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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport Equations

We present a positive- and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on the well-known line source benchmark problem with the usual uniform material medium as well as a medium composed of different materials that are arranged in a checkerboard pattern. We also tested the scheme on a Riemann problem with a nonuniform material medium. The observed order of space-time accuracy of the proposed scheme is reported.

nite difference methods↗
DOE OSTI2018

Local bounds preserving stabilization for continuous Galerkin discretization of hyperbolic systems

The objective of this paper is to present a local bounds preserving stabilized finite element scheme for hyperbolic systems on unstructured meshes based on continuous Galerkin (CG) discretization in space. A CG semi-discrete scheme with low order artificial dissipation that satisfies the local extremum diminishing (LED) condition for systems is used to discretize a system of conservation equations in space. The low order artificial diffusion is based on approximate Riemann solvers for hyperbolic conservation laws. In this case we consider both Rusanov and Roe artificial diffusion operators. In the Rusanov case, two designs are considered, a nodal based diffusion operator and a local projection stabilization operator. The result is a discretization that is LED and has first order convergence behavior. To achieve high resolution, limited antidiffusion is added back to the semi-discrete form where the limiter is constructed from a linearity preserving local projection stabilization operator. The procedure follows the algebraic flux correction procedure usually used in flux corrected transport algorithms. To further deal with phase errors (or terracing) common in FCT type methods, high order background dissipation is added to the antidiffusive correction. The resulting stabilized semi-discrete scheme can be discretized in time using a wide variety of time integrators. Numerical examples involving nonlinear scalar Burgers equation, and several shock hydrodynamics simulations for the Euler system are considered to demonstrate the performance of the method. In conclusion, for time discretization, Crank–Nicolson scheme and backward Euler scheme are utilized.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

Simple inequalities for the Riemann problem for a Hamilton-Jacobi equation in N space dimension when neither the initial data nor the Hamiltonian need be convex (or concave) are presented. The initial data is globally continuous, affine in each orthant, with a possible jump in normal derivative across each coordinate plane, x sub i = 0. The inequalities become equalities wherever a maxmin equals a minmax and thus an exact closed form solution to this problem is then obtained.

Osher, Stanley↗
NASA NTRS1994

Response of a grounded dielectric slab to an impulse line source using leaky modes

This paper describes how expansions in leaky (or improper) modes may be used to represent the continuous spectrum in an open radiating waveguide. The technique requires a thorough knowledge of the life history of the improper modes as they migrate from improper to proper Riemann surfaces. The method is illustrated by finding the electric field resulting from an impulsively forced current located in the free space above a grounded dielectric slab.

DIELECTRIC SLABS↗
NASA NTRS1995

New higher-order Godunov code for modelling performance of two-stage light gas guns

A new quasi-one-dimensional Godunov code for modeling two-stage light gas guns is described. The code is third-order accurate in space and second-order accurate in time. A very accurate Riemann solver is used. Friction and heat transfer to the tube wall for gases and dense media are modeled and a simple nonequilibrium turbulence model is used for gas flows. The code also models gunpowder burn in the first-stage breech. Realistic equations of state (EOS) are used for all media. The code was validated against exact solutions of Riemann's shock-tube problem, impact of dense media slabs at velocities up to 20 km/sec, flow through a supersonic convergent-divergent nozzle and burning of gunpowder in a closed bomb. Excellent validation results were obtained. The code was then used to predict the performance of two light gas guns (1.5 in. and 0.28 in.) in service at the Ames Research Center. The code predictions were compared with measured pressure histories in the powder chamber and pump tube and with measured piston and projectile velocities. Very good agreement between computational fluid dynamics (CFD) predictions and measurements was obtained. Actual powder-burn rates in the gun were found to be considerably higher (60-90 percent) than predicted by the manufacturer and the behavior of the piston upon yielding appears to differ greatly from that suggested by low-strain rate tests.

Bogdanoff, D. W.↗
DOE OSTI2016

Some issues in the simulation of two-phase flows: The relative velocity

In this paper we compare numerical approximations for solving the Riemann problem for a hyperbolic two-phase flow model in two-dimensional space. The model is based on mixture parameters of state where the relative velocity between the two-phase systems is taken into account. This relative velocity appears as a main discontinuous flow variable through the complete wave structure and cannot be recovered correctly by some numerical techniques when simulating the associated Riemann problem. Simulations are validated by comparing the results of the numerical calculation qualitatively with OpenFOAM software. Simulations also indicate that OpenFOAM is unable to resolve the relative velocity associated with the Riemann problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Flux-difference split parabolized Navier-Stokes algorithm for non-equilibrium chemically reacting flows

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rather than the steady Riemann problem, is solved. The algorithm allows either a second or an approximately third-order accurate upwind treatment of the convection terms by employing the unsteady approximate Riemann solver of Roe. The source terms of the species transport equations are treated in either an explicit or implicit manner, and the species diffusion terms are modeled with either a Fickian or a multicomponent model. A validation of the algorithm is performed by comparing computational results with the 2-D Mach 14, 15 degree compression-corner data of Holden. The three-dimensional capability of the algorithm is demonstrated by computing Mach 2.7 flow over a swept wedge scramjet fuel injector, and three-dimensional reacting flow capability is demonstrated by a computing a shock-jet interaction concept for mixing and combustion enhancement.

White, J. A.↗
NASA NTRS1991

The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations

Simple inequalities are presented for the viscosity solution of a Hamilton-Jacobi equation in N space dimensions when neither the initial data nor the Hamiltonian need be convex (or concave). The initial data are uniformly Lipschitz and can be written as the sum of a convex function in a group of variables and a concave function in the remaining variables, therefore including the nonconvex Riemann problem. The inequalities become equalities wherever a 'maxmin' equals a 'minmax', and thus a representation formula for this problem is obtained, generalizing the classical Hopi formulas.

Bardi, Martino↗
DOE OSTI2013

An angularly refineable phase space finite element method with approximate sweeping procedure

An angularly refineable phase space finite element method is proposed to solve the neutron transport equation. The method combines the advantages of two recently published schemes. The angular domain is discretized into small patches and patch-wise discontinuous angular basis functions are restricted to these patches, i.e. there is no overlap between basis functions corresponding to different patches. This approach yields block diagonal Jacobians with small block size and retains the possibility for S{sub n}-like approximate sweeping of the spatially discontinuous elements in order to provide efficient preconditioners for the solution procedure. On the other hand, the preservation of the full FEM framework (as opposed to collocation into a high-order S{sub n} scheme) retains the possibility of the Galerkin interpolated connection between phase space elements at arbitrary levels of discretization. Since the basis vectors are not orthonormal, a generalization of the Riemann procedure is introduced to separate the incoming and outgoing contributions in case of unstructured meshes. However, due to the properties of the angular discretization, the Riemann procedure can be avoided at a large fraction of the faces and this fraction rapidly increases as the level of refinement increases, contributing to the computational efficiency. In this paper the properties of the discretization scheme are studied with uniform refinement using an iterative solver based on the S{sub 2} sweep order of the spatial elements. The fourth order convergence of the scalar flux is shown as anticipated from earlier schemes and the rapidly decreasing fraction of required Riemann faces is illustrated. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Gauss-Bonnet Lagrangian GlnG and cosmological exact solutions

For the Lagrangian L=GlnG where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedmann models using a state-finder parametrization. Further we show that among all Lagrangians F(G) this L is the only one not having the form G{sup r} with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R) theories in two-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n=4.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

An elliptic regularity theorem for fractional partial differential operators

We present and prove a version of the elliptic regularity theorem for partial differential equations involving fractional Riemann–Liouville derivatives. In this case, regularity is defined in terms of Sobolev spaces H{sup s}(X): if the forcing of a linear elliptic fractional PDE is in one Sobolev space, then the solution is in the Sobolev space of increased order corresponding to the order of the derivatives. We also mention a few applications and potential extensions of this result.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Fivebranes and 3-manifold homology

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that vebrane compacti cations provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N = 2 theory T[M 3 ] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categori cation of Chern-Simons partition function. Finally, some of the new key elements include the explicit form of the S-transform and a novel connection between categori cation and a previously mysterious role of Eichler integrals in Chern-Simons theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

High resolution finite volume methods on arbitrary grids via wave propagation

A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.

Leveque, Randall J.↗
NASA NTRS1990

Domain decomposition methods in aerodynamics

Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.

Venkatakrishnan, V.↗
NASA NTRS1992

Cosmic curvature and condensation

It is shown that the universe may consist of a patchwork of domains with different Riemann curvature constants k = 0, +/-1. Features of a phase transition in which flat space breaks up in a transition 2k0 - k(-) + k(+) with initial scale factors R(-) = R(+) are postulated and explored. It is shown that such a transition is energetically permitted, has the equivalent of a Curie temperature, and can lead in a natural way to the formation of voids and galaxies. It is predicted that, if the ambient universe on average is well fitted by a purely k(-) space, with only occasional domains of k(+) containing galaxies, a density parameter of (A(z sub c + 1)) super -1 should be expected, where z sub c represents the redshift of the earliest objects to have condensed, and A takes on values ranging from about 5 to 3. Present observations of quasars would suggest a density of about 0.03 or 0.05, respectively, but it could be lower if earlier condensation took place.

Harwit, Martin↗
DOE OSTI2018

Anomalies of duality groups and extended conformal manifolds

A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields. The extended space $\cal N$ forms a bundle over $\cal M$ with fiber $\cal F$, and the topology of the bundle is determined by the anomaly. For example, the ${\cal G}=SL(2,\mathbb{Z})$ duality of the 4d Maxwell theory has an anomaly, and the space ${\cal F}=S^1$ for the gravitational theta-angle is nontrivially fibered over ${\cal M}=\mathbb{H}/SL(2,\mathbb{Z})$. We will explain a simple method to determine the anomaly when the 4d theory is obtained by compactifying a 6d theory on a Riemann surface in terms of the anomaly polynomial of the parent 6d theory. Our observations resolve an apparent contradiction associated with the global structure of the Kahler potential on the space of exactly marginal couplings of supersymmetric theories.

59 BASIC BIOLOGICAL SCIENCES↗