Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

The anomalous properties of cold and supercooled water, such as the fact that at sufficiently low temperatures it becomes more compressible and less dense when cooled, and more fluid when compressed, have attracted the attention of physical scientists for a long time. The discovery in the 1970s that several thermodynamic and transport properties of supercooled water exhibit a pronounced temperature dependence and appear to diverge slightly below the homogeneous nucleation temperature inspired a large number of experimental and theoretical studies. Likewise, an important body of work on glassy water has been stimulated by experiments, starting in the mid-1980s and continuing to this date, which suggest that vitreous water can exist in at least two apparently distinct forms. A coherent theory of the thermodynamic and transport properties of supercooled and glassy water does not yet exist. Nevertheless, significant progress towards this goal has been made during the past 20 years. This article summarizes the known experimental facts and reviews critically theoretical and computational work aimed at interpreting the observations and providing a unified viewpoint on cold, non-crystalline, metastable states of water.

https://iopscience.iop.org/article/10.1088/0953-8984/15/45/R01/pdf

Supercooled and glassy water

The unusual low‐temperature behavior of liquid water is interpreted using a simple model based upon connectivity concepts from correlated‐site percolation theory. Emphasis is placed on examining the physical implications of the continuous hydrogen‐bonded network (or ’’gel’’) formed by water molecules. Each water molecule A is assigned to one of five species based on the number of ’’intact bonds’’ (the number of other molecules whose interaction energy with A is stronger than some cutoff VHB). It is demonstrated that in the present model the spatial positions of the various species are not randomly distributed but rather are correlated. In particular, it is seen that the infinite hydrogen‐bonded network contains tiny ’’patches’’ of four‐bonded molecules. Well‐defined predictions based upon the putative presence of these tiny patches are developed. In particular, we predict the detailed dependence upon (a) temperature, (b) dilution with the isotope D2O, (c) hydrostatic pressure greater than atmospheric, and...

Interpretation of the unusual behavior of H2O and D2O at low temperatures: Tests of a percolation model

Several physical effects allow free floatation of solid and even liquid matter. Materials may be levitated by a jet of gas, by intense sound waves, or by beams of laser light. In addition, conductors levitate in strong radio-frequency fields, charged particles in alternating electric fields, and magnets above superconductors or vice versa. Although levitation by means of ferromagnets is unstable, supper-conductors may be suspended both above and below a magnet as a result of flux pinning. Levitation is used for containerless processing and investigation of materials, for frictionless bearings and high-speed ground transportation, for spectroscopy of single atoms and microparticles, and for demonstrating superconductivity in the new oxide superconductors.

https://science.sciencemag.org/content/sci/243/4889/349.full.pdf

Levitation in Physics

The study of metallic melts, their physical properties, and their solidification behaviour is of relevance to understanding of fundamental principles and to metallurgical applications. Many, if not...

Containerless processing in the study of metallic melts and their solidification

The experimental observation of the behavior of acoustically rotated free drops in the microgravity environment of low earth orbit has yielded the first data which meet the restrictions of existing theoretical treatments. Rotating drops displayed both 'axisymmetric' and 'two-lobed' shapes in the presence and absence of applied torques. Their dimensions and general development confirm the existence of the distinct shape families and the bifurcation point between them. The data also indicate that the secular instability in the axisymmetric family occurs at a lower rotation velocity than predicted

Shapes of rotating free drops: Spacelab experimental results

An unprecedented microgravity observation of maximal shape oscillations of a surfactant-bearing water drop the size of a ping-pong ball was observed during a mission of Space Shuttle Columbia. The goal of the research, of which this observation is a part, was to study the rheological properties of liquid drop surfaces on which are adsorbed surfactant molecules under conditions not possible at 1g. Numerical computation of the evolution of the shape of greatly deformed drops using the boundary integral method has successfully predicted the observed drop shapes over a complete cycle of oscillation, thereby permitting the calculation of the dynamic surface tension under these unique conditions.

Free Oscillations and Surfactant Studies of Superdeformed Drops in Microgravity

Ultrasonic sound velocity data in supercooled water are analyzed in the light of present theories. Preliminary evidence for a minimum in the sound speed versus temperature curve is shown to be consistent with available data for other thermodynamic properties. A simple two‐state mixture model combined with experimental data may be used to yield similar evidence. Sound speed data in superheated water are used to determine other thermodynamic parameters in the 100 to 170 °C temperature range under atmospheric pressure.

The sound velocity in metastable liquid water under atmospheric pressure

The capability of ultrasonic levitators operating in air to perform density measurements has been demonstrated. The remote determination of the density of ordinary liquids as well as low density solid metals can be carried out using levitated samples with size on the order of a few millimeters and at a frequency of 20 kHz. Two basic methods may be used. The first one is derived from a previously known technique developed for acoustic levitation in liquid media, and is based on the static equilibrium position of levitated samples in the earth’s gravitational field. The second approach relies on the dynamic interaction between a levitated sample and the acoustic field. The first technique appears more accurate (1% uncertainty), but the latter method is directly applicable to a near gravity‐free environment such as that found in space.

Acoustic levitation methods for density measurements

A standard optical Schlieren method has been adapted to the problem of measuring the speed of sound in moderately supercooled and in superheated liquids under atmospheric pressure. The estimated accuracy is ±3 m/s. Results in supercooled water down to −16.75 °C and in superheated water up to 176.5 °C are reported.

Eugene Trinh

Papers

Shapes of rotating free drops: Spacelab experimental results

Free Oscillations and Surfactant Studies of Superdeformed Drops in Microgravity

The sound velocity in metastable liquid water under atmospheric pressure

Acoustic levitation methods for density measurements

Method for the measurement of the sound velocity in metastable liquids, with an application to water