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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 73 records · Page 4
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NASA NTRS1988

Efficient implementation of essentially non-oscillatory shock capturing schemes, 2

Earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock capturing schemes is continued. A new simplified expression is provided for the ENO construction procedure based again on numerical fluxes rather than cell averages. Also considered are two improvements which are labeled ENO-LLF (local Lax-Friedrichs) and ENO-Roe, which yield sharper shock transitions, improved overall efficiency, and lower computational cost than previous implementation of the ENO schemes. Two methods of sharpening contact discontinuities, i.e., the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors used originally in the cell-average framework, are supplied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations. The implementation for nonlinear systems and multi-dimensions is given. Finally, many numerical examples, including a compressible shock turbulence interaction flow calculation, are given.

Shu, Chi-Wang↗
NASA NTRS1987

Shocked relativistic magnetohydrodynamic flows with application to pulsar winds

The time-dependent behavior of a shocked spherically symmetric relativistic fluid with tangential magnetic field is investigated, considering the case where the boundaries of the shocked fluid move at constant velocity so that self-similar solutions exist. The behavior of the fluid in the ultrarelativistic regime is compared to that in the nonrelativistic regime; there is a smooth transition between these limits. If a magnetic field is present, the magnetic pressure becomes increasingly important with distance from the shock wave; the gas pressure vanishes at the contact discontinuity that bounds the flow. Analytic expressions are given which describe the flow. The solutions can be applied to the evolution of shocked relativistic pulsar winds, which are probably observed as Crab-like supernova remnants. A model for the Crab Nebula, based on the steady-state model of Kennel and Coroniti (1984), indicates that sigma = 0.0016, where sigma is twice the ratio of magnetic to particle energy in the wind as measured in the fluid frame. This is about half the value suggested by Kennel and Coroniti and is much smaller than the value that might be expected for a pulsar wind.

Emmering, Robert T.↗
NASA NTRS1988

An artificial compression method for ENO schemes: The slope modification method

A simple and effective method of artificial compression is introduced. This method is based on a modification of the slopes of the ENO (essentially nonoscillatory) reconstruction and, with the help of suitable chosen parameters, greatly improves the resolution of the contact discontinuities. Numerical examples are provided to test the performance of the method and to give some suggestions as to the choice of the parameters.

Yang, Huanan↗
NASA NTRS1989

Efficient implementation of essentially non-oscillatory shock-capturing schemes. II

The present elaboration of essentially nonoscillatory (ENO) shock-capturing schemes proceeds with a novel, simplified expression for the ENO construction procedure having its basis in numerical fluxes rather than cell-averages. The ENO-local Lax-Friedrichs and ENO-Roe schemes introduced yield sharper shock transitions and greater overall accuracy than previous ENO-scheme implementations. Numerical fluxes and TVD Runge-Kutta time discretizations are used to apply Harten's subcell-resolution concept (1986) and Yang's artificial compression method to the current ENO schemes, in the interest of sharper contact discontinuities.

Shu, Chi-Wang↗
NASA NTRS1989

Numerical simulations of magnetized jets

The present axisymmetric numerical simulations of light hypersonic jets allow unmagnetized jets and jets carrying a dynamically important magnetic field to be contrasted. After decelerating a weakly magnetized jet through a series of weak, oblique shocks, a Mach disk and a strong annular shock are encountered near the outer edges of the contact discontinuity separating the shocked fluid from the shocked ambient gas. Upon passing the annular shock, the gas quickly expands and enters a backflowing cocoon surrounding the jet. The overall speed of advance of the jet is reduced; matter near the jet axis which passes through the terminal Mach disk accumulates in a plug, and gas is discharged into the cocoon by the intermittent shedding of vortices. When magnetic stresses dominate, however, the jet is rapidly decelerated via a Mach disk and strong annular shock.

Lind, Kevin R.↗
NASA NTRS1990

Comparison of several finite-difference methods

The present numerical study establishes that, with the MacCormack and 'two-four' methods, the solution accuracy obtainable in problems involving wave propagation, shock-wave and contact discontinuities, and viscous effects, will be strongly dependent on Courant number. The application of flux correction to the MacCormack and two-four methods is noted to significantly attenuate dispersion errors; the ensuing solutions capture the discontinuities in the shock-tube problem with improved accuracy and resolution, and are free of dispersion errors for the viscous Burgers' equation.

Biringen, S.↗
NASA NTRS1990

An artificial compression method for ENO schemes - The slope modification method

A simple and effective method of artificial compression is introduced. This method is based on a modification of the slopes of the END (essentially nonoscillatory) reconstruction and, with the help of suitable chosen parameters, greatly improves the resolution of the contact discontinuities. Numerical examples are provided to test the performance of the method and to give some suggestions as to the choice of the parameters.

Yang, Huanan↗
NASA NTRS1990

Cosmic-ray gradient measurements and modulation beyond the inner solar wind termination shock

Data provided by the IMP, Voyager, and Pioneer spacecraft for the cosmic-ray particles with E greater than 60 MeV show the existence of integral radial cosmic-ray-density gradients which were nearly constant from 1977 to 1982. In this paper, these measurements are explained using a model in which significant modulation occurs in the turbulent shocked plasma flow between the inner solar wind termination and the outer contact discontinuity separating the interstellar medium flow from the heliospheric plasma.

Quenby, J. J.↗
NASA NTRS1991

FLIP MHD - A particle-in-cell method for magnetohydrodynamics

The fluid-implicit-particle, or 'FLIP' method presently extended to 2D and 3D MHD flow incorporates a Lagrangian field representation and yields a grid magnetic Reynolds number of up to 16 while preserving contact continuities that retain the Galilean invariance of the MHD flow equations. Analytical arguments and numerical examples demonstrate the conservation of mass, momentum, magnetic flux, and energy; 2D calculation results for the illustrative cases of contact discontinuity convection, Rayleigh-Taylor unstable flow.

Brackbill, J. U.↗
NASA NTRS1991

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗
NASA NTRS1992

A fast implicit upwind solution algorithm for three-dimensional unstructured dynamic meshes

A fast implicit upwind algorithm for the solution of the time-dependent Euler equations is presented for aerodynamic analysis involving unstructured dynamic meshes. The spatial discretization of the scheme is based on the upwind approach of Roe, referred to as flux-difference splitting (FDS). The FDS approach is naturally dissipative and captures shock waves and contact discontinuities sharply. The temporal discretization of the scheme involves an implicit time-integration using a two-sweep Gauss-Seidel relaxation procedure. The procedure is computationally efficient for either steady or unsteady flow problems. A detailed description is given of the implicit upwind solution algorithm along with results which assess the capability. The results are presented for the NACA 0012 airfoil and for the Boeing 747 aircraft. The 747 geometry includes the fuselage, wing, horizontal and vertical tails, under-wing pylons, and flow-through engine nacelles. Euler solutions for the 747 aircraft on an unstructured tetrahedral mesh containing approximately 100,000 cells were obtained to engineering accuracy in less than one hour CPU time on a Cray-2 computer.

Batina, John T.↗
NASA NTRS1992

A test suite for magnetohydrodynamical simulations

A collection is presented of MHD problems that will provide researchers who have interests in modeling MHD phenomena with a battery of tests (a 'test suite') for calibrating their numerical algorithms. Use of these tests will provide a common reference for comparison of different numerical MHD algorithms. The test suite includes both 1D and 2D problems. Taken together, these problems test the abilities of a numerical method to propagate accurately all of the MHD wave families in moving and stationary media, to capture MHD shocks and contact discontinuities, and to model accurately Lorentz force terms in multiple dimensions. An example solution of each test problem is presented. Diagnostic convergence-testing procedures that provide a quantitative evaluation of MHD algorithms are demonstrated.

Stone, James M.↗
NASA NTRS1993

Numerical simulations of bent, disrupted radio jets

We present preliminary results from three-dimensional hydrodynamical simulations designed to investigate the physics of jet bending and disruption. The specific scenario considered here involves a mildly supersonic jet crossing a contact discontinuity at the interface between the interstellar medium (ISM) and the intercluster medium (ICM) and then encountering a cross-wind in the ICM. The resultant morphologies show many of the features observed in radio sources including jet flaring, bending, and extended tails.

Loken, Chris↗
NASA NTRS1991

Shock waves and the Ffowcs Williams-Hawkings equation

The expansion of the double divergence of the generalized Lighthill stress tensor, which is the basis of the concept of the role played by shock and contact discontinuities as sources of dipole and monopole sound, is presently applied to the simplest transonic flows: (1) a fixed wing in steady motion, for which there is no sound field, and (2) a hovering helicopter blade that produces a sound field. Attention is given to the contribution of the shock to sound from the viewpoint of energy conservation; the shock emerges as the source of only the quantity of entropy.

Isom, Morris P.↗
NASA NTRS1994

Practical formulation of a positively conservative scheme

Approximate Riemann solvers have been highly successful for computing the Euler/Navier-Stokes equations, but linearized Riemann solvers are known to fail occasionally by predicting non-physical states with negative density or internal energy. Positively conservative schemes, in contrast, guarantee physical solutions from realistic input. The Harten-Lax-van Leer-Einfeldt (HLLE) scheme is a typical example of a positively conservative scheme. However, the HLLE scheme is highly dissipative at contact discontinuities and shear layers and thus it is not applicable to practicle simulations. An existing modification to the HLLE scheme, known as HLLEM, enhances the resolution to that of the Roe scheme. However, this modification violates the positivity of density and internal energy. Precise derivation of the modification yields a quatratic inequality and thus requires a case-by-case treatment. This Note describes a new, modified HLLE scheme that satisfies the positively conservative condition approximately. Sample computationa are included to demonstrate the resolution and the robustness of the scheme.

Obayashi, Shigeru↗
NASA NTRS1995

Radio jet propagation and wide-angle tailed radio sources in merging galaxy cluster environments

The intracluster medium (ICM) within merging clusters of galaxies is likely to be in a violent or turbulent dynamical state which may have a significant effect on the evolution of cluster radio sources. We present results from a recent gas + N-body simulation of a cluster merger, suggesting that mergers can result in long-lived, supersonic bulk flows, as well as shocks, within a few hundred kiloparsecs of the core of the dominant cluster. These results have motivated our new two-dimensional and three-dimensional simulations of jet propagation in such environments. The first set of simulations models the ISM/ICM transition as a contact discontinuity with a strong velocity shear. A supersonic (M(sub j) = 6) jet crossing this discontinuity into an ICM with a transverse, supersonic wind bends continuously, becomes 'naked' on the upwind side, and forms a distended cocoon on the downwind side. In the case of a mildly supersonic jet (M(sub j) = 3), however, a shock is driven into the ISM and ISM material is pulled along with the jet into the ICM. Instabilities excited at the ISM/ICM interface result in the jet repeatedly pinching off and reestablishing itself in a series of 'disconnection events.' The second set of simulations deals with a jet encountering a shock in the merging cluster environment. A series of relatively high-resolution two-dimensional calculations is used to confirm earlier analysis predicting that the jet will not disrupt when the jet Mach number is greater than the shock Mach number. A jet which survives the encounter with the shock will decrease in radius and disrupt shortly thereafter as a result of the growth of Kelvin-Helmholtz instabilities. We also find, in disagreement with predictions, that the jet flaring angle decreases with increasing jet density. Finally, a three-dimensional simulation of a jet crossing an oblique shock gives rise to a morphology which resembles a wide-angle tailed radio source with the jet flaring at the shock and disrupting to form a long, turbulent tail which is dragged downstream by the preshock wind.

Loken, Chris↗
NASA NTRS1995

Efficient implementation of weighted ENO schemes

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher and Chan. It was shown by Liu et al. that WENO schemes constructed from the r-th order (in L1 norm) ENO schemes are (r+1)-th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of the approximation, which results in a 5-th order WENO scheme for the case r = 3, instead of the 4-th order with the original smoothness measurement by Liu et al. This 5-th order WENO scheme is as fast as the 4-th order WENO scheme of Liu et al., and both schemes are about twice as fast as the 4-th order ENO schemes on vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest computing the weights from pressure and entropy instead of the characteristic values to simplify the costly characteristic procedure. The resulting WENO schemes are about twice as fast as the WENO schemes using the characteristic decompositions to compute weights, and work well for problems which do not contain strong shocks or strong reflected waves. We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent. Many numerical tests, including the 1D steady state nozzle flow problem and 2D shock entropy wave interaction problem, are presented to demonstrate the remarkable capability of the WENO schemes, especially the WENO scheme using the new smoothness measurement, in resolving complicated shock and flow structures. We have also applied Yang's artificial compression method to the WENO schemes to sharpen contact discontinuities.

Jiang, Guang-Shan↗