A numerical analysis of a class of generalized Boussinesq‐type equations using continuous/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time‐dependent varying seabed are included. Thus, high‐order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher‐order models, an extra O(μ²ⁿ⁺²) term (n ∈ ?) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth‐order models. The discretization of the spatial variables is made using continuous P₂ Lagrange elements. A predictor‐corrector scheme with an initialization given by an explicit Runge–Kutta method is also used for the time‐variable integration. Moreover, a CFL‐type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Charge generation and electrostatic equilibrium for single granules during sliding

Electrostatic phenomena are commonly observed in the processing of solids. However, the working mechanism of electrostatic charge generation for single granules and particularly, their electrostatic equilibria have not been properly understood. In this work, repeated-sliding charging experiments with single granules were investigated for their electrostatic generation particularly from the perspective of triboelectrification equilibrium. Factors including granule length-ratio, sliding face shape, sliding times, sliding area, sliding velocity, front-facing edge, and sliding-plate inclined-angle were found to have an obvious effect on granule charge generation. Length-ratio and sliding area have significant effects as the granules evolved toward an equilibrium state. Equilibrium charge is suggested as a variable expressing the charging propensity of the material. In addition, under the same working conditions, a semi-cylindrical granule generates greater charge than a rectangular granule.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

Physically cross‐linked networks of POSS‐capped poly(acrylate amide)s: Synthesis,morphologies, and shape memory behavior

In this work, we synthesized a novel organic–inorganic semitelechelic polymer from polyhedral oligomeric silsesquioxane (POSS) and poly(acrylate amide) (PAA) via reversible addition‐fragmentation chain transfer (RAFT) polymerization. The organic–inorganic semitelechelic polymers have been characterized by means of nuclear magnetic resonance spectroscopy, thermal gravimetric analysis, and dynamic mechanical thermal analysis. It was found that capping POSS groups to the single ends of PAA chains caused a series of significant changes in the morphologies and thermomechanical properties of the polymer. The organic–inorganic semitelechelics were microphase‐separated; the POSS microdomains were formed via the POSS–POSS interactions. In a selective solvent (e.g., methanol), the organic–inorganic semitelechelics can be self‐assembled into the micelle‐like nanoobjects. Compared to plain PAA, the POSS‐capped PAAs significantly displayed improved surface hydrophobicity as evidenced by the measurements of static contact angles and surface atomic force microscopy. More importantly, the organic–inorganic semitelechelics displayed typical shape memory properties, which was in marked contrast to plain PAA. The shape memory behavior is attributable to the formation of the physically cross‐linked networks from the combination of the POSS–POSS interactions with the intermolecular hydrogen‐bonding interactions in the organic–inorganic semitelechelics. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 587–600     

Compressive advection and multi‐component methods for interface‐capturing

This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P₁DG‐P₂(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

Shape memory induced structural evolution of high performance copolyimides

In this work, two kinds of high temperature shape memory copolyimides were prepared and the shape memory cycles induced structural evolution of macromolecular chains was investigated in detail. The glass transition temperature (T_g) of poly(benzoxazole‐co‐imide) (PI1) and poly(benzimidazole‐co‐imide) (PI2) are 280 °C and 355 °C, respectively. The results show that PI1 could keep stable macromolecular chain structure under shape memory cycles and exhibit outstanding shape memory performance (R_f > 98%, R_r > 97%) under different stretch condition. Whereas, shape memory cycles induced orientation with more ordered macromolecular chains packing is formed for PI2 after several thermal mechanical cycles, which strongly affect physical crosslinking points, thermal mechanical properties as well as shape memory behaviors. The study on macroscopic property and microscopic structure evolution will promote a better understanding of the shape memory effect of polyimides and accelerate development of high performance polyimides for shape memory applications. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3858–3867     

Synthesis and design of polyurethane and its nanocomposites derived from canola-castor oil: Mechanical,thermal and shape memory properties

The recent global pandemic and its tremendous effect on the price fluctuations of crude oil illustrates the side effects of petroleum dependency more evident than ever. Over the past decades, both academic and industrial communities spared endless efforts in order to replace petroleum-based materials with bio-derived resources. In the current study, a series of shape memory polymer composites (SMPC's) was synthesized from epoxidized vegetable oils, namely canola oil and castor oil fatty acids (COFA's) as a 100% bio-based polyol and isophorone diisocyanate (IPDI) as an isocyanate using a solvent/catalyst-free method in order to eventuate polyurethanes (PU's). Thereafter, graphene oxide (GO) nanoplatelets were synthesized and embedded in the neat PU in order to overcome the thermomechanical drawbacks of the neat matrix. The chemical structure of the synthesized components, as well as the dispersion and distribution levels of the nanoparticles, was characterized. In the following, thermal and mechanical properties as well as shape memory behavior of the specimens were comprehensively investigated. Likewise, the thermal conductivity was determined. This study proves that synthesized PU's based on vegetable oil polyols, including graphene nanoparticles, exhibit proper thermal and mechanical properties, which make them stand as a potential candidate to compete with traditional petroleum-based SMPC's.