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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Chakravarthy, Sukumar R.↗
NASA NTRS1991

Artificial Dissipation In Computations Of Hypersonic Flows

Four artificial-dissipation mathematical models introduced to suppress spurious numerical oscillations in finite-difference computations of hypersonic external flows. Models tested for their effects in capturing details of shocks in hypersonic flows about bodies of various shapes.

Yoon, S.↗
NASA NTRS1991

Entropy-Based Approach To Nonlinear Stability

NASA technical memorandum suggests schemes for numerical solution of differential equations of flow made more accurate and robust by invoking second law of thermodynamics. Proposes instead of using artificial viscosity to suppress such unphysical solutions as spurious numerical oscillations and nonlinear instabilities, one should formulate equations so that rate of production of entropy within each cell of computational grid be nonnegative, as required by second law.

Merriam, Marshal L.↗
NASA NTRS1992

Finite element computation of incompressible flows

Among the solution techniques presented for FEM computation of incompressible flows are stabilized formulations designed to prevent the numerical oscillations that may be generated by (1) the presence of dominant advection terms in the governing equations, or (2) the failure to use an acceptable combination of interpolation functions to represent velocity and pressure fields. It is shown that the space-time formulation, in conjunction with the Galerkin-least squares methods, can be used to compute steady incompressible flows involving moving boundaries and interfaces; it is recommended that iteration methods be used to reduce the associated computational costs.

Tezduyar, T. E.↗
NASA NTRS1994

New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems

A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity.

Chang, Sin-Chung↗
NASA NTRS1995

An investigation of bleed configurations and their effect on shock wave/boundary layer interactions

The design of high efficiency supersonic inlets is a complex task involving the optimization of a number of performance parameters such as pressure recovery, spillage, drag, and exit distortion profile, over the flight Mach number range. Computational techniques must be capable of accurately simulating the physics of shock/boundary layer interactions, secondary corner flows, flow separation, and bleed if they are to be useful in the design. In particular, bleed and flow separation, play an important role in inlet unstart, and the associated pressure oscillations. Numerical simulations were conducted to investigate some of the basic physical phenomena associated with bleed in oblique shock wave boundary layer interactions that affect the inlet performance.

Hamed, Awatef↗
NASA NTRS1999

Implicit and Multigrid Method for Ideal Multigrid Convergence: Direct Numerical Simulation of Separated Flow Around NACA 0012 Airfoil

Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.

Liu, Chao-Qun↗
NASA NTRS2001

Microphysics, Radiation and Surface Processes in the Goddard Cumulus Ensemble (GCE) Model

The response of cloud systems to their environment is an important link in a chain of processes responsible for monsoons, frontal depression, El Nino Southern Oscillation (ENSO) episodes and other climate variations (e.g., 30-60 day intra-seasonal oscillations). Numerical models of cloud properties provide essential insights into the interactions of clouds with each other, with their surroundings, and with land and ocean surfaces. Significant advances are currently being made in the modeling of rainfall and rain-related cloud processes, ranging in scales from the very small up to the simulation of an extensive population of raining cumulus clouds in a tropical- or midlatitude-storm environment. The Goddard Cumulus Ensemble (GCE) model is a multi-dimensional nonhydrostatic dynamic/microphysical cloud resolving model. It has been used to simulate many different mesoscale convective systems that occurred in various geographic locations. In this paper, recent GCE model improvements (microphysics, radiation and surface processes) will be described as well as their impact on the development of precipitation events from various geographic locations. The performance of these new physical processes will be examined by comparing the model results with observations. In addition, the explicit interactive processes between cloud, radiation and surface processes will be discussed.

Tao, Wei-Kuo↗
NASA NTRS2013

Implicit Coupling Approach for Simulation of Charring Carbon Ablators

This study demonstrates that coupling of a material thermal response code and a flow solver with nonequilibrium gas/surface interaction for simulation of charring carbon ablators can be performed using an implicit approach. The material thermal response code used in this study is the three-dimensional version of Fully Implicit Ablation and Thermal response program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting Navier-Stokes equations using Data Parallel Line Relaxation method. Coupling between the material response and flow codes is performed by solving the surface mass balance in flow solver and the surface energy balance in material response code. Thus, the material surface recession is predicted in flow code, and the surface temperature and pyrolysis gas injection rate are computed in material response code. It is demonstrated that the time-lagged explicit approach is sufficient for simulations at low surface heating conditions, in which the surface ablation rate is not a strong function of the surface temperature. At elevated surface heating conditions, the implicit approach has to be taken, because the carbon ablation rate becomes a stiff function of the surface temperature, and thus the explicit approach appears to be inappropriate resulting in severe numerical oscillations of predicted surface temperature. Implicit coupling for simulation of arc-jet models is performed, and the predictions are compared with measured data. Implicit coupling for trajectory based simulation of Stardust fore-body heat shield is also conducted. The predicted stagnation point total recession is compared with that predicted using the chemical equilibrium surface assumption

Ablation↗
NASA NTRS2016

Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

Mazaheri, Alireza↗
DOE OSTI2023

Symmetrized Drude Oscillator Force Fields Improve Numerical Performance of Polarizable Molecular Dynamics

Drude oscillator potentials are a popular and computationally efficient class of polarizable models that represent each polarizable atom as a positively charged Drude core harmonically bound to a negatively charged Drude shell. Here we show that existing force fields that place all non-Coulomb forces on the Drude core and none on the shell inadvertently couple the dipole to non-Coulombic forces. This introduces errors where interactions with neutral particles can erroneously induce atomic polarization, leading to spurious polarizations in the absence of an electric field, exacerbating violations of equipartition in the employed Carr–Parinello scheme. A suitable symmetrization of the interaction potential that correctly splits the force between the Drude core and shell can correct this shortcoming, improving the stability and numerical performance of Drude oscillator-based simulations. The symmetrization procedure is straightforward and only requires the rescaling of a few force field parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Unsteady separated boundary layer in a transonic diffuser flow with self-excited oscillations

A numerical investigation of two-dimensional unsteady boundary layer in a transonic diffuser flow with self-excited oscillations and strong flow separation by solving the compressible, Reynolds-averaged, thin-layer Navier-Stokes equations with two-equations turbulence model is described. Three different meshes with constant streamwise mesh distribution and varying vertical mesh distribution were used. Results obtained indicate that a refinement of mesh studied here has minimal effect on the mean boundary layer flow but significantly increases the amplitude of oscillation of all flow variables. Comparisons of unsteady wall pressure, velocity profile, terminal shock, and separation pocket among computations and with experiment are presented.

Hsieh, T.↗
NASA NTRS2004

Numerical Simulation of the Oscillations in a Mixer: An Internal Aeroacoustic Feedback System

The space-time conservation element and solution element method is employed to numerically study the acoustic feedback system in a high temperature, high speed wind tunnel mixer. The computation captures the self-sustained feedback loop between reflecting Mach waves and the shear layer. This feedback loop results in violent instabilities that are suspected of causing damage to some tunnel components. The computed frequency is in good agreement with the available experimental data. The physical phenomena are explained based on the numerical results.

Jorgenson, Philip C. E.↗
NASA NTRS1989

Numerical experiments on the oscillations of a rotating, axisymmetric galaxy

Modes of oscillation in six rotating, axisymmetric N-body systems are studied in a sequence of self-consistent, three-dimensional numerical experiments. The experimental systems are realizations of theoretical models of galaxies which are stellar-dynamical counterparts of uniformly rotating polytropes of index equal to 0.5. The ratio of the rotational kinetic energy to the gravitational potential energy ranges from 0.13 to 0.20. The systems oscillate axisymmetrically; the oscillations are interpreted as superpositions of a mode of radial pulsation and a Kelvin-like mode of oscillation. The experimental frequencies of these modes agree very well with theoretical predictions. When these modes are suppressed, the states of the experimental systems are very steady. The systems are dynamically unstable with respect to a toroidal mode when the ratio of the rotational kinetic energy to the gravitational potential energy exceeds a value lying between 0.16 and 0.17.

Miller, R. H.↗
NASA NTRS1991

Numerical prediction of turbulent oscillating flow and associated heat transfer

A crucial point for further development of engines is the optimization of its heat exchangers which operate under oscillatory flow conditions. It has been found that the most important thermodynamic uncertainties in the Stirling engine designs for space power are in the heat transfer between gas and metal in all engine components and in the pressure drop across the heat exchanger components. So far, performance codes cannot predict the power output of a Stirling engine reasonably enough if used for a wide variety of engines. Thus, there is a strong need for better performance codes. However, a performance code is not concerned with the details of the flow. This information must be provided externally. While analytical relationships exist for laminar oscillating flow, there has been hardly any information about transitional and turbulent oscillating flow, which could be introduced into the performance codes. In 1986, a survey by Seume and Simon revealed that most Stirling engine heat exchangers operate in the transitional and turbulent regime. Consequently, research has since focused on the unresolved issue of transitional and turbulent oscillating flow and heat transfer. Since 1988, the University of Minnesota oscillating flow facility has obtained experimental data about transitional and turbulent oscillating flow. However, since the experiments in this field are extremely difficult, lengthy, and expensive, it is advantageous to numerically simulate the flow and heat transfer accurately from first principles. Work done at the University of Minnesota on the development of such a numerical simulation is summarized.

Koehler, W. J.↗
NASA NTRS1976

Oscillations and stability of numerical solutions of the heat conduction equation

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Kozdoba, L. A.↗