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Results for “explicit solution”

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 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

User's guide for the computer code COLTS for calculating the coupled laminar and turbulent flow over a Jovian entry probe

A user's guide for a computer code 'COLTS' (Coupled Laminar and Turbulent Solutions) is provided which calculates the laminar and turbulent hypersonic flows with radiation and coupled ablation injection past a Jovian entry probe. Time-dependent viscous-shock-layer equations are used to describe the flow field. These equations are solved by an explicit, two-step, time-asymptotic finite-difference method. Eddy viscosity in the turbulent flow is approximated by a two-layer model. In all, 19 chemical species are used to describe the injection of carbon-phenolic ablator in the hydrogen-helium gas mixture. The equilibrium composition of the mixture is determined by a free-energy minimization technique. A detailed frequency dependence of the absorption coefficient for various species is considered to obtain the radiative flux. The code is written for a CDC-CYBER-203 computer and is capable of providing solutions for ablated probe shapes also.

Kumar, A.↗
DOE OSTI2021

Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing in the small Atwood number limit

Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing incompressible turbulent Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing in planar geometry are derived in the small Atwood number (Boussinesq) limit. The models are based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar (heavy-fluid mass fraction) variance S and its dissipation rate Χ modeled either differentially or algebraically. The models allow for a simultaneous description of mechanical and scalar mixing, i.e., mixing layer growth and molecular mixing, respectively. Mixing layer growth parameters and other physical observables relevant to each instability are obtained explicitly as functions of the model coefficients. The turbulent fields are also expressed in terms of the model coefficients, with their temporal power-law scalings obtained by requiring that the self-similar equations are explicitly time-independent. The model calibration methodology is described and discussed. Expressions for a subset of the various physical observables are used to calibrate each of the two-, three-, and four-equation models, such that the self-similar solutions are consistent with experimental and numerical simulation data corresponding to these values of the observables and to specific canonical Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz turbulent flows. A calibrated four-equation model is then used to reconstruct the mean and turbulent fields, and late-time turbulent equation budgets for each instability-induced flow across the mixing layer. The reference solutions derived here can provide systematic calibrations and better understanding of mechanical–scalar turbulence models and their predictions for instability-induced turbulent mixing in the very large Reynolds number limit.

42 ENGINEERING↗
DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

ff19SB: Amino-acid specific protein backbone parameters trained against quantum mechanics energy surfaces in solution

Molecular dynamics (MD) simulations have become increasingly popular in studying the motions and functions of biomolecules. The accuracy of the simulation, however, is highly determined by the molecular mechanics (MM) force field (FF), a set of functions with adjustable parameters to compute the potential energies from atomic positions. However, the overall quality of the FF, such as our previously published ff99SB and ff14SB, can be limited by assumptions that were made years ago. In the updated model presented here (ff19SB), we have significantly improved the backbone profiles for all 20 amino acids. We fit coupled Φ/ψ parameters using 2D Φ/ψ conformational scans for multiple amino acids, using as reference data the entire 2D quantum mechanics (QM) energy surface. We address the polarization inconsistency during dihedral parameter fitting by using both QM and MM in solution. Finally, we examine possible dependency of the backbone fitting on side chain rotamer. To extensively validate ff19SB parameters, we have performed a total of ~5 milliseconds MD simulations in explicit solvent. Here, our results show that after amino-acid specific training against QM data with solvent polarization, ff19SB not only reproduces the differences in amino acid specific Protein Data Bank (PDB) Ramachandran maps better, but also shows significantly improved capability to differentiate amino acid dependent properties such as helical propensities. We also conclude that an inherent underestimation of helicity is present in ff14SB, which is (inexactly) compensated by an increase in helical content driven by the TIP3P bias toward overly compact structures. In summary, ff19SB, when combined with a more accurate water model such as OPC, should have better predictive power for modeling sequence-specific behavior, protein mutations, and also rational protein design.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2018

Resolving orbital pathways for intermolecular electron transfer

Over 60 years have passed since Taube deduced an orbital-mediated electron transfer mechanism between distinct metal complexes. This concept of an orbital pathway has been thoroughly explored for donor–acceptor pairs bridged by covalently bonded chemical residues, but an analogous pathway has not yet been conclusively demonstrated for formally outer-sphere systems that lack an intervening bridge. In our present study, we experimentally resolve at an atomic level the orbital interactions necessary for electron transfer through an explicit intermolecular bond. This finding was achieved using a homologous series of surface-immobilized ruthenium catalysts that bear different terminal substituents poised for reaction with redox active species in solution. This arrangement enabled the discovery that intermolecular chalcogen···iodide interactions can mediate electron transfer only when these interactions bring the donor and acceptor orbitals into direct contact. This result offers the most direct observation to date of an intermolecular orbital pathway for electron transfer.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1974

Adjustment technique without explicit formation of normal equations /conjugate gradient method/

For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

Saxena, N. K.↗
NASA NTRS1982

Laminar flow transition: A large-eddy simulation approach

A vectorized, semi-implicit code was developed for the solution of the time-dependent, three dimensional equations of motion in plane Poiseuille flow by the large-eddy simulation technique. The code is tested by comparing results with those obtained from the solutions of the Orr-Sommerfeld equation. Comparisons indicate that finite-differences employed along the cross-stream direction act as an implicit filter. This removes the necessity of explicit filtering along this direction (where a nonhomogeneous mesh is used) for the simulation of laminar flow transition into turbulence in which small scale turbulence will be accounted for by a subgrid scale turbulence model.

Biringen, S.↗
NASA NTRS1981

Analytic approximations to the modon dispersion relation

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Boyd, J. P.↗
NASA NTRS1988

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

Shebalin, John V.↗
NASA NTRS1988

Unsteady transonic airfoil computation using implicit Euler scheme on body-fixed grid

The unsteady Euler equations have been derived for the flow relative motion with respect to a frame of reference that is rigidly attached to the moving airfoil. The grid is generated once by an elliptic solver without a need for dynamic grid computation. An implicit factored finite-volume scheme has been developed and implemented through a fully vectorized computer program. Implicit second-order and explicit second and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The scheme is applied to steady and unsteady transonic airfoil flows and the results are in good agreement with the experimental data. For forced harmonic airfoil motions, periodic solutions are achieved within the third cycle of oscillation.

Kandil, Osama A.↗
NASA NTRS1991

A natural partitioning scheme for parallel simulation of multibody systems

A parallel partitioning scheme based on physical-coordinate variables is presented to systematically eliminate system constraint forces and yield the equations of motion of multibody dynamics systems in terms of their independent coordinates. Key features of the present scheme include an explicit determination of the independent coordinates, a parallel construction of the null space matrix of the constraint Jacobian matrix, an easy incorporation of the previously developed two-stage staggered solution procedure, and Schur complement based parallel preconditioned conjugate gradient numerical algorithm.

Chiou, J. C.↗
NASA NTRS1993

A natural partitioning scheme for parallel simulation of multibody systems

A parallel partitioning scheme based on physical-co-ordinate variables is presented to systematically eliminate system constraint forces and yield the equations of motion of multibody dynamics systems in terms of their independent coordinates. Key features of the present scheme include an explicit determination of the independent coordinates, a parallel construction of the null space matrix of the constraint Jacobian matrix, an easy incorporation of the previously developed two-stage staggered solution procedure and a Schur complement based parallel preconditioned conjugate gradient numerical algorithm.

Chiou, J. C.↗
NASA NTRS1995

Implicit schemes and parallel computing in unstructured grid CFD

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

Venkatakrishnam, V.↗
NASA NTRS2003

An Advanced Hierarchical Hybrid Environment for Reliability and Performance Modeling

The key issue we intended to address in our proposed research project was the ability to model and study logical and probabilistic aspects of large computer systems. In particular, we wanted to focus mostly on automatic solution algorithms based on a state-space exploration as their first step, in addition to the more traditional discrete-event simulation approaches commonly employed in industry. One explicitly-stated goal was to extend by several orders of magnitude the size of models that can be solved exactly, using a combination of techniques: 1) Efficient exploration and storage of the state space using new data structures that require an amount of memory sublinear in the number states; and 2) Exploitation of the existing symmetries in the matrices describing the system behavior using Kronecker operators. Not only we have been successful in achieving the above goals, but we exceeded them in many respects.

Ciardo, Gianfranco↗
NASA NTRS2002

Human motion planning based on recursive dynamics and optimal control techniques

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

Non-NASA Center↗
NASA NTRS1982

Solution of the unsteady subsonic thin airfoil problem

The problem of a thin airfoil subject to simple harmonic disturbances in a uniform subsonic free stream is solved by extension of a technique developed earlier for a stationary strip vibrating in a uniform fluid. Explicit expressions are given for the lift and moment, acoustic directivity pattern, and total acoustic power for arbitrary upwash and, in particular, for the 'elementary disturbances': plunge, pitch and a stationary transverse gust. Numerical results for a simple skewed gust are presented and compared to the high-frequency asymptotic theory of Martinez and Widnall.

Williams, M. H.↗
NASA NTRS1989

First and second order convex approximation strategies in structural optimization

In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.

Fleury, C.↗
NASA NTRS1996

An Open Computing Infrastructure that Facilitates Integrated Product and Process Development from a Decision-Based Perspective

Computer applications for design have evolved rapidly over the past several decades, and significant payoffs are being achieved by organizations through reductions in design cycle times. These applications are overwhelmed by the requirements imposed during complex, open engineering systems design. Organizations are faced with a number of different methodologies, numerous legacy disciplinary tools, and a very large amount of data. Yet they are also faced with few interdisciplinary tools for design collaboration or methods for achieving the revolutionary product designs required to maintain a competitive advantage in the future. These organizations are looking for a software infrastructure that integrates current corporate design practices with newer simulation and solution techniques. Such an infrastructure must be robust to changes in both corporate needs and enabling technologies. In addition, this infrastructure must be user-friendly, modular and scalable. This need is the motivation for the research described in this dissertation. The research is focused on the development of an open computing infrastructure that facilitates product and process design. In addition, this research explicitly deals with human interactions during design through a model that focuses on the role of a designer as that of decision-maker. The research perspective here is taken from that of design as a discipline with a focus on Decision-Based Design, Theory of Languages, Information Science, and Integration Technology. Given this background, a Model of IPPD is developed and implemented along the lines of a traditional experimental procedure: with the steps of establishing context, formalizing a theory, building an apparatus, conducting an experiment, reviewing results, and providing recommendations. Based on this Model, Design Processes and Specification can be explored in a structured and implementable architecture. An architecture for exploring design called DREAMS (Developing Robust Engineering Analysis Models and Specifications) has been developed which supports the activities of both meta-design and actual design execution. This is accomplished through a systematic process which is comprised of the stages of Formulation, Translation, and Evaluation. During this process, elements from a Design Specification are integrated into Design Processes. In addition, a software infrastructure was developed and is called IMAGE (Intelligent Multidisciplinary Aircraft Generation Environment). This represents a virtual apparatus in the Design Experiment conducted in this research. IMAGE is an innovative architecture because it explicitly supports design-related activities. This is accomplished through a GUI driven and Agent-based implementation of DREAMS. A HSCT design has been adopted from the Framework for Interdisciplinary Design Optimization (FIDO) and is implemented in IMAGE. This problem shows how Design Processes and Specification interact in a design system. In addition, the problem utilizes two different solution models concurrently: optimal and satisfying. The satisfying model allows for more design flexibility and allows a designer to maintain design freedom. As a result of following this experimental procedure, this infrastructure is an open system that it is robust to changes in both corporate needs and computer technologies. The development of this infrastructure leads to a number of significant intellectual contributions: 1) A new approach to implementing IPPD with the aid of a computer; 2) A formal Design Experiment; 3) A combined Process and Specification architecture that is language-based; 4) An infrastructure for exploring design; 5) An integration strategy for implementing computer resources; and 6) A seamless modeling language. The need for these contributions is emphasized by the demand by industry and government agencies for the development of these technologies.

Hale, Mark A.↗