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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Development of an upwind, finite-volume code with finite-rate chemistry

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.

Molvik, Gregory A.↗
NASA NTRS1989

A set of strongly coupled, upwind algorithms for computing flows in chemical nonequilibrium

Two new algorithms have been developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both take advantage of the benefits of upwind differencing, Total Variation Diminishing (TVD) techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithym is a time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a new temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms.

Molvik, Gregory A.↗
DOE OSTI2017

Implementation of a pressure correction term in the CTF sub-channel code

CTF [1] is a modernized and improved version of the legacy subchannel code, COBRA-TF [2], that is being jointly developed and maintained by Oak Ridge National Laboratory (ORNL) and North Carolina State University. The code was adopted by ORNL for use in the Consortium for Advanced Simulation of Light Water Reactors (CASL) in 2012 for aiding in addressing CASL challenge problems. Since that time, activities related to CTF have included implementing software quality assurance measures, implementing new features and models, performing validation and verification testing, establishing and supporting a CTF User Group, and developing the code for use in coupled applications [3, 4, 5]. CTF is applicable to single- and two-phase flows in light water reactor geometries at normal and accident operating conditions. The two-phase flow model consists of the six-equation two-phase flow model [6] augmented by equations for the droplet field and also includes appropriate source terms. This work focuses on the numerical stability of the six-equation two-phase flow model and is part of a recent eort to improve CTF capabilities for simulating flows in boiling nuclear reactors (BWRs). As it is of common knowledge among the thermodynamic community, the six-equation two-phase flow model is not strongly hyperbolic, meaning some of its eigenvalues are either not real or not distinct [7]. In a Cauchy sense and for an initial-value problem, strong hyperbolicity was found to be equivalent to well-posedness which ensures uniqueness of the solution in the space-time used. This concept is also of importance when designing high-order numerical methods and also when implementing boundary conditions that rely on real eigenvalues such as Riemann solvers. A tremendous amount of research is available in the literature on how to hyperbolize the six-equation two-phase flow model by adding ad hoc terms to the system of equations often referred to as virtual mass or interfacial pressure correction term. From a mathematical prospective, the main idea driving this approach is to add terms to the phasic momentum equation containing first-order partial derivatives of the unknowns to modify the Jacobian matrix and thus canceling the imaginary part of the eigenvalues.For this work it was chosen to implement a interfacial pressure correction (IPC) term on the same model as what was done for the CATHARE system code [8], that allows to recover a two-pressure formulation. In the following, the six-equation two-phase flow model is recalled along with the IPC term and its influence on the eigenvalues. Then, numerical results and convergence studies are presented for a water-faucet problem [9] at a pressure of 10 bar. Finally, conclusions and future work are addressed.

Delchini, Marco↗
DOE OSTI2017

Implementation of a Pressure Correction Term in the CTF Subchannel Code

CTF is a modernized and improved version of the legacy subchannel code COBRA-TF, being jointly developed and maintained by Oak Ridge National Laboratory (ORNL) and North Carolina State University. The code was adopted by ORNL for use in the Consortium for Advanced Simulation of Light Water Reactors (CASL) in 2012 to help address CASL challenge problems. Since that time, activities related to CTF have included implementing software quality assurance measures, implementing new features and models, performing validation and verification testing, establishing and supporting a CTF user group, and developing the code for use in coupled applications. CTF is applicable to single- and two-phase flows in light water reactor geometries at normal and accident operating conditions. The two-phase flow model consists of the six-equation two-phase flow model augmented by equations for the droplet field, and it also includes appropriate source terms. This work focuses on the numerical stability of the six-equation two-phase flow model and is part of a recent effort to improve CTF capabilities for simulating flows in boiling water reactors (BWRs). The six-equation two-phase flow model is not strongly hyperbolic, meaning that some of its eigenvalues are either not real or not distinct. In a Cauchy sense, and for an initial-value problem, strong hyperbolicity was found to be equivalent to well-posedness, which ensures the uniqueness of the solution in the space-time used. This concept is also of importance when designing high-order numerical methods and also when implementing boundary conditions that rely on real eigenvalues such as Riemann solvers. A tremendous amount of research is available in the literature on how to hyperbolize the six-equation two-phase flow model by adding ad hoc terms to the system of equations. Such terms are often referred to as virtual mass or interfacial pressure correction terms. From a mathematical perspective, this approach adds terms to the phasic momentum equation containing first-order partial derivatives of the unknowns to modify the Jacobian matrix, thus the imaginary part of the eigenvalues. For this work, an interfacial pressure correction (IPC) term on the same model as what was used for the CATHARE system code, is implemented in CTF. This allows for recovery of a two-pressure formulation. In the following, the six-equation two-phase flow model is recalled, along with the IPC term and its influence on the eigenvalues. Then, numerical results and convergence studies are presented for a water-faucet problem at a pressure of 10 bar. Finally, conclusions and future work are addressed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Shortening anomalies in supersymmetric theories

We present new anomalies in two-dimensional N = (2, 2) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from N = (2, 2) spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond N = (2; 2). These anomalies explain why the conformal manifolds of the K 3 and T 4 sigma models are not Kähler and do not factorize into chiral and twisted chiral moduli spaces and why there are no N = (2, 2) gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Information transfer with a twist

Holographic duals for CFTs compactified on a Riemann surface Σ with a twist are cast in the language of wedge holography. Σ starts as part of the field theory geometry in the UV and becomes part of the internal space in the IR. This allows to associate entanglement entropies with splits of the internal space in the IR geometry. Decomposing the internal space in the IR and geometrizing the corresponding subsystems separately leads to two interacting gravitational systems, similar to the intermediate holographic description in braneworld models. For Σ = T 2 the setups are used to model information transfer from a black hole to a gravitating bath. This leads to Page curves with a phase structure which precisely mirrors that in braneworld models. The transition from geometric to non-geometric entropies is also discussed for Σ = S 2 as a model for more general internal spaces in AdS/CFT.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

A space–angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement

In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introduced that is based on the solution of a generalized eigenvalue problem. The resulting numerical fluxes for the various possible cases where neighboring elements have an equal, higher or lower level of refinement in angle are derived based on tensor algebra and the resulting expressions have a very clear physical interpretation. The choice of discontinuous trial functions not only has the advantage of easing local refinement, it also facilitates the use of efficient sweep-based solvers due to decoupling of unknowns on a large scale thereby approaching the efficiency of discrete ordinates methods with local angular resolution. The approach is illustrated by a series of numerical experiments. Results show high orders of convergence for the scalar flux on angular refinement. The generalized Riemann upwinding procedure leads to stable and consistent solutions. Further the sweep-based solver performs well when used as a preconditioner for a Krylov method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Wedge dislocations, three-dimensional gravity, and the Riemann-Hilbert problem

An expression for the free energy of an arbitrary static distribution of wedge dislocations in a solid is proposed. It represents a Euclidean version of (1+2)-dimensional gravity interacting with an arbitrary number of point particles. It is shown that the solution of the equilibrium equations leads to the Cauchy problem for effective equations determining the form of dislocations, while the problem of finding a metric leads to the Riemann-Hilbert problem for a frame with an O(3) monodromy representation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxation terms to model heat and mass transfer and hence liquid–vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid–vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Rarefaction waves in van der Waals fluids with an arbitrary number of degrees of freedom

The isentropic expansion of an instantaneously and homogeneously heated foil is calculated using a 1D fluid model. The initial temperature and density are assumed to be in the vicinity of the critical temperature and solid density, respectively. The fluid is assumed to satisfy the van der Waals equation of state with an arbitrary number of degrees of freedom. Self-similar Riemann solutions are found. With a larger number of degrees of freedom f, depending on the initial dimensionless entropy $˜\atop{s_0}$, a richer family of foil expansion behaviors have been found. We calculate the domain in parameter space where these behaviors occur. In total, eight types of rarefaction waves are found and described.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2002

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Lorenzo, Carl F.↗
DOE OSTI2015

Relaxation approximations to second-order traffic flow models by high-resolution schemes

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Covariant constraints for generic massive gravity and analysis of its characteristics

We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates 5 degrees of freedom; this is also verified by a new and streamlined Hamiltonian description. Here, the constraint’s covariant expression permits computation of the model’s caustics. Although new features such as the dynamical Riemann tensor appear in the characteristic matrix, the model still exhibits the pathologies uncovered in earlier work: superluminality and likely acausalities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2018

Tetrahedral-Mesh Simulations of Shock-Turbulence Interaction

Despite decades of development of unstructured mesh methods, direct numerical simulations (DNS) of turbulent flows are still predominantly performed on structured or unstructured hexahedral meshes with high-order finite-difference methods, weighted essentially nonoscillatory (WENO) schemes, or hybrid schemes formed by their combinations. Tetrahedral meshes offer easy mesh generation and adaptation around complex geometries and the potential of an orientation-free grid that would benefit the isotropic nature of small-scale dissipation, as well as the solution accuracy of intermediate scales. To advance the state of the art of unstructured-mesh simulation capabilities for shock/turbulence interaction, DNS using pure tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method in this research. By its design, the CESE method is constructed based on a non-dissipative scheme and is a genuinely multidimensional numerical framework that is free from the use of an approximate Riemann-solver. The numerical framework also provides the ability to add numerical dissipation (the nondissipative scheme acts as the reference state like that of the reversible state in thermodynamics) when needed (with justification from mathematics/physics). The above-mentioned features along with the CESE method's consistent shock-capturing approach and strong enforcement of flux conservation in spacetime offers a novel method to accurately simulate turbulent flows and their interaction with shocks using tetrahedral meshes. Two canonical problems, namely, isotropic turbulence interaction with a normal shock and a Mach 2.9 turbulent boundary layer flow over a 24deg compression corner are investigated in this study. Computational results show reasonably good agreement with experimental data and results from structured-mesh, high-order simulations available in the literature. Successful validation of these canonical problems demonstrated here paves the way for future high-fidelity supersonic flow simulations involving complex-geometries.

Venkatachari, Balaji Shankar↗
NASA NTRS1980

A body-fitted conformal mapping method with grid-spacing control

It is demonstrated by analyses and by numerical illustrations that any arbitrarily prescribed contour, open or closed, can be mapped conformally onto a simple contour, such as a unit circle, using any arbitrarily prescribed distribution of scale factor of transformation. This flexibility of selecting a scale factor distribution on the contour is not in violation of the well-known Riemann's uniqueness theory for conformal mapping.

Wu, J. C.↗
NASA NTRS1974

Elementary solutions of coupled model equations in the kinetic theory of gases

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

Kriese, J. T.↗
NASA NTRS1995

Time accurate application of the MacCormack 2-4 scheme on massively parallel computers

Many recent computational efforts in turbulence and acoustics research have used higher order numerical algorithms. One popular method has been the explicit MacCormack 2-4 scheme. The MacCormack 2-4 scheme is second order accurate in time and fourth order accurate in space, and is stable for CFL's below 2/3. Current research has shown that the method can give accurate results but does exhibit significant Gibbs phenomena at sharp discontinuities. The impact of adding Jameson type second, third, and fourth order artificial viscosity was examined here. Category 2 problems, the nonlinear traveling wave and the Riemann problem, were computed using a CFL number of 0.25. This research has found that dispersion errors can be significantly reduced or nearly eliminated by using a combination of second and third order terms in the damping. Use of second and fourth order terms reduced the magnitude of dispersion errors but not as effectively as the second and third order combination. The program was coded using Thinking Machine's CM Fortran, a variant of Fortran 90/High Performance Fortran, and was executed on a 2K CM-200. Simple extrapolation boundary conditions were used for both problems.

Hudson, Dale A.↗
DOE OSTI2012

A non-linear discontinuous Petrov-Galerkin method for removing oscillations in the solution of the time-dependent transport equation

This paper describes a Non-Linear Discontinuous Petrov-Galerkin method and its application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The added dissipation is calculated at each node of the finite element mesh based on local behaviour of the transport solution on both the spatial and temporal axes of the problem. Thus a different dissipation is used in different elements. The magnitude of dissipation that is used is obtained from a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is implemented within a very general finite element Riemann framework. This makes it completely independent of choice of angular basis function allowing one to use different descriptions of the angular variation. Results show the non-linear scheme performs consistently well in demanding time-dependent multi-dimensional neutron transport problems. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗