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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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution of a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Canonical transformations and Hamiltonian evolutionary systems

In many Lagrangian field theories, one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different cases. These three cases depend on the specific dimensions of the vector bundle of the theory and the associated Hamiltonian differential operator. We also show how a canonical transformation transforms a Hamiltonian evolutionary system and its conservation laws. Finally, we illustrate these ideas with three examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Direct discrete simulation of the kinetic Landau-Fokker-Planck equation with an alternating external electromagnetic field

A stochastic method of simulation of Coulomb interaction is considered. The main idea of the method is to approximate the nonlinear Landau kinetic collision integral by the Boltzmann integral. In its realization, the method can be attributed to a wide class of Monte Carlo-type methods. It is easily combined with the existing particle methods used to simulate collisionless plasmas. This is important for simulation of the dynamics of both laboratory and space plasmas when the mean free path of plasma particles is comparable with the plasma inhomogeneity scale length. Illustrative examples of relaxation of two-temperature plasma being subject to a high-frequency alternating electric field are given, and differences from their classical description are considered. The method satisfies the conservation laws for the number of particles, momentum, and energy and is simple and efficient in implementation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2000

DRAGON Grid: A Three-Dimensional Hybrid Grid Generation Code Developed

Because grid generation can consume 70 percent of the total analysis time for a typical three-dimensional viscous flow simulation for a practical engineering device, payoffs from research and development could reduce costs and increase throughputs considerably. In this study, researchers at the NASA Glenn Research Center at Lewis Field developed a new hybrid grid approach with the advantages of flexibility, high-quality grids suitable for an accurate resolution of viscous regions, and a low memory requirement. These advantages will, in turn, reduce analysis time and increase accuracy. They result from an innovative combination of structured and unstructured grids to represent the geometry and the computation domain. The present approach makes use of the respective strengths of both the structured and unstructured grid methods, while minimizing their weaknesses. First, the Chimera grid generates high-quality, mostly orthogonal meshes around individual components. This process is flexible and can be done easily. Normally, these individual grids are required overlap each other so that the solution on one grid can communicate with another. However, when this communication is carried out via a nonconservative interpolation procedure, a spurious solution can result. Current research is aimed at entirely eliminating this undesired interpolation by directly replacing arbitrary grid overlapping with a nonstructured grid called a DRAGON grid, which uses the same set of conservation laws over the entire region, thus ensuring conservation everywhere. The DRAGON grid is shown for a typical film-cooled turbine vane with 33 holes and 3 plenum compartments. There are structured grids around each geometrical entity and unstructured grids connecting them. In fiscal year 1999, Glenn researchers developed and tested the three-dimensional DRAGON grid-generation tools. A flow solver suitable for the DRAGON grid has been developed, and a series of validation tests are underway.

Liou, Meng-Sing↗
DOE OSTI2017

Stochastic symplectic and multi-symplectic methods for nonlinear Schrödinger equation with white noise dispersion

We indicate that the nonlinear Schrödinger equation with white noise dispersion possesses stochastic symplectic and multi-symplectic structures. Based on these structures, we propose the stochastic symplectic and multi-symplectic methods, which preserve the continuous and discrete charge conservation laws, respectively. Moreover, we show that the proposed methods are convergent with temporal order one in probability. Numerical experiments are presented to verify our theoretical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Solutions and reductions for radiative energy transport in laser-heated plasma

A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential symmetries and to an integrable nonlinear model. Classical point symmetries, potential symmetries, and nonclassical symmetries are used to effect variable reductions and exact solutions. The simplest time-dependent solution is shown to be stable and relevant to a closed system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Bang-Bang Theorem for a Coupled ODE-PDE Control System

An optimal control problem for a system of one dimensional hyperbolic conservation laws is considered. The system is controlled through the boundary condition, which depends on the state of a nonlinear control system. It is proven that the problem has an optimal solution; moreover, it admits ε-optimal solutions generated by bang-bang controls. Bibliography: 8 titles. Illustrations: 1 figure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Action principle for Coulomb collisions in plasmas

In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural Lagrangian exists for the Landau-Fokker-Planck equation, an Eulerian variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order Lagrangians and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Principle of relative locality

We propose a deepening of the relativity principle according to which the invariant arena for nonquantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming energy-momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of energy-momentum space geometry, such as its curvature, torsion and nonmetricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of energy-momentum space with a metric compatible connection and constant curvature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Stability analysis of restricted non-static axial symmetry

This paper aims to investigate the instability of very restricted class of non-static axially symmetric spacetime with anisotropic matter configuration. The perturbation scheme is established for the Einstein field equations and conservation laws. The instability range in the Newtonian and post-Newtonian regions are explored by constructing the collapse equation in this scenario. It is found that the adiabatic index plays an important role in the stability analysis which depends upon the physical parameters i.e., energy density and anisotropic pressure of the fluid distribution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Group-invariant solutions of semilinear Schrödinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schrödinger equations in dimensions n ≠ 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schrödinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether's theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schrödinger equations involving an extra modulation term with a parameter m = 2−n ≠ 0 is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Plasma heating power dissipation in low temperature hydrogen plasmas

A theoretical framework for power dissipation in low temperature plasmas in corona equilibrium is developed. The framework is based on fundamental conservation laws and reaction cross sections and is only weakly sensitive to plasma parameters, e.g., electron temperature and density. The theory is applied to low temperature atomic and molecular hydrogen laboratory plasmas for which the plasma heating power dissipation to photon emission, ionization, and chemical potential is calculated. The calculated photon emission is compared to recent experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Non abelian hydrodynamics and heavy ion collisions

The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Dynamic of charged planar geometry in tilted and non-tilted frames

We investigate the dynamics of charged planar symmetry with an anisotropic matter field subject to a radially moving observer called a tilted observer. The Einstein-Maxwell field equations are used to obtain a relation between non-tilted and tilted frames and between kinematical and dynamical quantities. Using the Taub mass formalism and conservation laws, two evolution equations are developed to analyze the inhomogeneities in the tilted congruence. It is found that the radial velocity (due to the tilted observer) and the electric charge have a crucial effect on the inhomogeneity factor. Finally, we discuss the stability in the non-tilted frame in the pure diffusion case and examine the effects of the electromagnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

An efficient numerical method for computing dynamics of spin F = 2 Bose-Einstein condensates

In this paper, we extend the efficient time-splitting Fourier pseudospectral method to solve the generalized Gross-Pitaevskii (GP) equations, which model the dynamics of spin F = 2 Bose-Einstein condensates at extremely low temperature. Using the time-splitting technique, we split the generalized GP equations into one linear part and two nonlinear parts: the linear part is solved with the Fourier pseudospectral method; one of nonlinear parts is solved analytically while the other one is reformulated into a matrix formulation and solved by diagonalization. We show that the method keeps well the conservation laws related to generalized GP equations in 1D and 2D. We also show that the method is of second-order in time and spectrally accurate in space through a one-dimensional numerical test. We apply the method to investigate the dynamics of spin F = 2 Bose-Einstein condensates confined in a uniform/nonuniform magnetic field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A flux-splitting method for hyperbolic-equation system of magnetized electron fluids in quasi-neutral plasmas

A flux-splitting method is proposed for the hyperbolic-equation system (HES) of magnetized electron fluids in quasi-neutral plasmas. The numerical fluxes are split into four categories, which are computed by using an upwind method which incorporates a flux-vector splitting (FVS) and advection upstream splitting method (AUSM). The method is applied to a test calculation condition of uniformly distributed and angled magnetic lines of force. All of the pseudo-time advancement terms converge monotonically and the conservation laws are strictly satisfied in the steady state. The calculation results are compared with those computed by using the elliptic–parabolic-equation system (EPES) approach using a magnetic-field-aligned mesh (MFAM). Both qualitative and quantitative comparisons yield good agreements of results, indicating that the HES approach with the flux-splitting method attains a high computational accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Applications of Noether conservation theorem to Hamiltonian systems

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗