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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Entropy Stable Conservative Flux Form Neural Networks

We propose an entropy-stable conservative flux form neural network (CFN) to predict the dynamics of unknown governing conservation laws. The design of the network is based on the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN, hereafter referred to as ESCFN, uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Importantly, our method is designed to predict long term dynamics of the unknown conservation law exclusively from a short temporal window of observed data, that is, without oracle knowledge of the PDE or later-time solution profiles. Numerical experiments demonstrate that the ESCFN achieves both stability and conservation while maintaining accuracy over extended time domains, and successfully predicts shock propagation speeds in long-term simulations. Furthermore, it is also robust to both noisy and sparse data environments.

Hyperbolic conservation laws↗
DOE OSTI2021

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. Here in this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Neural entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined numerical discretization. While recent neural network architectures have successfully integrated classical numerical principles into learned models, most rely on prior knowledge of the governing equations or assume a fixed discretization. Our approach removes this dependency by embedding entropy-stable design principles into the learning process itself, enabling the discovery of physically consistent dynamics in a fully data-driven setting. By jointly learning both the flux function and a corresponding entropy, NESCFN promotes conservation and entropy dissipation, which is critical for long-term stability and fidelity in the system of hyperbolic conservation laws. Furthermore, numerical results demonstrate that the method achieves stability and conservation over extended time horizons and accurately captures shock propagation speeds, even without oracle access to future-time solution profiles in the training data.

Conservative flux form↗
DOE OSTI2019

Entropy Stable Discretization of Compressible Flows in Thermochemical Nonequilibrium

Entropy stable numerical methods for compressible flow have been demonstrated to exhibit better robustness than purely linearly stable methods and need less overall artificial dissipation for long simulations in subsonic and transonic flows. In this work we seek to extend these benefits to multicomponent, multitemperature flows in thermochemical nonequilibrium such as combustion and hypersonic flight. We first derive entropy functions that symmetrize the governing equations and allow stability proofs for such systems. The impact of diffusion model selection on provable entropy stability is considered in detail, including both rigorous models of irreversible thermodynamics and simplified models of greater practical interest. Based on the proven entropy functions we develop affordable, entropy conservative two-point flux functions for solution in conservation form. We derive entropy conservative fluxes for calorically and thermally perfect mixtures, with heat capacities described by either polynomials of the temperature or formulas from statistical thermodynamics.

42 ENGINEERING↗
DOE OSTI2022

Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods

In this work, we propose entropy-preserving and entropy-stable partitioned Runge–Kutta (RK) methods. In particular, we extend the explicit relaxation Runge–Kutta methods to IMEX–RK methods and a class of explicit second-order multirate methods for stiff problems arising from scale-separable or grid-induced stiffness in a system. The proposed approaches not only mitigate system stiffness but also fully support entropy-preserving and entropy-stability properties at a discrete level. The key idea of the relaxation approach is to adjust the step completion with a relaxation parameter so that the time-adjusted solution satisfies the entropy condition at a discrete level. The relaxation parameter is computed by solving a scalar nonlinear equation at each timestep in general; however, as for a quadratic entropy function, we theoretically derive the explicit form of the relaxation parameter and numerically confirm that the relaxation parameter works the Burgers equation. Several numerical results for ordinary differential equations and the Burgers equation are presented to demonstrate the entropy-conserving/stable behavior of these methods. We also compare the relaxation approach and the incremental direction technique for the Burgers equation with and without a limiter in the presence of shocks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard DG method. Numerical results are shown demonstrating the effectiveness of the method on a variety of test cases, including Burgers’ equation and the Euler equations, in one, two, and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Low Thermal Conductivity and Diffusivity at High Temperatures Using Stable High–Entropy Spinel Oxide Nanoparticles

The realization of low thermal conductivity at high temperatures (0.11 W m –1 K –1 800 °C) in ambient air in a porous solid thermal insulation material, using stable packed nanoparticles of high-entropy spinel oxide with 8 cations (HESO-8 NPs) with a relatively high packing density of ≈50%, is reported. The high-density HESO-8 NP pellets possess around 1000-fold lower thermal diffusivity than that of air, resulting in much slower heat propagation when subjected to a transient heat flux. The low thermal conductivity and diffusivity are realized by suppressing all three modes of heat transfer, namely solid conduction, gas conduction, and thermal radiation, via stable nanoconstriction and infrared-absorbing nature of the HESO-8 NPs, which are enabled by remarkable microstructural stability against coarsening at high temperatures due to the high entropy. Furthermore, this work can elucidate the design of the next-generation high-temperature thermal insulation materials using high-entropy ceramic nanostructures.

thermal insulation↗
DOE OSTI2024

Design and Development of Stable Nanocrystalline High‐Entropy Alloy: Coupling Self‐Stabilization and Solute Grain Boundary Segregation Effects

Abstract Grain growth is prevalent in nanocrystalline (NC) materials at low homologous temperatures. Solute element addition is used to offset excess energy that drives coarsening at grain boundaries (GBs), albeit mostly for simple binary alloys. This thermodynamic approach is considered complicated in multi‐component alloy systems due to complex pairwise interactions among alloying elements. Guided by empirical and GB‐segregation enthalpy considerations for binary‐alloy systems, a novel alloy design strategy, the “ pseudo‐binary thermodynamic ” approach, for stabilizing NC‐high entropy alloys (HEAs) and other multi‐component‐alloy variants is proposed. Using Al 25 Co 25 Cr 25 Fe 25 as a model‐HEA to validate this approach, Zr, Sc, and Hf, are identified as the preferred solutes that would segregate to HEA‐GBs to stabilize it against growth. Using Zr, NC‐Al 25 Co 25 Cr 25 Fe 25 HEAs with minor additions of Zr are synthesized, followed by annealing up to 1123 K. Using advanced characterization techniques— in situ X‐ray diffraction (XRD), scanning/transmission electron microscopy (S/TEM), and atom probe tomography, nanograin stability due to coupling self‐stabilization and solute‐GB segregation effects is reported in HEAs up to substantially high temperatures. The self‐stabilization effect originates from the preferential GB‐segregation of constituent HEA‐elements that stabilizes NC‐Al 25 Co 25 Cr 25 Fe 25 up to 0.5 T m ( T m –melting temperature). Meanwhile, solute‐GB segregation originates from Zr segregation to NC‐Al 25 Co 25 Cr 25 Fe 25 GBs; this results in further stabilization of the phase and grain‐size (≈14 nm) up to ≈0.58 and ≈0.64 T m , respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗