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Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

ESG

Updates and Modernization of NASA’s Chemical Equilibrium with Applications (CEA) Code

NASA’s Chemical Equilibrium with Applications (CEA) code is a foundational tool for propulsion system analysis. It provides equilibrium chemistry, rocket performance, shock, and detonation calculations used across NASA and the broader aerospace community. NASA Engineering and Safety Center (NESC) Activity TI-22-01730 modernized the legacy CEA2 Fortran code into CEA v3, a Fortran 2008, object-oriented software package with expanded interface support, updated thermochemical data, improved maintainability, and substantially improved workflow integration. The modernized code preserves backward compatibility with legacy CEA input workflows while enabling direct use from modern analysis environments, including Python, C, MATLAB, and automated design studies.

Mark K Leader

Updates and Modernization of the Chemical Equilibrium with Applications (CEA) Code

NASA’s Chemical Equilibrium with Applications (CEA) code is a foundational tool for propulsion system analysis. It provides equilibrium chemistry, rocket performance, shock, and detonation calculations used across NASA and the broader aerospace community. NASA Engineering and Safety Center (NESC) Activity TI-22-01730 modernized the legacy CEA2 Fortran code into CEA v3, a Fortran 2008, object-oriented software package with expanded interface support, updated thermochemical data, improved maintainability, and substantially improved workflow integration. The modernized code preserves backward compatibility with legacy CEA input workflows while enabling direct use from modern analysis environments, including Python, C, MATLAB, and automated design studies.

Combustion

Equilibrium and non-equilibrium effects in high pressure phase transformations of carbon

The behavior of carbon in the range 1–100 GPa and 1–10 kK is central to problems in planetary interiors, inertial confinement fusion targets, and high-pressure synthesis of carbon-based materials, but experiments in this regime are difficult and often provide only indirect constraints on phase behavior. As a result, phase boundary loci, structure, and limits of metastability at high pressure remain uncertain. In this work, machine-learning enhanced atomistic simulations are used to address this knowledge gap. We determine the melt line up to 100 GPa, the graphite-diamond phase boundary up to the melt line, and analyze structure of the coexisting phases. We show that the coexisting liquid evolves smoothly with pressure without evidence for a first-order liquid–liquid transition. Orientation-resolved graphite melting simulations indicate that basal-plane interfaces develop a dewetting layer and undergo layer-by-layer melting, producing kinetic hysteresis and an apparent orientation dependence of the melt line. Non-equilibrium quenches from the melt are used to construct a kinetically limiting graphite–diamond phase boundary for rapid quenches from above the melt line, and show that graphite is metastable at pressures of up to ≈ 25 GPa. These results provide bounds on equilibrium and metastable behavior in carbon relevant for interpreting high-pressure experiments and for designing synthesis pathways to specific carbon microstructures.

Lyu, Yanjun [Department of Materials Science and E

Pressure Safety Training (Rev. 8)

This is the workbook for the Pressure Safety Training Course. It is intended as a reference manual and guide for all work with pressurized liquids or gases. This workbook contains basic references to make work with pressure safer. It is intended to supplement classroom instruction, rather than serve as a definitive text on pressure. Earlier versions of the manual were intended specifically for training at Lawrence Livermore National Laboratory. This revision is a generic version intended for training at all DOE facilities. The information in the Standards chapter is from the LLNL Health and Safety Manual. It is included here as a convenient reference and guide for developing similar standards at your own facility.

42 ENGINEERING

Vidyut3d: A Gpu Accelerated Fluid Solver for Non-Equilibrium Plasmas on Adaptive Grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure twin electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate approximately 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

Sitaraman, Hariswaran

Thermochemically-Closed Sonic-Flow Inversion for Enthalpy and Temperature in Multispecies Arc-Jet Flows

A thermochemically-closed sonic-flow inversion framework (TSIF) is developed to infer bulk enthalpy and total temperature upstream of a choked nozzle in arc-jet flows. The formulation recasts a pressure-rise total enthalpy quantification technique as an inverse problem in characteristic-velocity c * space using measured mass flow rate, upstream total pressure, gas composition, and nozzle throat geometry as inputs. Unlike calorimetric energy-balance approaches or optical diagnostics, the method relies primarily on routinely measured facility quantities combined with explicit thermochemical closure. Thermochemical states are obtained using NASA’s open-source Chemical Equilibrium with Applications (CEA) code, enabling construction of a chemistry-consistent relation between characteristic velocity, total enthalpy, and total temperature under equilibrium or frozen assumptions. A discharge coefficient is self-calibrated using cold-flow (arc-off) operation data and applied to hot-flow (arc-on) measurements, enabling upstream losses to be accounted for without empirical correlations. The framework is applied to air, N 2 , and CO 2 –N 2 arc-jet flows and demonstrates expected trends for the inferred thermochemical states as function of arc power, specific energy input, mass-flow, heater configuration, and test gas. In the air limit, under equilibrium assumptions, the method recovers the classical high-enthalpy asymptotic correlation of Winovich with a mean residual of 4.4%, demonstrating compatibility with established sonic-flow scaling, while extending applicability to arbitrary multi-species mixtures and non-equilibrium chemistry. The framework provides a mixture-flexible methodology for determining bulk thermochemical states in modern arc-jet environments using routine facility pressure, mass-flow, gas-composition, and nozzle-geometry information together with a cold-flow calibration.

inviscid theory

The impact of metastability on the high-pressure behavior of cerium

The structures adopted by solids under pressure are often assumed to reflect thermodynamic equilibrium, yet in many materials phase selection is strongly influenced by kinetic pathways and microstructural inheritance. Elemental cerium (Ce) exemplifies this challenge, with decades of conflicting reports describing different high-pressure crystal structures emerging under nominally identical conditions. Here we use neutron diffraction from large ( ~ 60 mm 3 ) sample volumes to follow the structural evolution in ultra-high-purity Ce during controlled pressure-temperature cycling between 85 and 295 K and up to 8 GPa. We find that the crystal structure formed at high pressure depends on the compression pathway: slow compression ( ~ 0.25 GPa hr −1 ) at room temperature favors an orthorhombic phase (α'), whereas slow ( ~ 0.25 GPa hr −1 ) and also moderately faster ( ~ 0.5 GPa hr −1 ) compression at low temperature stabilizes a pure monoclinic phase (α"). The low-temperature phase persists metastably over a wide temperature range but transforms irreversibly upon heating above ~ 280 K, or modest pressure cycling. Remarkably, the lower-pressure γ phase remains trapped far beyond the expected stability field, persisting to the highest pressures studied. These observations show that phase selection in Ce is governed by kinetics and microstructural memory rather than equilibrium thermodynamics or sample morphology alone, establishing path dependence as a defining feature of its high-pressure behavior.

Ridley, Christopher J. [Oak Ridge National Laborat

The Effect of Temperature and Pressure on the Distribution of Iron Group Elements Between Metal and Olivine Phases in the Process of Differentiation of Protoplanetary Material

The distribution patterns of Ni, Co, Mn, and Cr were studied in olivines of various origins: from meteorites (chondrites, achondrites, pallasites), which are likely analogs of the protoplanetary material, to peridotite inclusions in kimberlite pipes, which are analogs of mantle material. According to X-ray microanalysis data, each genetic group of olivines is characterized by a specific concentration of these elements. Nickel is concentrated (up to 0.34 percent) in peridotite olivines, while manganese is concentrated in meteoritic olivines. The maximum chromium content (0.2 percent) was found in ureilites, which were formed under reducing conditions. Experiments at pressures of 20 to 70 kbar and temperatures of 1100 to 2000°C have shown that in a mixture of olivine and Ni metal or NiO nickel enters the silicate phase (up to 4 percent), displacing Fe into the metallic phase. Equilibrium temperatures were estimated from the Fe, Ni distribution coefficients between the metal and olivine: 1500 K for pallasites, 1600 K for olivine-bronzite H6 chondrites, 1200 K for olivine-hypersthene L6, 900 K for LL6, and 1900 K for ureilites (at P = 1 atm). The equilibrium conditions of peridotites are close to T = 1800 K and P over 100 kbar. The distribution patterns of the transition elements are explained on the basis of physical-chemical properties. It is concluded that there is a sharp difference between the conditions of differentiation of the protoplanetary material at the time meteorites were formed and the conditions of differentiation of the planets into concentric layers.

A P Vinogradov

Turbo-Design: Open-Source Radial Equilibrium Turbomachinery Solver: Part I - Turbines

Advances in 3D Geometrical Designs and Cooling have played a significant role in improving the efficiency of turbomachinery. However, these advancements must be effectively translated back to the modeler. Machine learning can facilitate this transition. Specifically, machine learning–based loss models can bridge the gap between 3D and 1D designs, enabling modelers not only to predict velocity triangles but also to extract additional geometric features. Currently, the design tools used at NASA have not been updated to support such integration—until now. TurboDesign is an open-source, Python-based framework that replaces TD2 (LEW-11029-1) and AXOD2 (LEW-16323-1), both of which are radial equilibrium solvers for axial turbines. The goal of this update is to enable the integration of machine learning loss models into radial equilibrium equations. Additionally, TurboDesign is designed to support radial machines. This paper presents the governing equations, the assumptions underlying the code, the integration of legacy loss models, an example of machine learning model integration, and a validation comparison with CFD. All code, tutorials, and documentation are available at: https://www.github.com/nasa/turbo-design

Radial Equilibrium

Optimization of a 10–Step Reduced CH₄/O₂ Combustion Mechanism for RDRE Applications

A 10-step, 9-species reduced mechanism for methane/oxygen combustion is evaluated and optimized for use in rotating detonation rocket engine (RDRE) simulations at an operating pressure of 10 bar. The mechanism is assessed against GRI-Mech 3.0 for ignition delay times, adiabatic equilibrium temperature and species, Chapman-Jouguet (CJ) detonation parameters, and laminar flame speed. A sequential Nelder–Mead optimization procedure is applied to the rate constants of reactions R1, R4, and R5, targeting ignition delay agreement over the equivalence ratio range φ = 1.0–1.4 and temperature range T = 1400–2000 K. The optimized mechanism achieves ignition delay agreement within 28% of GRI-Mech 3.0 for the temperature range relevant to RDRE operation (τ ≥ 5 μs). Adiabatic equilibrium temperatures and CJ detonation parameters are reproduced within 0.15% of GRI-Mech 3.0 values, confirming thermodynamic consistency of the mechanism. Laminar flame speed predictions deviate significantly from GRI-Mech 3.0, which is attributed to the absence of HO₂ chemistry in the reduced mechanism; this limitation does not affect RDRE simulation fidelity since laminar flame propagation is of secondary importance in RDREs.

Computational Fluid Dynamics

Two-dimensional non-equilibrium melting of charged colloids

Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.

critical phenomena

Laser-heated diamond anvil cell synthesis and recovery of metastable MnSb 2 and YbZn 2 for post-synthesis transport studies

The creation and exploration of new materials under extreme pressure–temperature conditions has become increasingly reliant on laser-heated diamond anvil cell (LHDAC) techniques, which provide direct access to previously unexplored regions of multinary phase diagrams. Whereas numerous high-pressure phases have been identified in situ, systematic recovery and post-synthesis physical property characterization of these materials remain significant challenges. In this work, we describe the setup and implementation of an LHDAC-based synthesis and recovery workflow and demonstrate its application to metastable MnSb 2 and YbZn 2 phases. Synchrotron x-ray diffraction and spatial mapping confirm dominant formation of the targeted phases, whereas laboratory-based refinement quantifies phase fractions despite intrinsic microstrain and minor secondary phases. High-pressure transport measurements on recovered samples reveal pressure-tunable electronic instabilities in both systems. In MnSb 2 , pressure suppresses two high-temperature magnetic ordering anomalies, observed in transport, by ∼5 GPa and, for higher pressures, induces a new low-temperature feature that increases with further pressure increase. In hexagonal high-pressure YbZn 2 , an electronic reconstruction emerges at ∼11 GPa, characterized by semiconducting-like behavior from ∼30 to 300 K and a broad low-temperature coherence crossover near 30 K. Our results establish LHDAC synthesis not only as a structural discovery tool but also as an experimental platform for investigating correlated quantum states stabilized far from equilibrium thermodynamic conditions.

Huyan, S. [Iowa State University, Ames, IA (United

Asymmetric pathways for lithium extraction and recovery based on the two-phase equilibrium of layered oxides

Electrochemical intercalation offers a promising platform for Li + extraction. However, only limited types of electrode materials have been investigated. The challenge to broaden and tailor materials for electrochemical intercalation-based Li + extraction lies in the lack of understanding of material’s response upon co-intercalation of multiple ions, therefore, paired process design to enable reversible Li + extraction and recovery. Here, we showcase the design of asymmetric ion pathways for Li + extraction and recovery for host material with complex Li + and Na + interaction using layered cobalt oxide as a model material. The two-phase equilibrium of Na 0.48 CoO 2 and Li 0.94 CoO 2 governs Li + selectivity when a high depth of intercalation is achieved (low vacancy level). We show that the relative rate between ion exchange and intercalation is critical to determine the ion pathways. The relationship can be quantitatively compared using the average pseudo ion exchange rate (C pseudoIX ) and the intercalation rate (C inter ). The ion pathways at the three regimes with C pseudoIX > C inter , C pseudoIX ~ C inter , and C pseudoIX < C inter are constructed. By selecting the optimized ion pathway and particle size, we demonstrate 9.7×10 4 Li + selectivity with 99% purity Li + recovery from an initial 1:1000 Li: Na molar ratio solution using 115 mAh/g specific capacity.

electrochemistry

Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo

The environments experienced by vehicles upon entry into planetary atmospheres generally result in severe aerothermodynamic loading. These flows are characterized by the formation of strong shock waves, behind which high temperatures and non-equilibrium environments are generated, and the accurate prediction of internal energy relaxation and chemical kinetics becomes important. This manuscript focuses on the internal relaxation of the rotational energy of polyatomic molecules. Previous work has described the implementation of a discrete rotational energy model for diatomic molecules (linear rotators). Later, Gimelshein et. al extended this model to include polyatomic molecular internal energies. However, they did not include details on how to generate the particles at equilibrium conditions and centrifugal distortion was not included in their model. The purpose of the present study is to extend the afore-mentioned models to the treatment of discrete rotational energy in polyatomic molecules with the addition of centrifugal distortion. An overview of the background theory needed for the implementation of the model will be given followed by the model itself and verification of the model. For example, sampled versus Boltzmann distributions are compared in Figure 1 for CH3 (oblate rotator – two quantum numbers) and examples of thermal relaxation behavior for linear and non-linear rotators are presented in Figure 2. In addition, comparisons of thermophysical properties will be presented, as well as examples of adiabatic relaxation and application to hypersonic flow.

Rarefied Gas Dynamics

Paleotribological models using preserved fossil tissue properties reveal functional significance of Eurasian mammoth dental evolution

Eurasian mammoths (Mammuthus) underwent substantial modifications in molar morphology as later-diverging species evolved progressively thinner enamel and increased enamel crest complexity. These features have been hypothesized to reduce whole-tooth wear and extend dental longevity as increasingly graze-dominated diets evolved within the lineage. This hypothesis has yet to be directly tested. Here, in this study, we developed an in-silico wear model using experimentally derived wear rates from fossil and extant proboscidean dental tissues. The models revealed that shifts in tissue topology do not affect whole-tooth wear rate, as inverse trends in lamellar frequency and enamel thickness preserve a consistent surface enamel area fraction; the determining factor of wear. Rather, topological shifts produce a wear-emergent secondary occlusal surface with greater numbers of triturating crests that create a regular, low-relief, file-like shearing pavement. These changes in occlusal architecture likely directly impacted the mastication capacity of Mammuthus dentitions, facilitating their dietary expansion to incorporate fibrous, lower-nutrient graze.

Dental wear

Quantum graph models for transport in filamentary switching

The formation of metallic nanofilaments bridging two electrodes across an insulator is a mechanism for resistive switching. Examples of such phenomena include atomic synapses, which constitute a distinct class of memristive devices the behavior of which is closely tied to the properties of the filament. Until recently, experimental investigation of the low-temperature regime and quantum transport effects has been limited. However, with growing interest in understanding the true impacts of the filament on device conductance, comprehending quantum effects has become crucial for quantum neuromorphic hardware. Here, we discuss quantum transport resulting from filamentary switching in a narrow region where the continuous approximation of the contact is not valid, and only a few atoms are involved. In this scenario, the filament can be represented by a graph depicting the adjacency of atoms and the overlap between atomic orbitals. Using the theory of quantum graphs with locally diffusive node scattering, we calculate the scattering amplitude of charge carriers on this graph and explore the interplay between filamentary formation and quantum transport effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Polynomial-time preparation of low-temperature Gibbs states for two-dimensional toric code

In this work, we propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial state, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. We prove that fast mixing at low temperature for the two-dimensional toric code can be achieved by augmenting local jump operators with simple global jump operators, which enable efficient transitions between logical sectors. To establish tight lower bounds on the spectral gap, we introduce a new reduction method that eventually maps the problem to estimating the spectral gap of a perturbed graph Laplacian on a stair graph. Our proof also shows that the Lindblad dynamics with a digitally implemented low-temperature local Davies generator is able to efficiently drive the quantum state toward the ground state manifold.

97 MATHEMATICS AND COMPUTING