Some considerations for high‐order ‘incremental remap’‐based transport schemes: edges,reconstructions, and area integration

The problem of two‐dimensional tracer advection on the sphere is extremely important in modeling of geophysical fluids and has been tackled using a variety of approaches. A class of popular approaches for tracer advection include ‘incremental remap’ or cell‐integrated semi‐Lagrangian‐type schemes. These schemes achieve high‐order accuracy without the need for multistage integration in time, are capable of large time steps, and tend to be more efficient than other high‐order transport schemes when applied to a large number of tracers over a single velocity field. In this paper, the simplified flux‐form implementation of the Conservative Semi‐LAgrangian Multi‐tracer scheme (CSLAM) is reformulated using quadratic curves to approximate the upstream flux volumes and Gaussian quadrature for integrating the edge flux. The high‐order treatment of edge fluxes is motivated because of poor accuracy of the CSLAM scheme in the presence of strong nonlinear shear, such as one might observe in the midlatitudes near an atmospheric jet. Without the quadratic treatment of upstream edges, we observe at most second‐order accuracy under convergence of grid resolution, which is returned to third‐order accuracy under the improved treatment. A shallow‐water barotropic instability also reveals clear evidence of grid imprinting without the quadratic correction. Consequently, these tests reveal a problem that might arise in tracer transport near nonlinearly sheared regions of the real atmosphere, particularly near cubed‐sphere panel edges. Although CSLAM is used as the foundation for this analysis, the conclusions of this paper are applicable to the general class of incremental remap schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Accurate integration over atomic regions bounded by zero‐flux surfaces

The approach for the integration over a region covered by zero‐flux surface is described. This approach based on the surface triangulation technique is efficiently realized in a newly developed program TWOE . The elaborated method is tested on several atomic properties including the source function. TWOE results are compared with those produced by using well‐known existing programs. Absolute errors in computed atomic properties are shown to range usually from 10^?6 to 10^?5 au. The demonstrative examples prove that present realization has perfect convergence of atomic properties with increasing size of angular grid and allows to obtain highly accurate data even in the most difficult cases. It is believed that the developed program can be bridgehead that allows to implement atomic partitioning of any desired molecular property with high accuracy. © 2012 Wiley Periodicals, Inc.     

ThSi2 Type Ytterbium Disilicide and its Analogues YbTxSi2–x (T = Cr,Fe, Co)

YbSi₂ and the derivatives YbT_xSi_2–x (T = Cr, Fe, Co) crystallizing in the α‐ThSi₂ structure type were obtained as single crystals from reactions run in liquid indium. All silicides were investigated by single‐crystal X‐ray diffraction, I4₁/amd space group and the lattice constants are: a = 3.9868(6) Å and c = 13.541(3) Å for YbSi₂, a = 4.0123(6) Å and c = 13.542(3) Å for YbCr_0.27Si_1.73, a = 4.0142(6) Å and c = 13.830(3) Å for YbCr_0.71Si_1.29, a = 4.0080(6) Å and c = 13.751(3) Å for YbFe_0.34Si_1.66, and a = 4.0036(6) Å, c = 13.707(3) Å for YbCo_0.21Si_1.79. YbSi₂ and YbT_xSi_2–x compounds are polar intermetallics with three‐dimensional Si and M (T+Si) polyanion sub‐networks, respectively, filled with ytterbium atoms. The degree of substitution of transition metal at the silicon site is signficant and leads to changes in the average bond lengths and bond angles substantially.     

Thermal measurements using ultrasonic acoustical pyrometry

Reflections from geometric discontinuities can be used with ultrasonic energy to predict the temperature of an interface where classical temperature measurement techniques are impractical because of physical access limitations or harsh environmental conditions. Additionally, these same ultrasonic measurements can be used with inversion methods commonly applied to ill-posed heat transfer problems to increase the accuracy of the measurement of surface temperature or heat flux at the surface of interest. Both methods for determining surface temperature are presented, along with a comparison of results both from a verification example and using data gathered in a field test of the methods. The results obtained with these two methods are shown to be in good agreement with an empirical relationship used in the design of large caliber guns.     

An Experimental Study of a Flux Modulated Solid State Metathesis Reaction

A solid state metathesis (SSM) reaction was investigated with respect to the formation of rare‐earth carbodiimides, the role of the co‐produced salt (LiCl), and the eutectic flux medium (LiCl/KCl). A SSM reaction is characterized by an exothermic reaction in which a salt (often LiCl) is coproduced. When the salt melts, it can serve as a useful medium for the crystallization of a desired product. An improved crystal growth can be observed by using an eutectic flux. However, the composition of an eutectic LiCl/KCl flux is altered when LiCl is produced during the reaction. The thermal effects concerning the endothermic melting of the flux and the exothermic ingnition of the SSM reaction may compensate each other, which is not necessarily a drawback for the reaction to proceed.     

Performance enhancement of a DC-operated micropump with electroosmosis in a hybrid nanofluid: fractional Cattaneo heat flux problem

The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional second-grade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semi-analytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.

     

迎风通量差分分裂法对边界层特性的数值模拟

迎风通量差分分裂法作为一种高效率的数值方法,已被广泛地用于模拟各种复杂流场,但用这类方法模拟有边界层存在的超音速粘性流场时,必须保证通量差分分裂为守恒的;否则,将在边界层内引入一个可观的虚假人工扩散项和压力梯度项,歪曲了边界层特性。本文就这个问题进行理论和数值的研究。     

Flux calculation at the interface between two rock types for two-phase flow in porous media

When simulating two-phase flow in porous media, one has to consider the case where there is a discontinuity in the medium. There relative permeabilities and capillary pressure functions may change and we address the problem of calculating the convective part of the numerical flux at the interface between the two rock types. Several solutions are compared.     

Nonfickian effect in time and space for diffusion processes

Diffusion processes are usually simulated using the classical diffusion equation. In certain scenarios, such equation induces anomalous behavior and consequently several improvements were introduced in the literature to overcome them. One of the most popular was the replacement of the diffusion equation by an integro‐differential equation. Such equation can be established considering a modification of Fick's mass flux where a delay in time is introduced. In this article, we consider mathematical models for diffusion processes that take into account a memory effect in time and space. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1589–1602, 2015     

On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems

Let u_? be the solution of the Poisson equation in a domain perforated by thin tubes with a nonlinear Robin‐type boundary condition on the boundary of the tubes (the flux here being β(?)σ(x,u_?)), and with a Dirichlet condition on the rest of the boundary of Ω. ? is a small parameter that we shall make to go to zero; it denotes the period of a grid on a plane where the tubes/cylinders have their bases; the size of the transversal section of the tubes is O(a_?) with a_???. A certain nonperiodicity is allowed for the distribution of the thin tubes, although the perimeter is a fixed number a. Here, is a strictly monotonic function of the second argument, and the adsorption parameter β(?) > 0 can converge toward infinity. Depending on the relations between the three parameters ?, a_?, and β(?), the effective equations in volume are obtained. Among the multiple possible relations, we provide critical relations, which imply different averages of the process ranging from linear to nonlinear. All this allows us to derive spectral convergence as ?→0 for the associated spectral problems in the case of σ a linear function of u_?. Copyright © 2014 John Wiley & Sons, Ltd.