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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Stability-preserving Lossy Compression for Large-scale Partial Differential Equations

Checkpoint/Restart (C/R) strategies are vital for fault tolerance in PDE-based scientific simulations, yet traditional checkpointing incurs significant I/O overhead. Lossy compression offers a scalable solution by reducing checkpoint data size, but conventional methods often lack control over physical invariants (e.g., energy), leading to instability such as oscillations or divergence in Partial Differential Equations (PDE) systems. This paper introduces a stability-preserving compression approach tailored for PDE simulations by explicitly controlling kinetic and potential energy perturbations to ensure stable restarts. Extensive experiments conducted across diverse PDE configurations demonstrate that our method maintains numerical stability with minimal error magnification—even across multiple checkpoint-restart cycles—outperforming state-of-the-art lossy compressors. Parallel evaluations on the Frontier supercomputer show up to 8.4× improvement in checkpoint write performance and 6.3× in read performance, while maintaining relative L2 errors ∼ 2e-6 throughout continued simulation. These results provide practical guidance for balancing compression accuracy, stability, and computational efficiency in large-scale PDE applications.

Gong, Qian [ORNL] (ORCID:0000000235704142)↗
DOE OSTI2023

Advancement of hybrid fluid-kinetic modeling for HEDP and ICF science

We report on the development progress of a hybrid fluid-kinetic code for simulating fluids and plasmas in a wide range of environments, such as laser–matter interactions, inertial confinement fusion, magnetic confinement fusion, and pulsed power. The suite of numerical tools under development utilizes heterogeneous computer architectures and leverages the benefits of particle–based simulation techniques. By working to combine the kinetic particle-in-cell (PIC) model with a particle-based fluid simulation technique, such as smoothed particle hydrodynamics, we are developing a flexible framework capable of accurately modeling complex flows within and between kinetic and fluid regimes. The TriForce code is under development as a C++ framework for parallel, 3D, particle-based, hybrid fluid-kinetic plasma simulations. The fluid half of TriForce will be based upon the meshless smoothed-particle-hydrodynamics (SPH) approach, well-suited for shear, mixing, and turbulence, whereas the kinetic half resembles a traditional particle-in-cell (PIC) code; other particle-based approaches to fluid modeling that do use a mesh are also possible to use and are under investigation. Maxwell’s electromagnetic field equations are solved either via explicit or implicit algorithms or approximated via resistive magnetohydrodynamics (MHD) using an Ohm’s law and resulting induction equation (extended MHD is under development). A primary goal of enabling direct comparisons, from the same code, between results from the variants of MHD and implicit electromagnetic solutions is to improve our fundamental understanding of systems with magnetic fields. The code is under development to recover results from both radiation-MHD and fully kinetic codes in those limits, and is continuing to be developed from other follow-on grants to operate in between where both descriptions may co-exist and interact. For certain applications, it is desired for a simulation to contain fluid ions and electrons as well as kinetic ions and electrons. Typically, it is too computationally intensive to model a full-scale ICF or HEDP experiment fully kinetically since many cycles are expended with very small time steps on modeling the fluid part of a material that is well treated by the fluid approximation. In this case, many traditional PIC particles can be replaced with a single fluid particle representing the thermal part of the distribution function, and there are fewer needed kinetic particles, which describe the non-thermal part and can be sub-cycled relative to the fluid particle advance. Furthermore, a pure fluid code may, depending on the problem, simply lack many physically important details that are beyond the scope of its reduced approximations and assumptions. In this report, we summarize the objectives achieved in the development of the collisional and kinetic half of the code, and the physics problems to which the code has been applied in the areas of advanced and innovative fusion concepts, pulsed power, and magneto-inertial fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1986

The effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendrite

The Ivantsov (1947) analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite, an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change epsilon, and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero epsilon, but the effect is of order epsilon and hence is seen to be minor for most values of epsilon and dimensionless supercooling that occur in practice.

Mcfadden, G. B.↗
NASA NTRS1997

Nonlinear Rescaling and Proximal-Like Methods in Convex Optimization

The nonlinear rescaling principle (NRP) consists of transforming the objective function and/or the constraints of a given constrained optimization problem into another problem which is equivalent to the original one in the sense that their optimal set of solutions coincides. A nonlinear transformation parameterized by a positive scalar parameter and based on a smooth scaling function is used to transform the constraints. The methods based on NRP consist of sequential unconstrained minimization of the classical Lagrangian for the equivalent problem, followed by an explicit formula updating the Lagrange multipliers. We first show that the NRP leads naturally to proximal methods with an entropy-like kernel, which is defined by the conjugate of the scaling function, and establish that the two methods are dually equivalent for convex constrained minimization problems. We then study the convergence properties of the nonlinear rescaling algorithm and the corresponding entropy-like proximal methods for convex constrained optimization problems. Special cases of the nonlinear resealing algorithm are presented. In particular a new class of exponential penalty-modified barrier functions methods is introduced.

Polyak, Roman↗
NASA NTRS1998

The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws: The Two Dimensional Time Marching Schemes - 1

A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly.

Chang, Sin-Chung↗
NASA NTRS2010

RANS Modeling of Benchmark Shockwave / Boundary Layer Interaction Experiments

This presentation summarizes the computations of a set of shock wave / turbulent boundary layer interaction (SWTBLI) test cases using the Wind-US code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock / boundary layer interaction workshop. The experiments involve supersonic flows in wind tunnels with a shock generator that directs an oblique shock wave toward the boundary layer along one of the walls of the wind tunnel. The Wind-US calculations utilized structured grid computations performed in Reynolds-averaged Navier-Stokes mode. Three turbulence models were investigated: the Spalart-Allmaras one-equation model, the Menter Shear Stress Transport wavenumber-angular frequency two-equation model, and an explicit algebraic stress wavenumber-angular frequency formulation. Effects of grid resolution and upwinding scheme were also considered. The results from the CFD calculations are compared to particle image velocimetry (PIV) data from the experiments. As expected, turbulence model effects dominated the accuracy of the solutions with upwinding scheme selection indicating minimal effects.!

Georgiadis, Nick↗
DOE OSTI2018

A comparative study of shear band tracking strategies in three-dimensional finite elements with embedded weak discontinuities

We present a computational framework for the treatment of shear localization in metallic materials under dynamic loading, based on the integration of a shear band tracking strategy into an explicit 3D finite element formulation with embedded weak discontinuities. Within this computational framework, an embedded shear band’s mid-surface is represented by an iso-surface of a level set function, which is obtained by solving a heatconduction type boundary value problem (BVP). The solution of this BVP is carried out either globally over the entire problem domain, or locally at the level of individual elements in the mesh. In this paper, we present a detailed comparison of these global and local algorithmic implementations of the shear band tracking strategy. Numerical results obtained using these two implementations, and using a simplified formulation without shear band tracking, are presented and compared. Moreover, we compare the computational efficiency and parallel scaling performance of the local and global implementations. This comparative study shows that both implementations can simulate the initiation of two independent shear bands and their propagation past each other without merging, whereas only the global implementation can successfully simulate the merging of two branches of a single shear band. This study also confirms that the global implementation is more computationally intensive, since it requires a global system of linear equations associated with the level set BVP to be solved at each time step. Both implementations exhibit very good scalability in domain decomposition-based parallel simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Revisiting diffusion-based moisture functions: why do they fail?

Microbial activities in soil are controlled by the balance between physical and biological mechanisms that are currently implied by soil moisture-respiration relationships, but not explicitly represented. Diffusion based moisture functions focus on physical controls, while substrate kinetics based models primarily address biological drivers. How to harmonize these two types of models for robust predictions of soil respiration and other processes has not been addressed. Here we derived a generalizable analytical solution of diffusion-limited nonlinear microbial uptake kinetics, in which microbial metabolic rates were governed by both physical and biological drivers via substrate diffusion and microbial affinity. We proposed a soil trait concept to integrate both physical and biological perspectives into one unified function, and tested it using both laboratory and field based observations from a variety of soils. This approach provides a tractable and scalable approach that incorporates soil heterogeneity and functional complexity in macroscopic model descriptions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

Here we propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in (1+1) dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude E 0 and frequency Ω with a period determined by the Stückelberg phase, (2) the cutoff order of HHG is determined by 2eE 0 ℏΩ 2 , with e being the electron charge, and that (3) noninteger harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter γ = (Δ/2)Ω/eE 0 ,with Δ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Three dimensional unstructured multigrid for the Euler equations

The three-dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite-element scheme, which employs an edge-based data-structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Mavriplis, D. J.↗
NASA NTRS1991

A direct algorithm for convective adjustment of the vertical temperature profile for an arbitrary critical lapse rate

An efficient direct algorithm of convective adjustment for an arbitrary critical value of the vertical temperature lapse rate gamma is proposed. The algorithm provides an exact and unique solution of a standard convective adjustment problem for models with temperature specified either on nonuniformly spaced levels or for layers of different thicknesses in pressure, sigma, or other vertical coordinate related to pressure. The algorithm may be recommended for use either directly in atmospheric models not explicitly including a hydrologic cycle with prescribed gamma, or as a part of more complicated parameterizations of moist convection, where gamma may be calculated depending on relative humidity.

Akmaev, Rashid A.↗
DOE OSTI2019

A Classical Field Theory Formulation for the Numerical Solution of Time Harmonic Electromagnetic Fields

Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the “curl-curl” equation for the fields. We present a variational formulation which solves for the four-potential instead, based on classical field theory. Borrowing from quantum electrodynamics, we modify the Lagrangian by adding an implicit gauge-fixing term. This reformulation explicitly accounts for Gauss’ law through the coupling between $\phi$ and $\rho$ , and enables the use of nodal basis functions instead of edge elements for time-harmonic problems. Here, we demonstrate how this formulation, adhering to the deeper underlying symmetries of the four-dimensional covariant field description, provides a highly general, robust numerical framework.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Covariant color-kinematics duality

We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/$\square$ is replaced with covariant 1/D 2 . Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F 3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F 3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A high-order finite difference method for moving immersed domain boundaries and material interfaces

Here, we present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite difference schemes with an immersed boundary treatment based on a weighted least-squares reconstruction of the solution, providing stable discretizations with up to sixth order accuracy for diffusion terms and third order accuracy for advection terms. The temporal discretization relies on a novel strategy for maintaining high-order temporal accuracy in problems with moving boundaries that minimizes implementation complexity and allows arbitrary explicit or diagonally-implicit Runge-Kutta schemes. The approach is broadly compatible with popular PDE-specialized Runge-Kutta time integrators, including low-storage, strong stability preserving, and diagonally implicit schemes. Through numerical experiments we demonstrate that the full discretization maintains high-order spatial and temporal accuracy in the presence of complex 3D geometries and for a range of boundary conditions, including Dirichlet, Neumann, and flux conditions with large jumps in coefficients.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Correlation energy of the uniform electron gas determined by ground-state conditional probability density functional theory

Conditional-probability density functional theory (CP-DFT) is a formally exact method for finding correlation energies from Kohn-Sham DFT without evaluating an explicit energy functional. We present details on how to generate accurate exchange-correlation energies for the ground-state uniform gas. We also use the exchange hole in a CP antiparallel spin calculation to extract the high-density limit. We give a highly accurate analytic solution to the Thomas-Fermi model for this problem, showing its performance relative to Kohn-Sham and may be useful at high temperatures. We explore several approximations to the CP potential. Furthermore, results are compared to accurate parameterizations for both exchange-correlation energies and holes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1978

CAVE3: A general transient heat transfer computer code utilizing eigenvectors and eigenvalues

The method of solution is a hybrid analytical numerical technique which utilizes eigenvalues and eigenvectors. The method is inherently stable, permitting large time steps even with the best of conductors with the finest of mesh sizes which can provide a factor of five reduction in machine time compared to conventional explicit finite difference methods when structures with small time constants are analyzed over long time periods. This code will find utility in analyzing hypersonic missile and aircraft structures which fall naturally into this class. The code is a completely general one in that problems involving any geometry, boundary conditions and materials can be analyzed. This is made possible by requiring the user to establish the thermal network conductances between nodes. Dynamic storage allocation is used to minimize core storage requirements. This report is primarily a user's manual for CAVE3 code. Input and output formats are presented and explained. Sample problems are included which illustrate the usage of the code as well as establish the validity and accuracy of the method.

Palmieri, J. V.↗
NASA NTRS1982

Development of mixed time partition procedures for thermal analysis of structures

The computational methods used to predict and optimize the thermal-structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. This proposed methodology would be readily adaptable to existing computer programs for structural thermal analysis.

Liu, W. K.↗
NASA NTRS1979

Artificial compressibility methods for numerical solutions of transonic full potential equation

New methods for transonic flow computations based on the full potential equation in conservation form are presented. The idea is to modify slightly the density (due to the artificial viscosity in the supersonic region), and solve the resulting elliptic-like problem iteratively. It is shown that standard discretization techniques (central differencing) as well as some standard iterative procedures (SOR, ADI, and explicit methods) are applicable to the modified transonic mixed-type equation. Calculations of transonic flows around cylinders and airfoils are discussed with special emphasis on the explicit methods that are suitable for vector processing on the STAR 100 computer.

Hafez, M.↗