Meshless and analytical solutions to the time-dependent advection-diffusion-reaction equation with variable coefficients and boundary conditions

A variety of physical problems in science may be expressed using the advection-diffusion-reaction (ADR) equation that covers heat transfer and transport of mass and chemicals into a porous or a nonporous media. In this paper, the meshless generalised reproducing kernel particle method (RKPM) is utilised to numerically solve the time-dependent ADR problem in a general n-dimensional space with variable coefficients and boundary conditions. A time-dependent Robin boundary condition is formulated and precisely enforced in a novel approach. The accuracy and robustness of the meshless solution is verified against finite element simulations and a general one-dimensional analytical solution obtained in this study.     

Influence of Macro-pores on DNAPL Migration in Double-Porosity Soil Using Light Transmission Visualization Method

Double porosity is a substantial microstructure characteristic in a wide range of geomaterials. It is a natural phenomenon that can be found in many types of soil, and it can result from biological, chemical or mechanical damage. In this paper, the influence of macro-pores on dense non-aqueous phase liquid (DNAPL) migration in double-porosity medium was investigated using light transmission visualization technique. Three experiments were carried out in two-dimensional flow chambers filled with a double-porosity medium composed of a mixture of local sand and sintered kaolin clay spheres arranged in a periodic manner. In each experiment, a different volumetric fraction of macro-pores and micropores was used. Tetrachloroethylene (PCE) was used to simulate DNAPL, and it was dyed using Oil-Red-O for better visualization. A predetermined amount of PCE was injected into the flow chambers and this amount was re-calculated using image analysis. A very strong correlation was found between the PCE amount injected and the amount calculated from image analysis in each experiment. The experiment was repeated by filling the flow chamber with silica sand to represent single-porosity medium. The results show that the macro-pores have a considerable effect on the PCE migration in double-porosity soil as the PCE movement was the fastest in the third experiment which contained the largest macro-pores volume. The accuracy of the method was validated using statistical analysis. The results show a slight difference between the means of the three experiments, indicating that the method is viable for monitoring NAPL migration in double-porosity medium under different volumetric fractions of macro-pores and micropores.     

A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Spin-polarized current and tunnel magnetoresistance in heterogeneous single-barrier magnetic tunnel junctions

Current in heterogeneous tunnel junctions is studied in the framework of the parabolic conduction-band model. The developed model of the electron tunneling takes explicitly into account the difference of effective masses between ferromagnetic and insulating layers and between conduction subbands. Calculations for Fe/MgO/Fe-like structures have shown the essential impact of effective mass differences in regions (constituents) of the structure on the tunnel magnetoresistance of the junction.     

Issue Information

Three‐dimensional direct numerical simulation results of flow past a circular cylinder are influenced by numerical aspects, for example the spanwise domain length and the lateral boundary condition adopted for the simulation. It is found that inappropriate numerical set‐up, which restricts the development of intrinsic wake structure, leads to an over‐prediction of the onset point of the secondary wake instability (Re_cr). A best practice of the numerical set‐up is presented for the accurate prediction of Re_cr by direct numerical simulation while minimizing the computational cost. The cylinder span length should be chosen on the basis of the intrinsic wavelength of the wake structure to be simulated, whereas a long span length is not necessary. For the wake transitions above Re_cr, because the wake structures no longer follow particular wavelengths but become disordered and chaotic, a span length of more than 10 cylinder diameters (approximately three times the intrinsic wavelength) is recommended for the simulations to obtain wake structures and hydrodynamic forces that are not strongly restricted by the numerical set‐up. The performances of the periodic and symmetry lateral boundary conditions are compared and discussed. The symmetry boundary condition is recommended for predicting Re_cr, while the periodic boundary condition is recommended for simulating the wake structures above Re_cr. The general conclusions drawn through a circular cylinder are expected to be applicable to other bluff body configurations. Copyright © 2017 John Wiley & Sons, Ltd.     

Progress in the synthesis and applications of hierarchical flower-like TiO2 nanostructures

Flower-like TiO₂ materials, with their advantages of high specific surface area, developed pore structure, and high photocatalytic activity, have been widely used in environmental management and air purification, sterilization, and surface self-cleaning, among other areas. This paper summarizes several methods used to fabricate the flower-like TiO₂ nanostructures, such as the hydrothermal, solvothermal, microemulsion, sol–gel, hydrolysis, and electrodeposition oxidation methods. In addition, the morphologies, properties, and performance of different flower-like TiO₂ structures are discussed. Meanwhile, the application progresses of different flower-like TiO₂ structures are also analyzed.     

BP neural network recognition algorithm for scour monitoring of subsea pipelines based on active thermometry

Scour monitoring is an important concern for subsea pipeline systems. The active-thermometry-based scour monitoring is based on the difference of heat transfer properties between sediment and sand, recognizes the surrounding media though temperature changing patterns during heating and cooling processes, and hence detects the free spans. Based on the scour monitoring system, a two-layer BP neural network was employed to process the monitoring data and achieved media recognition. The network's inputs were normalized temperature time histories. The network's outputs denoted different media: sediment and water. To validate the method, three experiments were conducted; one was used for training the network and the other two for testing. Also, the effect of noise on the network's performance was studied through simulation. The results demonstrated the feasibility and robustness of the neural network.