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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations [Review]

We investigate the two-dimensional (2D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the 2D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an in nite family of elliptic or hyperbolic, uniformly expanding or contracting \gas cloud" solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ordinary differential equations, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs with important benchmark problems from computational physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Equation of State Optimization and Uncertainty Quantization: Implementation in the LANL EOS Production Code OpenSesame

We detail the approaches of particle swarm optimization and Bayesian inference through Markov chain Monte Carlo for equation of state development. This work includes formulation of the modeling for the equation of state, numeric optimization of the parametric models via particle swarm optimization, and generation of probability distributions of equations of state from Markov chain Monte Carlo.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

The absence of ray-effects in the discrete ordinate solution to the transport equation in spherical coordinates in multi-dimensions

The streaming operator of the transport equation is derived for spherical coordinates by starting from Newton’s second law for a free particle expressed in spherical coordinates. We shall show that the partial derivatives with respect to the velocity variables of the particle, which are absent in the Cartesian coordinate formulation of the transport equation, arise in the spherical coordinate formulation of the transport equation in response to the centrifugal force which prevents a free particle from ‘falling into the origin’ of the coordinate system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Analysis of an Elasto-Hydrodynamic Seal by Using the Reynolds Equation

This paper reports numerical studies of an Elasto-Hydrodynamic (EHD) seal, which is being developed for supercritical CO2 (sCO2) turbomachinery applications. Current sCO2 turbomachinery suffers from high leakage rates, which is creating a major roadblock to the full realization of sCO2 power technology. The high leakage rates not only penalize the efficiencies but also create environmental concerns due to greenhouse effects caused by the increased CO2 discharge to the atmosphere. The proposed EHD seal needs to work at elevated pressures (10–35 MPa) and temperatures (350–700 °C) with low leakage and minimal wear. The unique mechanism of the EHD seal provides a self-regulated constriction effect to restrict the flow without substantial material contact, thereby minimizing leakage and wear. This work utilizes a physics-based modeling approach. The flow through the gradually narrowing seal clearance is modeled by the well-known Reynolds equation in EHD lubrication theory, while the deformation of the seal is modeled by using the governing equations of three-dimensional solid mechanics. As for the solution methodology, COMSOL’s Thin-Film Flow and Solid Mechanics modules were employed with their powerful capabilities. The numerical results were presented and discussed. It was observed that the Reynolds equation fully coupled with the surface deformation was able to successfully capture the constriction effect. The maximum and minimum leakages were calculated to be 2.25 g/s and 0.1 g/s at P = 5.5 MPa and P = 11 MPa for the design seal, respectively. It was interesting to observe that the seal leakage followed a quadratic trend with increasing pressure differential, which can become advantageous for high-pressure applications such as sCO2 power generation technology.

42 ENGINEERING↗
DOE OSTI2021

P–V–T Equation of State of Iridium Up to 80 GPa and 3100 K

In the present study, the high-pressure high-temperature equation of the state of iridium has been determined through a combination of in situ synchrotron X-ray diffraction experiments using laser-heating diamond-anvil cells (up to 48 GPa and 3100 K) and density-functional theory calculations (up to 80 GPa and 3000 K). The melting temperature of iridium at 40 GPa was also determined experimentally as being 4260 (200) K. The results obtained with the two different methods are fully consistent and agree with previous thermal expansion studies performed at ambient pressure. The resulting thermal equation of state can be described using a third-order Birch–Murnaghan formalism with a Berman thermal-expansion model. The present equation of the state of iridium can be used as a reliable primary pressure standard for static experiments up to 80 GPa and 3100 K. A comparison with gold, copper, platinum, niobium, rhenium, tantalum, and osmium is also presented. On top of that, the radial-distribution function of liquid iridium has been determined from experiments and calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Building an Equation of State Density Ladder

The confluence of major theoretical, experimental, and observational advances are providing a unique perspective on the equation of state of dense neutron-rich matter—particularly its symmetry energy—and its imprint on the mass-radius relation for neutron stars. In this contribution, we organize these developments in an equation of the state density ladder. Of particular relevance to this discussion are the impact of the various rungs on the equation of state and the identification of possible discrepancies among the various methods. A preliminary analysis identifies possible tension between laboratory measurements and gravitational-wave detections that could indicate the emergence of a phase transition in the stellar core.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

High-Fidelity Simulations of Supercritical CO2 Based Oxy-Combustion with Non-Ideal Equation of State

The supercritical carbon dioxide (sCO2) Allam-Fetvedt cycle employs high-temperature oxy-combustion using sCO2 as the working fluid, leading to a unique and challenging environment for materials. In this cycle, pressurized gaseous fuel is combusted in the presence of a hot oxidant flow containing a mixture of CO2 and oxygen and a hot CO2 diluent recycle stream at approximately 300 bar under lean combustion conditions. We present high-fidelity reacting simulations of this oxy-combustor environment and compare the results when performing simulations with ideal and non-ideal equations of state. By doing so, we identify if the combustor behavior at the regime of interest is sensitive enough to the equation of state to justify the added computational cost incurred with a non-ideal equation of state.

equation of state↗
DOE OSTI2021

Numerical solution of singular Lyapunov equations

We consider the numerical solution of large scale singular (continuous-time) Lyapunov equations of the form AX + XA T + BB T = 0, where A is semistable, that is, its spectrum is contained in the left half plane, with the exception of a few semisimple eigenvalues at zero. We also consider the case of a few semisimple eigenvalues on the imaginary axis. We assume that we know these few eigenvalues (zero or imaginary), and that we have or can compute the corresponding invariant subspaces. We use this information to build an appropriate newly proposed subspace on which to project the Lyapunov equations, and then compute a low-rank approximation to the least squares solution. Selected illustrative numerical examples are provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Stability in integrable nonlocal nonlinear equations

Recently a variety of nonlocal integrable systems has been introduced that besides fields located at particular space-time points simultaneously also contain fields that are located at different, but symmetrically related, points. Here we investigate different types of soliton solutions with regard to their stability against linear perturbations obtained for the nonlocal version of the Hirota/nonlinear Schrödinger equation and the so-called Alice and Bob versions of the Korteweg-de Vries and Bousinesq equations. In this work, we encounter different types of scenarios: Solition solutions that are linearly stable or unstable and also solutions that change their stability properties depending on the parameter regime they are in.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

Here we present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with Nv discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all Nv cell centers to each other. The overall CPU time and memory requirement scale as O(Nv log2 Nv) for any bounded two-dimensional (2D) domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an O(Nv4/3) CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency domain methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-of-the-art supercomputer at Lawrence Berkeley National Laboratory.

Hadamard--Babich ansatz↗
DOE OSTI2024

New insights into supradense matter from dissecting scaled stellar structure equations

The strong-field gravity in general relativity (GR) realized in neutron stars (NSs) renders the equation of state (EOS) P(ε) of supradense neutron star matter to be essentially nonlinear and refines the upper bound for Φ ≡ P/ε to be much smaller than the special relativity (SR) requirement with linear EOSs, where P and ε are respectively the pressure and energy density of the system considered. Specifically, a tight bound Φ ≲ 0.374 is obtained by perturbatively anatomizing the intrinsic structures of the scaled Tolman–Oppenheimer–Volkoff (TOV) equations without using any input nuclear EOS. New insights gained from this novel analysis provide EOS-model-independent constraints on the properties (e.g., density profiles of the sound speed squared s 2 = dP/dε and trace anomaly Δ = 1/3 – Φ) of cold supradense matter in NS cores. Using the gravity-matter duality in theories describing NSs, we investigate the impact of gravity on supradense matter EOS in NSs. In particular, we show that the NS mass M NS , radius R, and compactness ξ ≡ M NS /R scale with certain combinations of its central pressure and energy density (encapsulating its central EOS). Thus, observational data on these properties of NSs can straightforwardly constrain NS central EOSs without relying on any specific nuclear EOS model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Extended JT supergravity and random matrix models: The power of the string equation

A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain “string equation”. It was shown recently that in extended supergravity, when the number of BPS states scales as e$^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of $\mathcal{N} = 2$ and (small) $\mathcal{N} = 4$ JT supergravity, and then explore the new cases of spectra from $\mathcal{N} = 3$ and $\mathcal{N} = 4$ large JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.

Extended Supersymmetry↗
DOE OSTI2021

Analytic techniques for solving the transport equations in electroweak baryogenesis

We develop an efficient method for solving transport equations, particularly in the context of electroweak baryogenesis. It provides fully-analytical results under mild approximations and can also test semi-analytical results, which are applicable in more general cases. Key elements of our method include the reduction of the second-order differential equations to first order, representing the set of coupled equations as a block matrix of the particle densities and their derivatives, identification of zero modes, and block decomposition of the matrix. We apply our method to calculate the baryon asymmetry of the Universe (BAU) in a Standard Model effective field theory framework of complex Yukawa couplings to determine the sensitivity of the resulting BAU to modifications of various model parameters and rates, and to estimate the effect of the commonly-used thin-wall approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Difference equations and integral families for Witten diagrams

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

AdS-CFT Correspondence↗
DOE OSTI2023

Control of Fractional Diffusion Problems via Dynamic Programming Equations

In this study, we explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation, we use the Hamilton–Jacobi–Bellman equation. It is well known that this approach suffers from the curse of dimensionality, and to mitigate this problem we couple semi-Lagrangian schemes for the discretization of the dynamic programming principle with the use of Shepard approximation. This coupling enables approximation of high-dimensional problems. Numerical convergence toward the solution of the continuous problem is provided together with linear and nonlinear examples. The robustness of the method with respect to disturbances of the system is illustrated by comparisons with an open-loop control approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

New static solutions of symmetric $\phi^4$ equation

In this paper, we provide new exact solutions of nonlinear Klein–Gordon ( $\phi^4$) equation in 1 + 1-dimension. For simplicity, we focus on the static equation and ignore the time-dependence. The symmetric $\phi^4$ equation has played an important role in several areas of physics. We obtain several novel non-singular solutions of the symmetric $\phi^4$ model in terms of the Jacobi elliptic functions and compare them with the well-known solutions. Finally, we categorize these solutions in terms of the potential parameters.

36 MATERIALS SCIENCE↗