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Simulation of water flow from the rainbird nozzles has been accomplished using the Smoothed Particle Hydrodynamics (SPH). The advantage of using SPH is that no meshing is required, thus the grid quality is no longer an issue and accuracy can be improved.
Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of a nonhydrodynamical nature. Under this approach, SPH is viewed as strickly as interpolation scheme and, as such, suitable for solving general hyperbolic and parabolic equations. The SPI method is tested on (1) the wave equation with inhomogenous sound speed and (2) Burger's equation. The efficiency of SPI is studied by comparing SPI solutions to those obtained with standard finite-difference methods. It is shown that the power of SPI arises when the smoothing particles are free to move.
A wheel experiencing sinkage and slippage events poses a high risk to planetary rover missions as evidenced by the mobility challenges endured by the Mars Exploration Rover (MER) project. Current wheel design practice utilizes loads derived from a series of events in the life cycle of the rover which do not include (1) failure metrics related to wheel sinkage and slippage and (2) performance trade-offs based on grouser placement/orientation. Wheel designs are rigorously tested experimentally through a variety of drive scenarios and simulated soil environments; however, a robust simulation capability is still in development due to myriad of complex interaction phenomena that contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree nite element approaches enable simulations that capture su cient detail of wheel-soil interaction while remaining computationally feasible. This study implements the JPL wheel-soil benchmark problem in the commercial code environment utilizing the large deformation modeling capability of Smooth Particle Hydrodynamics (SPH) meshfree methods. The nominal, benchmark wheel-soil interaction model that produces numerically stable and physically realistic results is presented and simulations are shown for both wheel traverse and wheel sinkage cases. A sensitivity analysis developing the capability and framework for future ight applications is conducted to illustrate the importance of perturbations to critical material properties and parameters. Implementation of the proposed soil-wheel interaction simulation capability and associated sensitivity framework has the potential to reduce experimentation cost and improve the early stage wheel design proce
Impact cratering of the Venusian planetary surface by meteorites was investigated numerically using the Smoothed Particle Hydrodynamics (SPH) method. Venus presently has a dense atmosphere. Vigorous transfer of energy between impacting meteorites, the planetary surface, and the atmosphere is expected during impact events. The investigation concentrated on the effects of the atmosphere on energy partitioning and the flow of ejecta and gas. The SPH method is particularly suitable for studying complex motion, especially because of its ability to be extended to three dimensions. In our simulations, particles representing impactors and targets are initially set to a uniform density, and those of atmosphere are set to be in hydrostatic equilibrium. Target, impactor, and atmosphere are represented by 9800, 80, and 4200 particles, respectively. A Tillotson equation of state for granite is assumed for the target and impactor, and an ideal gas with constant specific heat ratio is used for the atmosphere. Two dimensional axisymmetric geometry was assumed and normal impacts of 10km diameter projectiles with velocities of 5, 10, 20, and 40 km/s, both with and without an atmosphere present were modeled.
We present a new method of three-dimensional smoothed particle hydrodynamics (SPH) designed to model systems dominated by deformation along a preferential axis. These systems cause severe problems for SPH codes using spherical kernels, which are best suited for modeling systems which retain rough spherical symmetry. Our method allows the smoothing length in the direction of the deformation to evolve independently of the smoothing length in the perpendicular plane, resulting in a kernel with a spheroidal shape. As a result the spatial resolution in the direction of deformation is significantly improved. As a test case we present the one-dimensional homologous collapse of a zero-temperature, uniform-density cloud, which serves to demonstrate the advantages of spheroidal kernels. We also present new results on the problem of the tidal disruption of a star by a massive black hole.
This paper describes the use of Smoothed Particle Hydrodynamics (SPH) to simulate the water flow from the rainbird nozzle system used in the sound suppression system during pad abort and nominal launch. The simulations help determine if water from rainbird nozzles will impinge on the rocket nozzles and other sensitive ground support elements.
The author's current simulations of Giant Impacts on the protoearth show the development of large hot rock vapor atmospheres. The Balbus-Hawley mechanism will pump mass and angular momentum outwards in the equatorial plane; upon cooling and expansion the rock vapor will condense refractory material beyond the Roche distance, where it is available for lunar formation. During the last seven years, the author together with several colleagues has carried out a series of numerical investigations of the Giant Impact theory for the origin of the Moon. These involved three-dimensional simulations of the impact and its aftermath using Smooth Particle Hydrodynamics (SPH), in which the matter in the system is divided into discrete particles whose motions and internal energies are determined as a result of the imposed initial conditions. Densities and pressures are determined from the combined overlaps of the particles, which have a bell-shaped density distribution characterized by a smoothing length. In the original series of runs all particle masses and smoothing lengths had the same values; the matter in the colliding bodies consisted of initial iron cores and rock (dunite) mantles. Each of 41 runs used 3,008 particles, took several weeks of continuous computation, and gave fairly good representations of the ultimate state of the post-collision body or bodies but at best crude and qualitative information about individual particles in orbit. During the last two years an improved SPH program was used in which the masses and smoothing lengths of the particles are variable, and the intent of the current series of computations is to investigate the behavior of the matter exterior to the main parts of the body or bodies subsequent to the collisions. These runs are taking times comparable to a year of continuous computation in each case; they use 10,000 particles with 5,000 particles in the target and 5,000 in the impactor, and the particles thus have variable masses and smoothing lengths (the latter are dynamically adjusted so that a particle typically overlaps a few tens of its neighbors). Since the matter in the impactor provides the majority of the mass left in orbit after the collision, and since the masses of the particles that originated in the impactor are smaller than those in the target, the mass resolution in the exterior parts of the problem is greatly improved and the exterior particles properly simulate atmospheres in hydrostatic equilibrium.
The extremely massive (> 90 Stellar Mass) and luminous (= 5 x 10(exp 6) Stellar Luminosity) star Eta Carinae, with its spectacular bipolar "Homunculus" nebula, comprises one of the most remarkable and intensely observed stellar systems in the Galaxy. However, many of its underlying physical parameters remain unknown. Multiwavelength variations observed to occur every 5.54 years are interpreted as being due to the collision of a massive wind from the primary star with the fast, less dense wind of a hot companion star in a highly elliptical (e approx. 0.9) orbit. Using three-dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) simulations of the binary wind-wind collision, together with radiative transfer codes, we compute synthetic spectral images of [Fe III] emission line structures and compare them to existing Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS) observations. We are thus able, for the first time, to tightly constrain the absolute orientation of the binary orbit on the sky. An orbit with an inclination of approx. 40deg, an argument of periapsis omega approx. 255deg, and a projected orbital axis with a position angle of approx. 312deg east of north provides the best fit to the observations, implying that the orbital axis is closely aligned in 3-D space with the Homunculus symmetry axis, and that the companion star orbits clockwise on the sky relative to the primary.
The extremely massive (> 90 Solar Mass) and luminous (= 5 x 10(exp 6) Solar Luminosity) star Eta Carinae, with its spectacular bipolar "Homunculus" nebula, comprises one of the most remarkable and intensely observed stellar systems in the galaxy. However, many of its underlying physical parameters remain a mystery. Multiwavelength variations observed to occur every 5.54 years are interpreted as being due to the collision of a massive wind from the primary star with the fast, less dense wind of a hot companion star in a highly elliptical (e approx. 0.9) orbit. Using three-dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) simulations of the binary wind-wind collision in Eta Car, together with radiative transfer codes, we compute synthetic spectral images of [Fe III] emission line structures and compare them to existing Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS) observations. We are thus able, for the first time, to constrain the absolute orientation of the binary orbit on the sky. An orbit with an inclination of i approx. 40deg, an argument of periapsis omega approx. 255deg, and a projected orbital axis with a position angle of approx. 312deg east of north provides the best fit to the observations, implying that the orbital axis is closely aligned in 3-1) space with the Homunculus symmetry axis, and that the companion star orbits clockwise on the sky relative to the primary.
Simulation of multi-terrain impact has been identified as an important research area for improved prediction of rotorcraft crashworthiness within the NASA Subsonic Rotary Wing Aeronautics Program on Rotorcraft Crashworthiness. As part of this effort, two vertical drop tests were conducted of a 5-ft-diameter composite fuselage section into water. For the first test, the fuselage section was impacted in a baseline configuration without energy absorbers. For the second test, the fuselage section was retrofitted with a composite honeycomb energy absorber. Both tests were conducted at a nominal velocity of 25-ft/s. A detailed finite element model was developed to represent each test article and water impact was simulated using both Arbitrary Lagrangian Eulerian (ALE) and Smooth Particle Hydrodynamics (SPH) approaches in LS-DYNA, a nonlinear, explicit transient dynamic finite element code. Analytical predictions were correlated with experimental data for both test configurations. In addition, studies were performed to evaluate the influence of mesh density on test-analysis correlation.
Calculations of the single-impact hypothesis for the origin of the moon were performed using the smoothed particle hydrodynamics (SPH) code developed by Benz et al. (1986). Results are presented from calculations of a relatively low-level collision with an impactor mass in the range 6-8 x 10 to the 26th g. Several runs of the calculations are conducted for this mass range with variations in the SPH code, the equation of state, and the initial planetary models. The effects of these variations are compared. It is found that the orbiting mass is injected by gravitational torques.
The effects of a giant impact on Uranus with respect to the axis tilt of Uranus and its satellites are discussed. The simulations of possible giant impacts were carried out using Cray supercomputers. The technique used is called smooth particle hydrodynamics (SPH). In this technique, the material in the proto-Uranus planet and in the impactor is divided into a large number of particles which can overlap one another so that local averages over these particles determine density and pressure in the problem, and the particles themselves have their own temperatures and internal energies. During the course of the simulation, these particles move around under the influence of the forces acting on them: gravity and pressure gradients. The results of model simulations are presented.
In view of previous efforts' demonstration that strongly dissipative planetesimals are immune to tidal disruption, an examination is presently conducted of the complementary case of inviscid planetesimals arising from collisions that are sufficiently energetic to entirely melt the resulting planetesimal and debris. The tidal disruption is numerically simulated by means of the smoothed particle hydrodynamics (SPH) code of Cameron and Benz (1991), concentrating on the tidal disruption of 0.01 earth-mass planetesimals passing by the earth with variations in the impact parameter at perigee and velocity at infinity. The SPH models show that tidal forces during a close encounter can efficiently convert orbital angular momentum into spin angular momentum, thereby initiating equatorial mass-shedding to inviscid planetesimals that have been spun up beyond the limit of rotational stability.
Roche showed that equilibrium is impossible for a small fluid body synchronously orbiting a primary within a critical radius now termed the Roche limit. Tidal disruption of orbitally unbound bodies is a potentially important process for planetary formation through collisional accumulation, because the area of the Roche limit is considerably larger then the physical cross section of a protoplanet. Several previous studies were made of dynamical tidal disruption and different models of disruption were proposed. Because of the limitation of these analytical models, we have used a smoothed particle hydrodynamics (SPH) code to model the tidal disruption process. The code is basically the same as the one used to model giant impacts; we simply choose impact parameters large enough to avoid collisions. The primary and secondary both have iron cores and silicate mantles, and are initially isothermal at a molten temperature. The conclusions based on the analytical and numerical models are summarized.
In the course of carrying out finite difference calculations, it was discovered that for large craters, a previously unrecognized type of crater (diameter) growth occurred which was called lip wave propagation. This type of growth is illustrated for an impact of a 1000 km (2a) silicate bolide at 12 km/sec (U) onto a silicate half-space at earth gravity (1 g). The von Misses crustal strength is 2.4 kbar. The motion at the crater lip associated with this wave type phenomena is up, outward, and then down, similar to the particle motion of a surface wave. It is shown that the crater diameter has grown d/a of approximately 25 to d/a of approximately 4 via lip propagation from Ut/a = 5.56 to 17.0 during the time when rebound occurs. A new code is being used to study partitioning of energy and momentum and cratering efficiency with self gravity for finite-sized objects rather than the previously discussed planetary half-space problems. These are important and fundamental subjects which can be addressed with smoothed particle hydrodynamic (SPH) codes. The SPH method was used to model various problems in astrophysics and planetary physics. The initial work demonstrates that the energy budget for normal and oblique impacts are distinctly different than earlier calculations for silicate projectile impact on a silicate half space. Motivated by the first striking radar images of Venus obtained by Magellan, the effect of the atmosphere on impact cratering was studied. In order the further quantify the processes of meteor break-up and trajectory scattering upon break-up, the reentry physics of meteors striking Venus' atmosphere versus that of the Earth were studied.
Recent observations of this famous ring galaxy, including optical and near-infrared CCD surface photometry, and VLA radio continuum and 21 cm line mapping (Higdon 1992b, in prep.), have inspired a renewed modeling effort. Toomre's (1978, in The Large-scale Structure of the Universe, eds. Longair and Einasto) series of restricted three-body simulations demonstrated how the multiple rings could be produced in a nearly head-on galaxy collision. New models with a halo-dominated potential based on the 21 cm rotation curve are able to reproduce such details as the spacing between rings, ring widths, offset of the nucleus, and several kinematical features, thus providing strong support for the collisional theory. The new observations have shown there are little or no old stars in Cartwheel; it may consist almost entirely of gas and stars produced as a result of compression in the ring wave. To model this process Smooth Particle Hydrodynamics (SPH) simulations of the Cartwheel disk have been performed. Fixed gravitational potentials were used to represent the Cartwheel and a roughly 30 percent mass collision partner. The interaction dynamics was treated as in the usual restricted three-body approximation, and the effects of local self-gravity between disk particles were calculated. We are particularly interested in testing the theory that enhanced star formation in waves is the result of gravitational instability in the compressed region (see e.g. Kennicutt 1989, ApJ 344, 685). The gas surface density in a number of simulations was initialized to a value slightly below the threshold for local gravitational instability throughout most of the disk. The first ring wave produces relatively modest compressions (a factor of order a few), triggering instability in a narrow range of wavelengths. Self-gravity in the disk is calculated over a comparable range of scales. Simulations were run with isothermal, adiabatic, and adiabatic with radiative cooling characterized by a relatively short timescale. The isothermal approximation is good except in the vicinity of the strong second (inner) ring, and several snapshots from one case are shown in the figure below. Flocculent spiral segments are present before the collision, and these are compressed into dense knots in the ring wave. These knots are likely to be sites of vigorous star formation. In the strong rarefaction behind the outer ring most of the knots are radially stretched and sheared, giving rise to spoke-like features. A few dense knots are evidently very tightly bound, because they retain their coherence and are stretched relatively little through the rarefaction. This is in accord with evidence for continuing star formation in some spokes (Marcum, Appleton and Higdon 1992). The number and spacing of spokes is a direct function of the scale of the gravitational instability in the disk. Thus, the gravitational instability theory, together with the hypothesis that massive stars are only formed in dense knots of gas, can account for most of the distinct morphology of the Cartwheel.
The galaxy merging is investigated with hydrodynamical processes taken into account. For this purpose, the 3D calculations are performed by the use of a smoothed particle hydrodynamics (SPH) scheme combined with an N-body scheme. In these calculations, we find a new merging criterion and the dependence of the central phase space density of merger remnants upon the gas fraction in progenitors. It is concluded that ellipticals can be formed just by merging of fairly gas-rich primordial galaxies, not ordinary spiral galaxies.
We describe the implementation of a smoothed particle hydrodynamics (SPH) scheme using GRAPE-1A, a special-purpose processor used for gravitational N-body simulations. The GRAPE-1A calculates the gravitational force exerted on a particle from all other particles in a system, while simultaneously making a list of the nearest neighbors of the particle. It is found that GRAPE-1A accelerates SPH calculations by direct summation by about two orders of magnitudes for a ten thousand-particle simulation. The effective speed is 80 Mflops, which is about 30 percent of the peak speed of GRAPE-1A. Also, in order to investigate the accuracy of GRAPE-SPH, some test simulations were executed. We found that the force and position errors are smaller than those due to representing a fluid by a finite number of particles. The total energy and momentum were conserved within 0.2-0.4 percent and 2-5 x 10 exp -5, respectively, in simulations with several thousand particles. We conclude that GRAPE-SPH is quite effective and sufficiently accurate for self-gravitating hydrodynamics.