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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 271 records · Page 15
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 OSTI2024

A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.

Computational Engineering, Finance, and Science (c↗
NASA NTRS1989

Ballistic transport in planetary ring systems due to particle erosion mechanisms. I - Theory, numerical methods, and illustrative examples

Ballistic transport, defined as the net radial transport of mass and angular momentum due to exchanges of meteoroid hypersonic-impact ejecta by neighboring planetary ring regions on time-scales orders-of-magnitude shorter than the age of the solar system, is presently considered as a problem in mathematical physics. The preliminary results of a numerical scheme for following the combined effects of ballistic transport and viscous diffusion demonstrate that ballistic transport generates structure near sharp edges already present in the ring-mass distribution; the entire ring system ultimately develops an undulatory structure whose length scale is typically of the order of the radial excursion of the impact ejecta.

Durisen, Richard H.↗
NASA NTRS2005

Numerical Simulations of Plasma Based Flow Control Applications

A mathematical model was developed to simulate flow control applications using plasma actuators. The effects of the plasma actuators on the external flow are incorporated into Navier Stokes computations as a body force vector. In order to compute this body force vector, the model solves two additional equations: one for the electric field due to the applied AC voltage at the electrodes and the other for the charge density representing the ionized air. The model is calibrated against an experiment having plasma-driven flow in a quiescent environment and is then applied to simulate a low pressure turbine flow with large flow separation. The effects of the plasma actuator on control of flow separation are demonstrated numerically.

Suzen, Y. B.↗
DOE OSTI2023

Pore-scale simulation of multiphase flow and reactive transport processes involved in geologic carbon sequestration

Multiphase flow and reactive transport are two essential physicochemical processes that govern the effectiveness of geological carbon sequestration (GCS). The interaction and feedback among different phases and components during intricate physicochemical processes hold great significance in understanding CO 2 sequestration. Pore-scale simulations can account for multiphase flow and reactive transport processes in porous media and obtain spatial distributions of parameters (density, velocity, concentration, etc.) in the pore space as well as their temporal evolutions. This proves especially valuable considering that experiments can be hindered by constraints in spatial and temporal resolution. The comprehensive insights garnered from pore-scale research can be leveraged for continuum modeling using the representative elementary volume (REV) concept. In this contribution, four sequential mechanisms of CO 2 -brine-rock interaction in three zones delineated by CO 2 saturation are elaborated to elucidate complicated physicochemical processes involved in GCS, which are followed by general descriptions of mathematical equations and pore-scale numerical methods. In addition, as interested and commonly encountered processes, leakage risks during GCS and CO 2 -enhanced oil recovery (CO 2 -EOR) processes are presented. The existing challenges and future directions are discussed for both the performance of the pore-scale models and the current gaps in the field of GCS. Importantly, we expect that this review will prove beneficial for researchers interested in pore-scale simulations, GCS, and related disciplines.

58 GEOSCIENCES↗
DOE OSTI2021

Water desalination through the dewpoint evaporative system

This paper presents the first numerical analysis of a novel Dew Point Desalination unit (DPD), which utilizes the phenomenon of the evaporative cooling process to minimize energy consumption. The proposed solution is based on a modular structure, which allows it to obtain any required water production capacity. The analyses for various operational parameters and various climatic conditions are based on the numerical simulations conducted using a validated mathematical model. The system performance was described with different factors, including specific energy consumption (SEC) and daily water production rate respected to 1 m^3*s^-1 of passing air stream (DWP). It is shown that the DPD system can operate in almost every climate zone, and the desalinated water production consumes less than 1.5 kWh*m^-3 of electric energy It is noted the best performance of the DPD system is achieved in the semi-arid, desert and subtropical climate zones. In these climate zones, the 2-stage DPD system allows the production of desalinated water with an electric energy consumption SEC lower than 0.5 kWh*m^-3. The additional benefit of the DPD system is its modularity. The presented DPD system stands as a module, that can be multiplied as needed to achieve the desired size of the desalination plant.

Desalination↗
DOE OSTI2025

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Parametric Finite Element Analysis of Naturally Corroded Steel Specimens Using 3D Surface Laser Scans

Corrosion is considered a uniform thickness reduction design guideline of the maritime industry. However, additionally, the corroded and irregular morphology of the surface affects the steel's load-bearing capacity and its impact on the strength and elongation behaviour of the steel is not yet fully understood. These effects on the local behaviour of steel structures under tensile loading were investigated with tensile tests on naturally corroded steel specimens and nonlinear finite element simulations including the corroded surface morphology with a uniform surface idealation. The models also include the deformed specimen shape. The developed approach led to highly accurate parametric finite element models predicting the ultimate tensile strength and longitudinal position of fracture. The results show that all included aspects are essential for accurate simulations, while solely the maximum available surface resolution was not as decisive.

corrosion↗
DOE OSTI2020

FPDetect: Efficient Reasoning About Stencil Programs Using Selective Direct Evaluation

We present FPDetect, a low-overhead approach for detecting logical errors and soft errors affecting stencil computations without generating false positives. We develop an offline analysis that tightly estimates the number of floating-point bits preserved across stencil applications. This estimate rigorously bounds the values expected in the data space of the computation. Violations of this bound can be attributed with certainty to errors. FPDetect helps synthesize error detectors customized for user-specified levels of accuracy and coverage. FPDetect also enables overhead reduction techniques based on deploying these detectors coarsely in space and time. Experimental evaluations demonstrate the practicality of our approach.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1970

Recovery of thrust magnitude from minitrack data for the SERT-2 spacecraft

An estimation of the thrust magnitude of the Space Electric Rocket Test (SERT) engine is obtained. This estimation is based on changes in the SERT-2 spacecraft orbit as determined from tracking data by using a revised definitive orbit determination system which includes the effect of thrust upon the motion of a spacecraft in general and the SERT-2 satellite in particular. The results of these computations are found to be in good agreement with values of acceleration as determined by an on-board accelerometer. A discussion of the mathematical model used to obtain the numerical results is also presented.

Jones, E. M.↗
NASA NTRS1974

Effect of gravity on methane-air combustion

Analytical and numerical techniques dealing with the theoretical description of the influence of zero and reduced gravitational acceleration on diffusion flames, with a view to improving understanding of fires in space vehicles, were developed in support of experimental work performed in this area. This was done in order to confirm qualitative understanding of the process, to determine the quantitative accuracy of numerical predictions, and to establish a mathematical model of the process for subsequent use as a predictive and exploratory tool. The following results were accomplished: (1) derivation of differential equations and boundary conditions describing the system, (2) details of the computations, using a FORTRAN computer program, for calculating the flow and heat and mass transfer in two dimensions (both steady and unsteady). It was shown that the experimental behavior can be reproduced with fair accuracy, provided that the time step is sufficiently short.

Elghobashi, S.↗
NASA NTRS1976

Transonic flow calculations

The development of relaxation methods to calculate transonic flows is discussed. Rather accurate predictions can be made for a number of flows of interest using the transonic potential flow equation, which may be derived from the Euler equations for inviscid compressible flow by introducing the assumption that the flow is irrotational. Once the choice of a mathematical model has been settled, the numerical procedure for actually computing a solution contains two main elements: the construction of a discrete approximation which converges to the solution of the continuous problem in the limit as the mesh width is reduced to zero, and the solution of the resulting set of nonlinear difference equations by a convergent iterative scheme. The choice of an appropriate coordinate system and its influence on the accuracy of the discrete approximation is discussed. Several applications of the general method are described.

Jameson, A.↗
NASA NTRS1979

Recent advances in the solution of three-dimensional flow over wings with leading edge vortex separation

Recent advances in a panel method for the solution of three-dimensional flow about wing and wing-body combinations with leading-edge vortex separation are presented. These advances were achieved as part of an ultimately successful assault on two shortcomings of the method, namely convergence failures in seemingly random cases, and overprediction of lift coefficient for high aspect-ratio wings. Advances include the implementation of improved panel numerics for the purpose of eliminating the highly non-linear effects of ring vortices around doublet panel edges, and the development of a least squares procedure for damping vortex sheet geometry update instabilities. A variety of cases generated by the computer program implementing the method are presented. These cases are of two types. The first type consists of numerical studies, which verify the underlying mathematical assumptions of the method and moreover show that the results are strongly invariant with respect to such user dependent input as wing panel layout, initial sheet shape, sheet rollup, etc. The second type consists of cases run for the purpose of comparing computed results with experimental data, and these comparisons verify the underlying physical assumptions made by the method.

Johnson, F. T.↗
NASA NTRS1985

Hypersonic merged-layer flow on a sphere

With the objective to achieve the desired reduction in velocity by aerodynamic forces, an aeroassisted orbital transfer vehicle (AOTV) is expected to fly in the higher region of the atmosphere for a sustained period of time. This aeroassist maneuver will occur in the transitional regime, if the vehicle is designed for a low ballistic coefficient. In this case, a merged-layer (ML) is formed around the space vehicle. The flow characteristics of the vehicle can be studied by making use of the full Navier-Stokes (NS) equations, taking into account slip and temperature jump conditions. The present investigation has the objective to obtain a two-term series solution of the full Navier-Stokes equations with surface slip and temperature jump conditions for the ML flow on a sphere. Attention is given to the mathematical formulation of the problem, the numerical method of integration, and the results.

Jain, A. C.↗
NASA NTRS1986

Analysis of boundary conditions for SSME subsonic internal viscous flow analysis

A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.

Baker, A. J.↗
NASA NTRS1991

Artificial Dissipation In Computations Of Hypersonic Flows

Four artificial-dissipation mathematical models introduced to suppress spurious numerical oscillations in finite-difference computations of hypersonic external flows. Models tested for their effects in capturing details of shocks in hypersonic flows about bodies of various shapes.

Yoon, S.↗
NASA NTRS1991

Mathematical Models Of Turbulence In Hypersonic Flow

Report discusses mathematical models of turbulence used in numerical simulations of complicated viscous, hypersonic flows. Includes survey of essential features of models and their statuses in applications.

Marvin, J. G.↗