A Control Volume Radial Basis Function Techniques for the Numerical Simulation of Saturated Flows in Semi-confined Aquifer

In this work, a Control Volume Radial Basis Function technique (CV-RBF) is adapted to solve ground water flow in the saturated zone of the semi-confined aquifer. The CV-RBF method differs from classical CV methods in the way that the flux at the cell surfaces is computed. A local RBF interpolation of the field variable is performed at the centres of the cell being integrated and its neighbours. This interpolation is then used to reconstruct the solution and its gradient in the integration points which support the flux computation. In addition, it is required that such interpolation satisfies the governing equation in a certain number of points placed around the cell centres. In this way, the local interpolations become equivalent to local boundary-value problems. The CV-RBF method is combined with a local remeshing technique in order to track the phreatic surface, where the gradients required to satisfy the kinematic condition are computed by the same local RBF interpolations used for the flux computation. The proposed numerical approach is validated in a series of three-dimensional groundwater flow problems where the operations of recharging and extracting water from a semi-confined aquifer are modelled.     

Numerical simulation of two‐dimensional Kelvin–Helmholtz instability using weakly compressible smoothed particle hydrodynamics

The growth of the Kelvin–Helmholtz instability generated at the interface between two ideal gases is studied by means of a Smoothed Particle Hydrodynamics (SPH) scheme suitable for multi‐fluids. The SPH scheme is based on the continuity equation approach where the densities of SPH particles are evolved during the simulation, in combination with a momentum equation previously proposed in the literature. A series of simulations were carried out to investigate the influence of viscosity, smoothing, the thickness of density and velocity transition layers. It was found that the effective viscosity of the presented results are strongly dependent on the artificial viscosity parameter α_AV, with a linear dependence of 0.15. The utilisation of a viscosity switch is found to significantly reduce the spurious viscosity dependence to 1.68 × 10^?4 and generated qualitatively improved behaviour for inviscid fluids. The linear growth rate in the numerical solutions is found to be in satisfactory agreement with analytical expectations, with an average relative error 〈η_smooth〉=13%. In addition, the role played by velocity and density transition layers is also in general agreement with the analytical theory, except for the sharp‐velocity, finite‐density gradient cases where the larger growth rate than the classical growth rate is expected. We argue the inherited smoothing properties of the velocity field during the simulations are responsible for causing this discrepancy. Finally, the SPH results are in good agreement for finite velocity and density gradient scenarios, where an average relative error of 〈η_smooth〉=11.5% is found in our work. Copyright © 2015 John Wiley & Sons, Ltd.     

Flax fibers: assessing the non-cellulosic polysaccharides and an approach to supramolecular design of the cell wall

Due to their particular tensile properties and composition, flax cellulosic fibres are widely used in various applications and are important in the stem architecture, as a source of mechanical support. Here, we have examined how various chemical extractions of cell-wall polysaccharides might improve our understanding of the structure and composition of these fibres. A set of chemical extractions, which had previously been independently studied on fibres of different origins and by different laboratories, was run on the same batch of technical fibres, variety Eden, and the released non-cellulosic polysaccharides were analyzed in terms of sugar composition and size exclusion chromatography. No single-step protocol was able to extract all the non-cellulosic polysaccharides estimated to be in the range of 130–140 mg per g of dry fibres. The major polymers consisted of rhamnogalacturonan and glucomannan, while the minor ones were xyloglucan and xylan. Several types of stepwise extractions helped to elucidate the subfractions of each polymer that are differently retained within cell wall. From our data, we have pointed out a new model which might help to approach the supramolecular design of the flax cellulosic fibres and, afterwards, the relationships between their chemical composition and their mechanical properties.     

Numerical Simulation of Coherent Structures over Plant Canopy

This paper reports large eddy simulations of the interaction between an atmospheric boundary layer and a canopy (representing a forest cover). The problem is studied for a homogeneous configuration representing the situation encountered above a continuous forest cover, as well as for a heterogeneous configuration representing the situation similar to an edge or a clearing in a forest. The numerical results reproduces correctly all the main characteristics of this flow as reported in the literature: the formation of a first generation of coherent structures aligned transversally with the wind flow direction, the reorganization and the deformation of these vortex tubes into horse-shoe structures. The results obtained when introducing a discontinuity in the canopy (reproducing a clearing or a fuel break in a forest), are compared with the experimental data collected in a wind tunnel; here, the results confirm the existence of a strong turbulence activity inside the canopy at a distance equal to 8 times the height of the canopy, referenced in the literature as the Enhance Gust Zone (EGZ) characterized by a local peak of the skewness factor.     

Interval Reductions and Extensions of Orders: Bijections to Chains in Lattices

We discuss bijections that relate families of chains in lattices associated to an order P and families of interval orders defined on the ground set of P. Two bijections of this type have been known:(1) The bijection between maximal chains in the antichain lattice A(P) and the linear extensions of P.(2) The bijection between maximal chains in the lattice of maximal antichains A_M(P) and minimal interval extensions of P.We discuss two approaches to associate interval orders with chains in A(P). This leads to new bijections generalizing Bijections 1 and 2. As a consequence, we characterize the chains corresponding to weak-order extensions and minimal weak-order extensions of P.Seeking for a way of representing interval reductions of P by chains we came upon the separation lattice S(P). Chains in this lattice encode an interesting subclass of interval reductions of P. Let S_M(P) be the lattice of maximal separations in the separation lattice. Restricted to maximal separations, the above bijection specializes to a bijection which nicely complements 1 and 2.(3) A bijection between maximal chains in the lattice of maximal separations S_M(P) and minimal interval reductions of P.     

Experimental evaluation of nonlinearities of small-sized insertable gradient coils

A phase imaging technique is proposed to map out and quantify gradient nonlinearities of small-sized insertable gradient coils, assuming the whole-body system gradients are highly linear in the domain of interest. The theory is developed and simple equations are derived to allow quantification. It is applied to a 4-loop 18-cm diameter cylindrical gradient coil of optimal design. Experimental gradient nonlinearity maps are obtained for different fields of view. Gradient non-linearities are quantified locally and in regions of interest, showing close agreement with model data.     

The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems

In this work an extension is proposed to the Local Hermitian Interpolation (LHI) method; a meshless numerical method based on interpolation with small and heavily overlapping radial basis function (RBF) systems. This extension to the LHI method uses interpolation functions which themselves satisfy the partial differential equation (PDE) to be solved. In this way, a much improved reconstruction of partial derivatives can be obtained, resulting in significantly improved accuracy in many cases.     

A note on the structure of spaces of domino tilings

We study spaces of tilings, formed by tilings which are on a geodesic between two fixed tilings of the same domain (the distance is defined using local flips). We prove that each space of tilings is homeomorphic to an interval of tilings of a domain when flips are classically directed by height functions.     

Numerical modeling of coherent structures attendant on impurity propagation in the atmospheric boundary layer over a forest canopy

Three-dimensional large eddy simulation is used to solve the problem for a homogeneous forest canopy. The development of the Kelvin-Helmholtz instability above the canopy leads to the formation of coherent structures in the atmosphere flow, which are reproduced in the calculations. The statistical characteristics of the flow obtained from the numerical modeling are compared with experimental data. The passive admixture transfer from the canopy to the clean atmosphere is studied for two cases, namely, for constant and variable coupled concentration of the impurity in the canopy.