Stable multispeed lattice Boltzmann methods

We demonstrate how to produce a stable multispeed lattice Boltzmann method (LBM) for a wide range of velocity sets, many of which were previously thought to be intrinsically unstable. We use non-Gauss--Hermitian cubatures. The method operates stably for almost zero viscosity, has second-order accuracy, suppresses typical spurious oscillation (only a modest Gibbs effect is present) and introduces no artificial viscosity. There is almost no computational cost for this innovation. DISCLAIMER: Additional tests and wide discussion of this preprint show that the claimed property of coupled steps: no artificial dissipation and the second-order accuracy of the method are valid only on sufficiently fine grids. For coarse grids the higher-order terms destroy coupling of steps and additional dissipation appears. The equations are true.Comment: Disclaimer about the area of applicability is added to abstrac

Cosmic dust

Dust is a ubiquitous component of our galaxy and the solar system. The collection and analysis of extraterrestrial dust particles is important to exobiology because it provides information about the sources of biogenically significant elements and compounds that accumulated in distant regions of the solar nebula and that were later accreted on the planets. The topics discussed include the following: general properties of interplanetary dust; the carbonaceous component of interplanetary dust particles; and the presence of an interstellar component

Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length -- the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.Comment: 10 pages, 3 figures, In Proc. A4A5, Chester UK, Jul. 18-22 200

Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function -- the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.Comment: 12 page

Intact capture of hypervelocity particles

Knowledge of the phase, structure, and crystallography of cosmic particles, as well as their elemental and isotopic compositions, would be very valuable information toward understanding the nature of our solar system. This information can be obtained from the intact capture of large mineral grains of cosmic particles from hypervelocity impacts. Hypervelocity experiments of intact capture in underdense media have indicated realistic potential in this endeaver. The recovery of the thermal blankets and louvers from the Solar Max spacecraft have independently verified this potential in the unintended capture of cosmic materials from hypervelocity impacts. Passive underdense media will permit relatively simple and inexpensive missions to capture cosmic particles intact, either by going to a planetary body or by waiting for the particles to come to the Shuttle or the Space Station. Experiments to explore the potential of using various underdense media for an intact comet sample capture up to 6.7 km/s were performed at NASA Ames Research Center Vertical Gun Range. Explorative hypervelocity experiments up to 7.9 km/s were also made at the Ernst Mach Institute. These experiments have proven that capturing intact particles at hypervelocity impacts is definitely possible. Further research is being conducted to achieve higher capture ratios at even higher hypervelocities for even smaller projectiles

Stabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining

The lattice-Boltzmann method (LBM) and its variants have emerged as promising, computationally efficient and increasingly popular numerical methods for modelling complex fluid flow. However, it is acknowledged that the method can demonstrate numerical instabilities, e.g., in the vicinity of shocks. We propose a simple and novel technique to stabilise the lattice-Boltzmann method by monitoring the difference between microscopic and macroscopic entropy. Populations are returned to their equilibrium states if a threshold value is exceeded. We coin the name Ehrenfests' steps for this procedure in homage to the vehicle that we use to introduce the procedure, namely, the Ehrenfests' idea of coarse-graining. The one-dimensional shock tube for a compressible isothermal fluid is a standard benchmark test for hydrodynamic codes. We observe that, of all the LBMs considered in the numerical experiment with the one-dimensional shock tube, only the method which includes Ehrenfests' steps is capable of suppressing spurious post-shock oscillations.Comment: 4 pages, 9 figure

The impact of dietary fibre intake on the physiology and health of the stomach and upper gastrointestinal tract

This review is the first in a series of three articles considering how different types of dietary fibre may affect how the gut functions and gut health. This first review will focus on the impact of dietary fibre intake on the upper gastrointestinal tract (i.e. the mouth, oesophagus and stomach). While a larger body of evidence links fibre intake to bowel health and disease, it is apparent that the presence of fibre, whether as an added ingredient in foods, or as an integral part of the structure of plant foods, also plays key roles on oral and gastric secretions and upper gut motility. These actions are possibly modulated through fibre’s effects on the physicochemical properties of luminal contents in the gut. The major physiological functions of the mouth, oesophagus and stomach are discussed and recent evidence relating dietary fibre intake to these actions is introduced. A summary of evidence linking habitual dietary fibre consumption to major mucosal diseases of the upper gastrointestinal tract is also provided