are similar because the higher surface coverage and stability of the [CHO] enolate is counterbalanced by the inhibition of C–C coupling by steric constraints when CHO is involved. In summary, the overall rank of products observed experimentally can be explained in terms of a combination of the following effects: relative surface coverage of the reactants, steric constraints for the C–C coupling, stability of the enolate, and effectiveness of the electrophile to accept an electron.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Experimental and computational kinetics study of the liquid-phase hydrogenation of C=C and C=O bonds

Solvent effects on adsorption equilibrium and reaction kinetics are evaluated for hydrogenation reactions catalyzed by Pd/alumina in a series of different solvents. Three reactants – cyclohexene, benzene and benzaldehyde – and three solvents – n-heptane (HEP), methylcyclohexane (MCHA), decalin (DL) – have been investigated. Kinetic analysis of hydrogenation of cyclohexene reveals that hydrogen adsorbs on different sites from those where cyclohexene and the solvents adsorb; however, the presence of hydrogen on these separate sites affects the heats of adsorption of the hydrocarbons. When the solvent is a weakly interacting linear alkane (HEP), the rate determining step of the reaction is the first hydrogenation of adsorbed cyclohexene. Furthermore, this conclusion is supported by DFT calculations that show a higher enthalpy barrier for the first hydrogenation than for the second, while statistical thermodynamics analysis validates the physical significance of the entropy of adsorption parameters derived from the kinetic fitting of experimental data. By contrast, with solvents such as MCHA and DL, which interact more strongly with the metal surface and compete for active sites with the reactant and the surface intermediate, the rate limiting step seems to shift to the second hydrogenation step.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Analysis and prediction of reaction kinetics using the degree of rate control

“Degree of rate control” (DRC) analysis provides a quantitative approach for analysing the kinetics of multi-step reaction mechanisms that has been widely applied to both heterogeneous and homogeneous catalysis research, as well as electrocatalysis. The DRC of any given transition state or intermediate is defined as a partial derivative such that it approximately equals the fractional increase in net rate to the product of interest per differential decrease in its standard-state free energy for that species (÷RT), holding constant the standard-state free energies of all other transition states and intermediates. Even very complex mechanisms usually have only a few species with non-zero DRCs and are thus the species whose interactions with the catalyst most strongly affect the net rate. These key DRC values thus offer a simple and intuitive route to optimize catalyst materials, especially with the assistance of computational methods like density functional theory (DFT). These high-DRC species are also the species whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. In simple cases with a single “rate-determining step”, the DRC for its transition state (TS) is + 1. Catalyst-bound intermediates, on the other hand, often have negative DRCs equal to a small integer times their fractional occupancy of catalyst sites. The apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all the species (intermediates, transition states and products) in the reaction mechanism, each weighted by its DRC (+RT). It has been shown that the apparent transfer coefficient in electrocatalysis, an inverted form of the Tafel slope, is a weighted average of the number of electrons transferred to generate each intermediate or product species in the mechanism, weighted again by the DRC. Quantitative analysis of kinetic isotope effects (KIEs, or the ratio of net rates for different reactant isotopes) in complex mechanisms has shown that the logarithm of the KIE equals the weighted average over all species in the mechanism of the difference between the two isotopes in their standard-state free energies (÷RT), again weighted by the DRC. The reaction orders with respect to fluid-phase concentrations of reactants, products and intermediates have also been proven to be directly related to DRCs. Thus, there are numerous experimental observables which equate to short linear combinations of DRCs, so that combinations of experimental measurements might provide access to DRC values. Since its invention for transition states in 1994 and its generalization to include intermediates in 2009, the DRC has thus far mainly been calculated for microkinetic models based either entirely on DFT or on DFT with the key energies (i.e., those for high-DRC species) being fine-tuned to match experiments. The relationships summarized in this work provide new opportunities for using experiments earlier in the development and optimization of microkinetic models that require input from computational catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Numerical schemes for 3-wave kinetic equations: A complete treatment of the collision operator

In our previous work Walton and Tran (2023), numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dynamics of the equation given the multiple blow-up time phenomenon. In this second work in the series, we propose numerical treatments for the complete 3-wave kinetic equations, in which the complete, much more complicated collision operators are fully considered based on a novel conservative form of the equation. Here we then derive an implicit finite volume scheme to solve the equation. The new discretization uses an adaptive time-stepping method which allows for the simulations to be carried to very long times. Our computed solutions are compared with previously derived long-time asymptotic estimates for the decay rate of total energy of time-dependent solutions of 3-wave kinetic equations and found to be in excellent agreement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A conservative discontinuous Galerkin algorithm for particle kinetics on smooth manifolds

A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using both canonical and non-canonical Hamiltonian formulations. Our schemes apply to both formulations, but the canonical formulation results in a particularly efficient scheme that also conserves particle density and energy exactly. The collisionless update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for relaxation to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation of the manifold is incorporated by modifying the Hamiltonian while ensuring a canonical formulation. Several test problems, including a kinetic version of the classical Sod shock problem, Kelvin-Helmholtz instability on the surfaces of a sphere and a hyperboloid, with and without rotations, are presented. A prospectus for further development of this approach to simulation of kinetic theory in general relativity is presented.

Discontinuous Galerkin↗