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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 OSTI2022

Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers

In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through the addition of new linear and nonlinear solvers classes, enhancements to the vector class, and the creation of modern Fortran interfaces. The vast majority of this work has been performed “behind-the-scenes,” with minimal changes to the user interface and no reduction in solver capabilities or performance. These changes allow SUNDIALS users to more easily utilize external solver libraries and create highly customized solvers, enabling greater flexibility on extreme-scale, heterogeneous computational architectures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fierro Version 2.x

FIERRO is a parallel C++ code designed to simulate fluid mechanics, heat transfer, and solid mechanics in two- and three-dimensional space. FIERRO is written to run on homogeneous (CPU) and heterogeneous (CPU+GPU) high performance computing machines. Fierro can aid a) modeling and design efforts that have historically relied on commercial implicit and explicit finite element codes, b) numerical methods research, c) manufacturing research, and d) computer science research. The code contains diverse numerical methods to solve the governing physics equations for both quasi-static and dynamic problems. Mathematical optimization solvers are coupled to the numerical methods to research topology and shape optimization that has application to additive manufacturing, and to create novel numerical approaches. Phase-field methods with micromechanical solvers are provided to simulate microstructure formation and evolution in manufacturing processes. The micromechanical solvers can also help research efforts create continuum-scale constitutive models for solids, as a function of the microstructure, in situ in a calculation or in a stand-alone manner. No physical data exists within the code.

Morgan, Nathaniel↗
DOE OSTI2023

Fierro

FIERRO is a parallel C++ code designed to simulate fluid mechanics, heat transfer, and solid mechanics in two- and three dimensional space. FIERRO is written to run on homogeneous (CPU) and heterogeneous (CPU+GPU) high performance computing machines. Fierro can aid a) modeling and design efforts that have historically relied on commercial implicit and explicit finite element codes, b) numerical methods research, c) manufacturing research, and d) computer science research. The code contains diverse numerical methods to solve the governing physics equations for both quasi-static and dynamic problems. Mathematical optimization solvers are coupled to the numerical methods to research topology and shape optimization that has application to additive manufacturing, and to create novel numerical approaches. Phase-field methods with micromechanical solvers are provided to simulate microstructure formation and evolution in manufacturing processes. The micromechanical solvers can also help research efforts create continuum-scale constitutive models for solids, as a function of the microstructure, in situ in a calculation or in a stand-alone manner. No physical data exists within the code.

Morgan, Nathaniel↗
NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗
NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗
NASA NTRS1985

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from a source surface, given the proper boundary conditions. The results of this work; describing the mathematical formalism that was developed, the numerical techniques employed, and the stability criteria developed for these numerical schemes are presented. An analytical solution is used for a test case; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent ( 5%).

Wu, S. T.↗
NASA NTRS1973

Preliminary numerical analysis of improved gas chromatograph model

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Woodrow, P. T.↗
NASA NTRS1983

Numerical simulation of airfoil ice accretion

A mathematical model of glaze and rime ice accretion on a two-dimensional airfoil is presented. The model employs standard methods for calculating the flow field and cloud droplet trajectories. This data is used as input to a thermodynamic analysis of the ice accretion process which includes liquid runback. The structure of the model allows for dynamic updating of the droplet collection efficiency and heat and mass transfer processes as the accreted ice shape changes. This results in the improved shape prediction over previously described methods. Simulations made with the model are compared to experimental results obtained for a NACA 0012 airfoil in the NASA/Lewis Icing Research Tunnel. The agreement with experiment is found to be generally satisfactory for some cases, but a need for improvements is indicated by others. Suggestions for improvements are made.

Macarthur, C. D.↗
NASA NTRS1990

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case.

Wu, S. T.↗
NASA NTRS1992

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains.

Freed, Alan D.↗
NASA NTRS2002

Error Estimation and Uncertainty Propagation in Computational Fluid Mechanics

Numerical simulation has now become an integral part of engineering design process. Critical design decisions are routinely made based on the simulation results and conclusions. Verification and validation of the reliability of the numerical simulation is therefore vitally important in the engineering design processes. We propose to develop theories and methodologies that can automatically provide quantitative information about the reliability of the numerical simulation by estimating numerical approximation error, computational model induced errors and the uncertainties contained in the mathematical models so that the reliability of the numerical simulation can be verified and validated. We also propose to develop and implement methodologies and techniques that can control the error and uncertainty during the numerical simulation so that the reliability of the numerical simulation can be improved.

Zhu, J. Z.↗
DOE OSTI2020

The Differential Equations That Model Diseases

In this brief tutorial, I will describe the simplest way of modeling a deadly infectious disease, such as COVID-19. I will show that at early times, the disease grows exponentially, but at late times, falls off like a Bell curve. I will solve the equations numerically with Python. A common mathematical model is the so-called compartmental model, where diseases can move people between "categories" such as healthy, infectious, or truly sick. This is a large, well established field and there are many good resources on this topic. I started with the SIAM review article The mathematics of infectious diseases. However, there are many excellent textbooks and more modern reviews as well.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Modeling the U.S. Western Electric Interconnection to Understand the Consequences of Hydrometeorological Extremes and Options for Risk Mitigation

Electricity grid operators around the world face a dual challenge; withstanding increasingly severe weather and the longer term impacts of climate change, while simultaneously decarbonizing. Extreme weather events such as heat waves and droughts are rising in both severity and frequency, which is threatening the reliability of electricity grids through increased demand, generation capacity losses, and equipment failures. Consequently, incorporating hydrometeorological stressors into computational power systems analysis is becoming an even more critical tool in long term planning and short term operations. However, there is a general lack of open-source customizable grid simulation software capable of exhaustively stress testing the grid under hydrometeorological uncertainty, and/or examining potential risk mitigation pathways. A related, persistent challenge for power system modelers is striking an appropriate balance between model fidelity (e.g. spatial scale and time resolution) and computational tractability (wall clock run-time). In this study, we are proposing a solution to this problem with open-source software that allows users to seamlessly customize the scale and track the accuracy of grid operations models. Our approach allows users to search over numerous model parameters (network topology, mathematical formulation, economic hurdle rates, and transmission line scaling) to identify model instantiations that accommodate experimental design. Further, we use this approach to demonstrate the importance of including extreme weather events in model validation and model selection. Focusing on the occurrence of heatwaves and droughts in the U.S. Western Interconnection, we examine role of extreme events in balancing tradeoffs between model fidelity and run-time at the model design stage.

Economics↗
NASA NTRS1972

Dynamic analysis for shuttle design verification

Two approaches that are used for determining the modes and frequencies of space shuttle structures are discussed. The first method, direct numerical analysis, involves finite element mathematical modeling of the space shuttle structure in order to use computer programs for dynamic structural analysis. The second method utilizes modal-coupling techniques of experimental verification made by vibrating only spacecraft components and by deducing modes and frequencies of the complete vehicle from results obtained in the component tests.

Fralich, R. W.↗
NASA NTRS1976

Acoustoelasticity

Internal sound fields are considered. Specifically, the interaction between the (acoustic) sound pressure field and the (elastic) flexible wall of an enclosure is discussed. Such problems frequently arise when the vibrating walls of a transportation vehicle induce a significant internal sound field. Cabin noise in various flight vehicles and the internal sound field in an automobile are representative examples. A mathematical model, simplified solutions, and numerical results and comparisons with representative experimental data are briefly considered. An overall conclusion is that reasonable grounds for optimism exist with respect to available theoretical models and their predictive capability.

Dowell, E. H.↗
NASA NTRS1979

Global Earth Response to Loading by Ocean Tide Models

Mathematical and programming techniques to numerically calculate Earth response to global semidiurnal and diurnal ocean tide models were developed. Global vertical crustal deformations were evaluated for M sub 2, S sub 2, N sub 2, K sub 2, K sub 1, O sub 1, and P sub 1 ocean tide loading, while horizontal deformations were evaluated for the M sub 2 tidal load. Tidal gravity calculations were performed for M sub 2 tidal loads, and strain tensor elements were evaluated for M sub 2 loads. The M sub 2 solution used for the ocean tide included the effects of self-gravitation and crustal loading.

Estes, R. H.↗
NASA NTRS1982

Fault-tolerance memory system architecture for radiation induced errors

A fault-tolerant memory (FTM) architecture is presented which can be used to overcome soft memory errors induced by alpha particles, cosmic radiation, or other random sources. The characteristics of the FTM are presented, a mathematical model is developed, and numerical examples are considered to illustrate the effectiveness of the approach. The FTM architecture has been incorporated in the NASA Standard Spacecraft Computer (NSSC-II) which will be employed in a variety of future space payloads and experiments.

White, J. B., Jr.↗