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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Numerical Experiments and Identification of Areas for Further Consideration (B639388 Subcontract Quarter II Report)

The second quarter of the project was spent carrying out numerical experiments on a variety of test matrices, using a combination of precisions, with the intent to study the numerical properties (namely, accuracy and convergence behavior) of the Conjugate Gradient (CG) method. We summarize our findings in the remainder of the document. Other activities include attending biweekly xSDK meetings. We are also currently collaborating with Steven Thomas (NREL) on the numerical stability analysis of “low-synch” Gram-Schmidt routines, for potential application within high-performance GMRES variants. This work is in progress. The subsequent quarter will be spent delving into the numerical analysis in order to provide theoretical explanation for the behavior observed in our experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

High-accuracy method for modeling nucleation and growth of particles

State-of-the-art numerical models describing the kinetics of aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method, in which particles that are smaller than the critical size are omitted from consideration because they are thermodynamically unfavorable. This omission is based on the assumption that most newly formed particles are above the critical size, so that subcritical-size particles are not important to take into account. Due to the nature of the nodal method, it suffers from numerical diffusion, which can cause an artificial broadening of the cluster size distribution leading to a significant overestimation of the number of large-size particles. To address these issues, we propose a more accurate numerical method that explicitly models particles of all sizes, and uses a special numerical scheme that substantially reduces the numerical diffusion and provides high solution accuracy and numerical stability. We extensively compare this novel method to the commonly used nodal solver of the general dynamic equation (GDE) for particle growth and demonstrate that it offers GDE solutions with higher accuracy with low numerical diffusion. Incorporating small subcritical clusters into the solution is crucial for: 1) more precise determination of the entire particle size distribution function and 2) wider applicability of the model to experimental studies with non-monotonic temperature variations leading to particle evaporation. The computational code implementing this numerical method in Python is available upon request.

42 ENGINEERING↗
NASA NTRS1980

UDU/T/ covariance factorization for Kalman filtering

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Thornton, C. L.↗
DOE OSTI2018

Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation

A numerical method for solving systems of nonlinear one-dimensional balance laws, based on multivariate sigmoidal functions approximation, is developed. Constructive approximation theorems are first established in both, uniform and L{sup p} norms. A priori as well as a posteriori error estimates are derived for the numerical solutions, when various kinds of sigmoidal functions, such as unit step, logistic and Gompertz functions, are chosen. The residual of the numerical method is also estimated. Numerical examples are given to test the performance of the algorithm, a comparison with the Godunov method is made concerning accuracy and computational cost. Finally, the numerical stability of the method is analyzed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

We present a semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose spatial discretization yields a tridiagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor semi-analytic solutions are available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

CTF-R: A novel residual-based thermal hydraulic solver

The traditional scientific process has been revolutionized by the advent of computational modeling, but the nuclear industry generally uses "legacy codes," which were developed early in the evolution of computers. One example of a legacy code, the thermal hydraulic subchannel code CTF, is modernized in this work through the development of a novel residual-based version, CTF-R. Unlike its predecessor, CTF-R is not limited by the strict computational limitations of the early 1980's, and can therefore be designed such that it is inherently flexible and easy to use. A case study is examined to demonstrate how the flexibility of the code can be used to improve simulation results. In this example, the coupling between the solid and liquid fields is examined. Traditionally, this coupling is modeled explicitly, which imposes numerical stability limits on the time step size. These limits are derived and it is shown that they are removed when the coupling is made implicit. Further, the development of CTF-R will enable future improvements in next generation reactor modeling, numerical methods, and coupling to other codes. Through the further development of CTF-R and other residual-based codes, state-of-the-art simulation is possible.

42 ENGINEERING↗
DOE OSTI2015

Condition‐based exciter model complexity reduction for improved transient stability simulation

A reduced model approach to decrease computational complexity in power system transient stability simulation is presented. This study investigates conditions that make fast modes active or inactive using practical power system examples. Modes in the original system where fast dynamics do not appear can be neglected, allowing simulation steps to be increased without numerical stability issues. During a transient simulation, the proposed method switches dynamically between the original exciter model and the reduced one, depending on the switching criterion presented. A high level of accuracy is achieved and computational efficiency is increased. Case studies with the Western Electricity Coordinating Council system are provided to validate the performance of the proposed method.

Kim, Soobae↗
NASA NTRS1972

Analytical treatment of gas flows through multilayer insulation, project 1

A theoretical investigation of gas flow inside a multilayer insulation system was made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was also investigated. It was shown that when the relaxation time is less than the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparisons with experimental data were made.

Lin, J. T.↗
NASA NTRS1973

Analysis of gas flow through a multilayer insulation system.

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparison with experimental data was made.

Lin, J. T.↗
NASA NTRS1973

Thermal engineering research

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.

Shih, C. C.↗
DOE OSTI2026

Assessment of the hydromechanical higher-order MPM for the simulation of geotechnical problems

The Material Point Method (MPM) has been increasingly used to simulate large strain deformations. Linear interpolation functions are commonly used to perform the spatial integration. It is well-known that the discontinuities in the interpolation function derivatives induce shock-like artifacts known as ‘cell-crossing’ error. These errors compound with volumetric locking errors when used with hydromechanical formulations for porous media, where different velocity fields are used for each phase. The capabilities of higher-order MPM frameworks have not been explored for real-scale geotechnical problems. As such, this paper aims to assess, validate, and further discuss a higher-order B-spline MPM (BS-MPM) framework. First, the BS-MPM framework is verified against the large-strain oedometer consolidation problem. Second, the framework is validated against a real-scale slope failure experiment triggered by pore water pressure recharge. Landslide features that are captured using the higher-order framework are specifically highlighted, and results (e.g., pore water pressure and deformation) are validated with field measurements. A generally convergent numerical solution is observed when using cubic interpolation functions. Third, a footing penetration problem is simulated using the multi-patch BS-MPM. Trends are examined with respect to penetration velocity and variation in hydraulic conductivity. The BS-MPM framework ultimately presents a stabilized numerical solution that captures plausible hydromechanical interaction trends important in geotechnical engineering applications.

36 MATERIALS SCIENCE↗
NASA NTRS1976

A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study

An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.

Thornton, C. L.↗
DOE OSTI2017

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof of the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Externally pressurized gas-lubricated journal bearings with herringbone grooves - Load capacity and stability analysis.

A small eccentricity analysis was performed to predict load capacity and stability. Numerical results were obtained for a range of feeding parameter, pressure ratio, groove length and orifice recess volume for compressibility numbers from 0 to 50. These results were obtained from a digital computer program. Results showed that the addition of herringbone grooving to an externally pressurized bearing increases stability, but reduces load capacity at low compressibility numbers. A fully-grooved bearing is more stable than a partially-grooved bearing. Orifice recesses reduce stability, especially at high compressibility numbers.

Fleming, D. P.↗
DOE OSTI2014

A stochastic extension of the explicit algebraic subgrid-scale models

The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

High-order multirate explicit time-stepping schemes for the baroclinic-barotropic split dynamics in primitive equations

In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong stability-preserving Runge-Kutta approach, we propose two high-order multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in this paper. The proposed schemes allow for a large time step to be used for the three-dimensional baroclinic (slow) mode and a small time step for the two-dimensional barotropic (fast) mode, in which each of the two mode solves just need to satisfy their respective CFL conditions for numerical stability. Specifically, at each time step, the baroclinic velocity is first computed by advancing the baroclinic mode and fluid thickness of the system with the large time-step and the assistance of some intermediate approximations of the barotropicmode obtained by substepping with the small time step; then the barotropic velocity is corrected by using the small time step to re-advance the barotropic mode un-der an improved barotropic forcing produced by interpolation of the forcing terms from the preceding baroclinic mode solves; lastly, the fluid thickness is updated by coupling the baroclinic and barotropic velocities. Additionally, numerical inconsistencies on the discretized sea surface height caused by the mode splitting are relieved via a reconciliation process with carefully calculated flux deficits. Here, two benchmark tests from the “MPAS-Ocean” platform are carried out to numerically demonstrate the performance and parallel scalability of the proposed SSPRK-SE schemes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1992

Numerical studies of transverse curvature effects on transonic flow stability

A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary-layer profile and a nonsimilar axisymmetric boundary-layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1-1.4) and aerodynamically relevant Reynolds numbers (5000-10,000 based on displacement thickness), the maximum growth rate is found to increase with curvature - the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.

Macaraeg, M. G.↗