SEARCH · Search NASA

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19

All sources NASA NTRS DOE OSTI

NASA NTRS2001

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Mei, Ren-Wei↗

NASA NTRS1982

A high-resolution numerical technique for inviscid gas-dynamic problems with weak solutions

The shock resolution of Harten's (1982) second-order explicit method for one-dimensional hyperbolic conservation laws is investigated for a two-dimensional gas-dynamic problem. The possible extension to a high resolution implicit method for both one- and two-dimensional problems is also investigated. Applications of Harten's method to the quasi-one-dimensional nozzle problem with two nozzle shapes (divergent and convergent-divergent) and the two-dimensional shock-reflection problem resulted in high shock resolution steady-state numerical solutions.

Yee, H. C.↗

NASA NTRS1995

Numerical solution of the full potential equation using a chimera grid approach

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

Holst, Terry L.↗

NASA NTRS1995

An Adaptive Semi-Implicit Scheme for Simulations of Unsteady Viscous Compressible Flows

A numerical scheme for simulation of unsteady, viscous, compressible flows is considered. The scheme employs an explicit discretization of the inviscid terms of the Navier-Stokes equations and an implicit discretization of the viscous terms. The discretization is second order accurate in both space and time. Under appropriate assumptions, the implicit system of equations can be decoupled into two linear systems of reduced rank. These are solved efficiently using a Gauss-Seidel method with multigrid convergence acceleration. When coupled with a solution-adaptive mesh refinement technique, the hybrid explicit-implicit scheme provides an effective methodology for accurate simulations of unsteady viscous flows. The methodology is demonstrated for both body-fitted structured grids and for rectangular (Cartesian) grids.

Steinthorsson, Erlendur↗

NASA NTRS1975

Some properties of extremal solutions of zero-sum differential games

Necessary conditions for infinite-time linear-quadratic two-player differential games with perfect state information are examined in the light of Willems' work on the algebraic Riccati equation. Necessary conditions for the nonzero-sum game do not always reduce precisely to those of the zero-sum game, when the weighting parameters of the cost index are taken as those of a zero-sum game. Formulation of zero-sum game problems in extended L2-spaces reveals the existence of nonstabilizing but infimal controls, and explicit frequency-domain conditions for existence of solutions and stabilizing solutions are established through the algebraic Riccati equation (ARE).

Johnson, T. L.↗

NASA NTRS1985

Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flow.

Howlett, J. T.↗

NASA NTRS1985

Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

Howlett, J. T.↗

NASA NTRS1993

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

Hagstrom, Thomas↗

NASA NTRS1988

Efficient Jacobian inversion for the control of simple robot manipulators

Symbolic inversion of the Jacobian matrix for spherical wrist arms is investigated. It is shown that, taking advantage of the simple geometry of these arms, the closed-form solution of the system Q = J-1X, representing a transformation from task space to joint space, can be obtained very efficiently. The solutions for PUMA, Stanford, and a six-revolute-joint coplanar arm, along with all singular points, are presented. The solution for each joint variable is found as an explicit function of the singular points which provides a better insight into the effect of different singular points on the motion and force exertion of each individual joint. For the above arms, the computation cost of the solution is on the same order as the cost of forward kinematic solution and it is significantly reduced if forward kinematic solution is already obtained. A comparison with previous methods shows that this method is the most efficient to date.

Fijany, Amir↗

NASA NTRS1983

A shock-fitting solution of the supersonic flowfield in a rounded internal corner

A comparison is presented of a computational investigation of the flowfield created by supersonic flow over an internal corner with rounding and experimental results at a freestream Mach number of 4.1. The computational study uses a shock-fitting finite difference scheme with explicit formulation of the transformation to computational coordinates. The solutions calculated agree with previous ones for the sharp corner case and with the experimental investigation results for the rounded corner case. Parametric effects were computed for variations in corner rounding, freestream Mach number, symmetric wedge angle and unsymmetric wedge angle. A region is described over which successful executions were obtained.

Martin, J. A.↗

NASA NTRS1991

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

Elmiligui, Alaa↗

NASA NTRS1993

Use of networked workstations for parallel nonlinear structural dynamic simulations of rotating bladed-disk assemblies

The principal objective of this research is to investigate, develop and demonstrate coarse-grained, parallel-processing strategies for nonlinear dynamic simulations for rotating bladed-disk assemblies. The parallel -processing strategies addressed include numerical algorithms for parallel nonlinear solutions and techniques to effect load balancing among processors. The parallel environment employed is a distributed-memory, coarse-grained one consisting of networked workstations. A parallel explicit time integration method has been implemented for transient nonlinear solutions of rotationg bladed-disk assemblies. Automatic domain partitioning techniques have been investigated for load balancing among processors. Advanced computing environments, data structures and interactive computer graphics all contribute to an integrated parallel finite element analysis system to facilitate more efficient and powerful dynamic simulations.

Hsieh, Shang-Hsien↗

DOE OSTI2023

Voltage-Dependent First-Principles Simulation of Insertion of Chloride Ions into Al/Al 2 O 3 Interfaces Using the Quantum Continuum Approximation

Experiments have shown that pitting corrosion can develop in aluminum surfaces at potentials > − 0.5 V relative to the standard hydrogen electrode (SHE). Until recently, the onset of pitting corrosion in aluminum has not been rigorously explored at an atomistic scale because of the difficulty of incorporating a voltage into density functional theory (DFT) calculations. We introduce the Quantum Continuum Approximation (QCA) which self-consistently couples explicit DFT calculations of the metal-insulator and insulator-solution interfaces to continuum Poisson-Boltzmann electrostatic distributions describing the bulk of the insulating region. By decreasing the number of atoms necessary to explicitly simulate with DFT by an order of magnitude, QCA makes the first-principles prediction of the voltage of realistic electrochemical interfaces feasible. After developing this technique, we apply QCA to predict the formation energy of chloride atoms inserting into oxygen vacancies in Al(111)/α-Al 2 O 3 (0001) interfaces as a function of applied voltage. We predict that chloride insertion is only favorable in systems with a grain boundary in the Al 2 O 3 for voltages > − 0.2 V (SHE). Here our results roughly agree with the experimentally demonstrated onset of corrosion, demonstrating QCA's utility in modeling realistic electrochemical systems at reasonable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1994

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.

Mcmanus, Hugh L.↗

NASA NTRS1990

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis

Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.

Chiou, Jin-Chern↗

DOE OSTI2021

Natural Charge-Transfer Analysis: Eliminating Spurious Charge-Transfer States in Time-Dependent Density Functional Theory via Diabatization, with Application to Projection-Based Embedding

For many types of vertical excitation energies, linear-response time-dependent density functional theory (LR-TDDFT) offers a useful degree of accuracy combined with unrivaled computational efficiency, although charge-transfer excitation energies are often systematically and dramatically underestimated, especially for large systems and those that contain explicit solvent. As a result, low energy electronic spectra of solution-phase chromophores often contain tens to hundreds of spurious charge-transfer states, making LR-TDDFT needlessly expensive in bulk solution. More nefariously, intensity borrowing by the low-energy charge-transfer states can affect intensities of the valence excitations even if those excitation energies are accurate. At higher excitation energies, it is difficult to distinguish spurious CT states from genuine charge-transfer-to-solvent (CTTS) excitations. In this work, we introduce an automated diabatization scheme that enables fast and effective screening of the CTTS acceptor space in bulk solution. Our procedure introduces the concept of “natural charge-transfer orbitals”, which provide a means to isolate characteristic pairs of orbitals that are most likely to participate in a CTTS excitation. The projection of these orbitals onto solvent-centered virtual orbitals provides a criterion for defining the most important solvent molecules in a given excitation. We apply this method to analyze an ab initio molecular dynamics (MD) trajectory of I-(aq) and report the lowest-energy CTTS band in the absorption spectrum. Our results are in excellent agreement with experimental measurements for bulk I-(aq), and only one-third of the water molecules in the I-(H2O)96 simulation cell need to be described with LR-TDDFT in order to obtain excitation energies that are converged to < 0.1 eV. The tools introduced herein will improve the accuracy, efficiency, and usability of LR-TDDFT in solution-phase environments

Carter-Fenk, Kevin D.↗

DOE OSTI2023

A 10d construction of Euclidean axion wormholes in flat and AdS space

Euclidean wormhole geometries sourced by axions and dilatons are puzzling objects in quantum gravity. From one side of the wormhole to the other, the scalar fields traverse a few Planck lengths in field space and so corrections from the UV might potentially affect the consistency of the solution, even when the wormholes are large. Motivated by this, we carry out the first explicit 10d lifts of regular Euclidean axion wormholes. We start off with the lift of Giddings-Strominger wormholes in $\mathcal{N}$ = 8 Euclidean supergravity over a 6-torus to 10d type IIA supergravity and find the solution can be everywhere tuned into the parametrically controlled supergravity regime. Secondly, we construct explicit wormholes in AdS spaces and find them again to be under parametric control. We find the first wormhole solutions in massive type IIA on S 3 × S 3 and in type IIB on T 1,1 . The latter has an explicit holographic dual, and similar to the earlier constructions in AdS 5 × S 5 /$\mathbb{Z}$ k , the wormholes violate operator positivity since Tr(F ± $\star$ F) 2 < 0. This puzzle might arise from subtleties related to computing holographic n-point functions in the presence of multiple boundaries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1979

A hybridized method for computing high-Reynolds-number hypersonic flow about blunt bodies

A hybridized method for computing the flow about blunt bodies is presented. In this method the flow field is split into its viscid and inviscid parts. The forebody flow field about a parabolic body is computed. For the viscous solution, the Navier-Stokes equations are solved on orthogonal parabolic coordinates using explicit finite differencing. The inviscid flow is determined by using a Moretti type scheme in which the Euler equations are solved, using explicit finite differences, on a nonorthogonal coordinate system which uses the bow shock as an outer boundary. The two solutions are coupled along a common data line and are marched together in time until a converged solution is obtained. Computed results, when compared with experimental and analytical results, indicate the method works well over a wide range of Reynolds numbers and Mach numbers.

Weilmuenster, K. J.↗