Waves in bars of mechanically unstable materials.
Waves in bars of mechanically unstable materials, discussing differential equation of motion, jump conditions, wave velocity and application to annealed aluminum
ALUMINUM↗
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Reduced shock relations in magnetohydrodynamics.
Jump conditions across MHD shock waves, reducing relations to identities applicable to nonequilibrium situations
Wilkerson, T. D.↗
Ballistic wake of turbulence in a plasma shock wave.
Ballistic wake structure and jump conditions for plane plasma shock waves with electrostatic turbulence
Krall, N. A.↗
A program for identification of linear systems
A program has been written for the identification of parameters in certain linear systems. These systems appear in biomedical problems, particularly in compartmental models of pharmacokinetics. The method presented here assumes that some of the state variables are regularly modified by jump conditions. This simulates administration of drugs following some prescribed drug regime. Parameters are identified by a least-square fit of the linear differential system to a set of experimental observations. The method is especially suited when the interval of observation of the system is very long.
Buell, J.↗
Comparison of characteristics and shock capturing methods with application to the space shuttle vehicle.
A critical appraisal is presented of a method-of-characteristics (MOC) and a shock-capturing technique (SCT) for calculating three-dimensional supersonic flow. Detailed comparisons are made for pointed and blunt-nosed bodies with a thick delta wing at angles of attack from 5 to 15 deg. The results show excellent agreement between the methods and with experiment. It is established that the SCT code yields accurate shock locations and jump conditions. The SCT code typically requires about three times as many mesh points as the MOC code in order to resolve the bow shock, but the total computation time is about the same. On a point for point basis, the SCT code is about four times faster than the MOC code.
Rakich, J. V.↗
The earth's bow shock in an oblique interplanetary field.
The pressure, magnetic field, temperature, particle density, and stream velocity throughout the magnetosheath have been calculated in the plane containing the interplanetary field and solar wind velocity vector for various orientations of the interplanetary magnetic field and various assumed ratios of specific heats of the compressed solar wind. Jump conditions at the bow shock gave initial conditions in the shocked plasma from which the appropriate hydromagnetic equations (for blunt bodies in the subsonic region near the subsolar point and for the method of characteristics in the supersonic region back in the tail) were integrated numerically back to the surface of the magnetosphere. Explicit consideration of the magnetic field shows that a net asymmetrical force on the magnetopause produces a side force, or 'lift' in addition to the well-known drag on the magnetosphere.
Shen, W.-W.↗
Dynamics of the inverse pinch.
Experiments are performed on the plasma produced in a large inverse pinch using argon with no applied magnetic fields or preheating. A direct observation is made of the precursor ionization which initially raises the electron temperature and electrical conductivity. Calculations show that most of the mass is entrained in the current sheet, but that less than complete sweeping occurs at the lower velocities. The shock which is embedded in the current sheet closely resembles an ordinary gasdynamic shock. Consideration of the shock jump condition derived from the induction equation is shown to determine the frequent inability of the shock to separate from the current sheet.
Weisbach, M. F.↗
Theoretical analysis of a rotating two-phase detonation in liquid rocket motors.
A nonlinear analysis to study tangential mode shock instabilities in a thin annular chamber is carried out by employing a one dimensional two phase detonation wave as a reaction model. It is assumed that phase change and reaction take place only within the wave, which is treated as a discontinuity. The annulus is unrolled and the flow is considered as two dimensional with the coordinate system fixed on the wave front. Between waves, the flow is assumed to be isentropic with no interaction between droplets and burned gases. Jump conditions across the wave are solved for two phase flow. The average pressure along the injection plate is related to the design chamber pressure by the use of overall conservation equations. The wave strength is written in terms of the design parameters of the chamber. The results compare favorably with existing experiments. Finally, the effects of drop size on the wave strength are discussed and a simple criterion which sets the lower limit of validity for this strong wave analysis, is presented.
Shen, P. I.-W.↗
Pioneer 10 observations of the solar wind interation with Jupiter
Pioneer 10 Plasma Analyzer experiment flight data during the Jupiter flyby are presented. The observations show that the interaction of Jupiter's magnetic field with the solar wind is similar in many ways to that at earth, but the scale size is over 100 times larger. Jupiter is found to have a detached standing bow shock wave of high Alfven Mach number. Jupiter has a prominent magnetopause which deflects the magnetosheath plasma and excludes its direct entry into the Jovian magnetosphere. The sunward hemisphere of Jupiter's outer magnetosphere is found to be highly inflated with thermal plasma and a high beta region which is highly responsive to changes in solar wind dynamic pressure. Observational arguments are presented which tend to discount a thin disklike magnetosphere but, rather, favor a Jovian magnetosphere, albeit probabily considerably flattened as compared to the earth's magnetosphere, yet still with reasonable thickness. Results concerning the shock jump conditions, the magnetosheath flow field and inferred internal magnetospheric plasma are presented.
Wolfe, J. H.↗
Numerical computation of three-dimensional blunt body flow fields with an impinging shock
A time-marching finite-difference method was used to solve the compressible Navier-Stokes equations for the three-dimensional wing-leading-edge shock impingement problem. The bow shock was treated as a discontinuity across which the exact shock jump conditions were applied. All interior shock layer detail such as shear layers, shock waves, jets, and the wall boundary layer were automatically captured in the solution. The impinging shock was introduced by discontinuously changing the freestream conditions across the intersection line at the bow shock. A special storage-saving procedure for sweeping through the finite-difference mesh was developed which reduces the required amount of computer storage by at least a factor of two without sacrificing the execution time. Numerical results are presented for infinite cylinder blunt body cases as well as the three-dimensional shock impingement case. The numerical results are compared with existing experimental and theoretical results.
Holst, T. L.↗
Computational procedures for mixed equations with shock waves
This paper discusses the procedures we have developed to treat a canonical problem involving a mixed nonlinear equation with boundary data that imply a discontinuous solution. This equation arises in various physical contexts and is basic to the description of the nonlinear acoustic behavior of a shock wave near a caustic. The numerical scheme developed is of second order, treats discontinuities as such by applying the appropriate jump conditions across them, and eliminates the numerical dissipation and dispersion associated with large gradients. Our results are compared with the results of a first-order scheme and with those of a second-order scheme we have developed. The algorithm used here can easily be generalized to more complicated problems, including transonic flows with imbedded shocks.
Yu, N. J.↗
Nonlinear acoustic behavior at a caustic - An approximate analytical solution
The present paper discusses an approximate analytical solution to the nonlinear behavior of a discontinuous acoustic signal near a caustic. The Seebass transformation (1970) is refined to provide results which satisfy the governing equation to any prescribed accuracy, except across the shock wave produced by reflection of the simple wave at the caustic. The solution is approximate in the sense that the basic equation is satisfied wherever the solution is continuous but can satisfy only one of the two jump conditions at the reflected shock. The results give essential geometric features of the exact solution and provide a quantitative estimate of the strength of the so-called superboom.
Gill, P. M.↗
Transonic potential flow calculations using conservation form
A method is presented for the solution of the full potential equation in conservation form. This assures that a weak solution satisfying proper isentropic jump conditions is obtained, giving an improved representation of shock waves in comparison with earlier nonconservative schemes. The method uses the concept of artificial viscosity to produce a stable difference scheme in the supersonic zone, and artificial time to generate a convergent iterative scheme for the solution of the difference equations. Results of calculations using the nonconservative and conservative schemes are compared.
Jameson, A.↗
Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 1: Computational technique
A numerical procedure has been developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second order accurate finite difference scheme is used to integrate the three dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.
Marconi, F.↗
Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 2: Code description
A numerical procedure was developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.
Marconi, F.↗
Numerical computation of transonic flows with shock waves
Some recent developments in numerical methods for calculating solutions to the transonic potential flow equation are reviewed, including (1) the construction of the stable coordinate independent difference schemes; (2) the use of conservation form to insure proper shock jump conditions; (3) analysis of the relaxation method by the time dependent analogy; (4) accelerated iterative schemes.
Jameson, A.↗
On the structure of contact binaries. I - The contact discontinuity
The problem of the interior structure of contact binaries is reviewed, and a simple resolution of the difficulties which plague the theory is suggested. It is proposed that contact binaries contain a contact discontinuity between the lower surface of the common envelope and the Roche lobe of the cooler star. This discontinuity is maintained against thermal diffusion by fluid flow, and the transition layer is thin to the extent that the dynamical time scale is short in comparison with the thermal time scale. The idealization that the transition layer has infinitesimal thickness allows a simple formulation of the structure equations which are closed by appropriate jump conditions across the discontinuity. The further imposition of the standard boundary conditions suffices to define a unique model for the system once the chemical composition, the masses of the two stars, and the orbital separation are specified.
Shu, F. H.↗
A numerical solution of the axisymmetric jet counterflow problem
A numerical computation of a normal shock case in which the shock waves and shear layers are modeled as normal and tangential discontinuities bounding the regions of an inviscid flow is discussed. Within these regions the unsteady gasdynamic equations are solved in finite-volume form on a moving computational mesh. The positions of discontinuities are determined from the jump conditions. The results obtained for values of the ratio of jet total pressure to free-stream total pressure ranging from 10.0 to 100.0 are found to be in agreement with the experimental results obtained by Fleeman and Nelson (1974).
Schiff, L. B.↗