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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 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

An implicit factored scheme for the compressible Navier-Stokes equations

An implicit finite difference scheme is developed for the numerical solution of the compressible Navier-Stokes equations in conservation-law form. The algorithm is second-order-time accurate, noniterative, and spatially factored. In order to obtain an efficient factored algorithm, the spatial cross-derivatives are evaluated explicitly. However, the algorithm is unconditionally stable and, although a three-time-level scheme, requires only two-time-levels of data storage. The algorithm is constructed in a 'delta' form (i.e., increments of the conserved variables and fluxes) that provides a direct derivation of the scheme and leads to an efficient computational algorithm. In addition, the delta form has the advantageous property of a steady-state (if one exists) independent of the size of the time step. Numerical results are presented for a two-dimensional shock boundary-layer interaction problem.

Beam, R. M.↗
NASA NTRS1988

Navier-Stokes calculations of scramjet-afterbody flowfields

Scramjet simulant-gas exhaust flows are computed using two-dimensional Navier-Stokes (NS) equations. The NS equations are solved using an implicit, upwind, finite-volume scheme, and the Reynolds stresses are modeled algebraically. The solutions are compared with experimental data where the freestream and the nozzle exhaust fluids are air. The NS equations for the flow, where the scramjet exhaust simulant gas is a mixture of Freon-12 and argon, are solved by an explicit, finite difference scheme. The results are compared with experimental data, and certain discrepancies are explained.

Baysal, O.↗
NASA NTRS2016

Correcting GOES-R Magnetometer Data for Stray Fields

Time-varying spacecraft magnetic fields or stray fields are a problem for magnetometer systems. While constant fields can be removed with zero offset calibration, stray fields are difficult to distinguish from ambient field variations. Putting two magnetometers on a long boom and solving for both the ambient and stray fields can be a good idea, but this gradiometer solution is even more susceptible to noise than a single magnetometer. Unless the stray fields are larger than the magnetometer noise, simply averaging the two measurements is a more accurate approach. If averaging is used, it may be worthwhile to explicitly estimate and remove stray fields. Models and estimation algorithms are provided for solar array, arcjet and reaction wheel fields.

Magnetometers↗
NASA NTRS1977

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Williams, S. D.↗
NASA NTRS1976

Electrostatic analysis of charge-coupled structures

An analysis is presented which is based upon a numerical solution of Gauss's law for the multiple dielectric semiconductor and electrode structure. The formulation resulted in a large set of equations, usually nonlinear, which were solved by an iterative scheme based upon the Gauss-Seidel method employing a relaxation parameter. Proper consideration of the nonlinearity of the space-charge in the semiconductor allowed convergent solutions which can give reasonable approximations to the channel potential profiles though not as good for estimating the space charge itself. The results of this work, which are three computer programs, are listed. None of the programs give the electric field explicitly as output data. However, when this information is desired, the programs can be expanded to include field estimations based on a polynominal fit to the potential field, or they may serve as subprograms for main programs dealing with general aspects of charge transfer.

Gassaway, J. D.↗
NASA NTRS1979

Analytical inversions in remote sensing of particle size distributions. IV - Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation

It is shown that the inverse analytical solutions, provided separately by Fymat and Box-McKellar, for reconstructing particle size distributions from remote spectral transmission measurements under the anomalous diffraction approximation can be derived using a cosine and a sine transform, respectively. Sufficient conditions of validity of the two formulas are established. Their comparison shows that the former solution is preferable to the latter in that it requires less a priori information (knowledge of the particle number density is not needed) and has wider applicability. For gamma-type distributions, and either a real or a complex refractive index, explicit expressions are provided for retrieving the distribution parameters; such expressions are, interestingly, proportional to the geometric area of the polydispersion.

Fymat, A. L.↗
NASA NTRS1994

Sloshing dynamics modulated angular momentum fluctuations actuated by gravity gradient acceleration associated with spacecraft slew motion

The mathematical formulation of orbital spacecraft sloshing dynamics for a partially filled cryogenic superfluid liquid helium II in a dewar container actuated by the gravity gradient acceleration associated with slew motion is studied. The Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) spacecraft is chosen as a practical example in this study. Explicit mathematical expressions which manage orbital galaxy gradient acceleration with slew motion which is acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinates and the solution of time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. This study discloses the capillary effect of sloshing dynamics governed liquid-vapor interface fluctuations, angular momentum and moment fluctuations of fluid system, and also buble mass center fluctuations driven by the gravity gradient acceleration associated with slew motion which affects the stability of the orbital spacecraft fluid system in a microgravity environment.

Hung, R. J.↗
NASA NTRS2004

Time-Extended Policies in Mult-Agent Reinforcement Learning

Reinforcement learning methods perform well in many domains where a single agent needs to take a sequence of actions to perform a task. These methods use sequences of single-time-step rewards to create a policy that tries to maximize a time-extended utility, which is a (possibly discounted) sum of these rewards. In this paper we build on our previous work showing how these methods can be extended to a multi-agent environment where each agent creates its own policy that works towards maximizing a time-extended global utility over all agents actions. We show improved methods for creating time-extended utilities for the agents that are both "aligned" with the global utility and "learnable." We then show how to crate single-time-step rewards while avoiding the pi fall of having rewards aligned with the global reward leading to utilities not aligned with the global utility. Finally, we apply these reward functions to the multi-agent Gridworld problem. We explicitly quantify a utility's learnability and alignment, and show that reinforcement learning agents using the prescribed reward functions successfully tradeoff learnability and alignment. As a result they outperform both global (e.g., team games ) and local (e.g., "perfectly learnable" ) reinforcement learning solutions by as much as an order of magnitude.

Tumer, Kagan↗
NASA NTRS2010

Incorporating User Preferences Within an Optimal Traffic Flow Management Framework

The effectiveness of future decision support tools for Traffic Flow Management in the National Airspace System will depend on two major factors: computational burden and collaboration. Previous research has focused separately on these two aspects without consideration of their interaction. In this paper, their explicit combination is examined. It is shown that when user preferences are incorporated with an optimal approach to scheduling, runtime is not adversely affected. A benefit-cost ratio is used to measure the influence of user preferences on an optimal solution. This metric shows user preferences can be accommodated without inordinately, negatively affecting the overall system delay. Specifically, incorporating user preferences will increase delays proportionally to increased user satisfaction.

Rios, Joseph Lucio↗
NASA NTRS1982

Engine dynamic analysis with general nonlinear finite element codes. II - Bearing element implementation, overall numerical characteristics and benchmarking

Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.

Padovan, J.↗
NASA NTRS1986

Magnetized thermal conduction fronts

The evolution of planar thermal conduction fronts in the presence of a dynamically weak, but otherwise self-consistent, magnetic field is considered. The field is assumed to be connected and untangled. In the diffusion limit for the thermal conductivity, these fronts exhibit self-similar behavior, even in the presence of a field. The role of the field is restricted to channeling the heat flux along its lines of force, and it enters into the problem as a dimensionless angle variable. 'Combing' (or opening) of insulating field lines by the evaporative flow is explicitly demonstrated. Unless the field is nearly perpendicular to the front normal in the hot gas, insulating effects are not profound. Self-similarity breaks down if the front becomes saturated, and under certain conditions magnetized saturated conduction fronts cannot propagate: the solution characteristics of the wave equation form caustics. The physical resolution is the advent of two-fluid (nonlocal) heating. Such Coulomb-heated fronts are expected to be relatively rare in typical astrophysical systems. The large-scale effects of a magnetic field on cloud evaporation in the interstellar medium are briefly discussed, and it is suggested that these fields preclude the presence of time-independent evaporative solutions. Thermal interfaces may then continue to evolve until radiative cooling halts their development; large tracts of warm 10,000 K gas may result.

Balbus, S. A.↗
NASA NTRS1987

Flow solution on a dual-block grid around an airplane

The compressible flow around a complex fighter-aircraft configuration (fuselage, cranked delta wing, canard, and inlet) is simulated numerically using a novel grid scheme and a finite-volume Euler solver. The patched dual-block grid is generated by an algebraic procedure based on transfinite interpolation, and the explicit Runge-Kutta time-stepping Euler solver is implemented with a high degree of vectorization on a Cyber 205 processor. Results are presented in extensive graphs and diagrams and characterized in detail. The concentration of grid points near the wing apex in the present scheme is shown to facilitate capture of the vortex generated by the leading edge at high angles of attack and modeling of its interaction with the canard wake.

Eriksson, Lars-Erik↗
NASA NTRS1991

Modified ICED-ALE method for astrogeophysical plasma flows

The Implicit-Continuous-Eulerian-Difference Mesh-Arbitrary-Lagrangian-Eulerian (ICED-ALE) algorithm of Brackbill and Pracht (1973) is modified for the study of astrophysical plasma flows in which dynamical effects are important. In the present study the general-energy-conservation law is directly applied to the iteration process, with the total (kinetic-, specific-internal-, and magnetic-) energy density being obtained implicitly at the end of the process. An example is computed in which the convergence speed of the latter method is substantially faster than that of the former. The initializing calculation, or explicit phase, in which the electric current density, magnetic diffusion of field, energy augmentation, and zero-order approximation of the flow velocity are given, is described. Consideration is given to the iteration process, or implicit phase, from which the exact Lagrangian solution for energy density, velocity, and a magnetic field is obtained.

Wu, S. T.↗
NASA NTRS1994

The real-world navigator

The success of every mobile robot application hinges on the ability to navigate robustly in the real world. The problem of robust navigation is separable from the challenges faced by any particular robot application. We offer the Real-World Navigator as a solution architecture that includes a path planner, a map-based localizer, and a motion control loop that combines reactive avoidance modules with deliberate goal-based motion. Our architecture achieves a high degree of reliability by maintaining and reasoning about an explicit description of positional uncertainty. We provide two implementations of real-world robot systems that incorporate the Real-World Navigator. The Vagabond Project culminated in a robot that successfully navigated a portion of the Stanford University campus. The Scimmer project developed successful entries for the AIAA 1993 Robotics Competition, placing first in one of the two contests entered.

Balabanovic, Marko↗
NASA NTRS1985

Generalized formulation of a class of explicit and implicit TVD schemes

A one parameter family of second order explicit and implicit total variation diminishing (TVD) schemes is reformulated so that a simpler and wider group of limiters is included. The resulting scheme can be viewed as a symmetrical algorithm with a variety of numerical dissipation terms that are designed for weak solutions of hyperbolic problems. This is a generalization of Roe and Davis's recent works to a wider class of symmetric schemes other than Lax-Wendroff. The main properties of the present class of schemes are that they can be implicit, and when steady state calculations are sought, the numerical solution is independent of the time step.

Yee, H. C.↗
NASA NTRS1987

Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory

A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.

Ramos, J. I.↗
NASA NTRS1990

A hybrid method for prediction of propeller performance

An analytical/computational code has been developed to predict the performance of advanced turboprop propellers. The method of solution is based on strip theory and conservation of linear and angular momenta applied to a control volume enclosing the propeller and its far wake. An iterative procedure is used to account for the induced axial and rotational velocities. Sectional aerodynamic coefficients are explicitly accounted for by thin airfoil theory and refinement of the results is obtained using a two-dimensional vortex panel method and Euler equations. The results obtained compare well with wind-tunnel data obtained for advanced propellers, such as the Hamilton Standard SR-2 and SR-7.

Takallu, M. A.↗
NASA NTRS1992

Acoustic analysis using numerical solutions of the Navier-Stokes equations

Numerical solutions of the time-dependent compressible Navier-Stokes equations are employed to analyze the unsteady features of jet flows which contribute to jet noise. The turbulent-mass flux spectra are examined in detail in the numerical analysis, and MacCormack's explicit finite difference algorithm is used to solve the governing equations. The computational grid is based on an axisymmetric jet with simple exponential stretching used to optimize the resolution of critical unsteady flow features. The time-varying numerical data are analyzed, and the time averages of the velocity and turbulence-intensity profiles are shown to agree with experimental data. Grid refinement and longer run times improved the prediction of the experimental mass-flux spectra. The numerical procedure can be extended to 3D jet-flow configurations to study the related 3D unsteady flow features.

Scott, James N.↗