Simulation of three‐dimensional flows over moving objects by an improved immersed boundary–lattice Boltzmann method

An improved immersed boundary–lattice Boltzmann method (IB–LBM) developed recently [28] was applied in this work to simulate three‐dimensional (3D) flows over moving objects. By enforcing the non‐slip boundary condition, the method could avoid any flow penetration to the wall. In the developed IB–LBM solver, the flow field is obtained on the non‐uniform mesh by the efficient LBM that is based on the second‐order one‐dimensional interpolation. As a consequence, its coefficients could be computed simply. By simulating flows over a stationary sphere and torus [28] accurately and efficiently, the proposed IB–LBM showed its ability to handle 3D flow problems with curved boundaries. In this paper, we further applied this method to simulate 3D flows around moving boundaries. As a first example, the flow over a rotating sphere was simulated. The obtained results agreed very well with the previous data in the literature. Then, simulation of flow over a rotating torus was conducted. The capability of the improved IB–LBM for solving 3D flows over moving objects with complex geometries was demonstrated via the simulations of fish swimming and dragonfly flight. The numerical results displayed quantitative and qualitative agreement with the date in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

A comparative study of truly incompressible and weakly compressible SPH methods for free surface incompressible flows

In this paper, the performance of the incompressible SPH (ISPH) method and an improved weakly compressible SPH (IWCSPH) method for free surface incompressible flows are compared and analyzed. In both methods, the Navier–Stokes equations are solved, and no artificial viscosity is used. The ISPH algorithm in this paper is based on the classical SPH projection method with common treatments on solid boundaries and free surfaces. The IWCSPH model includes some advanced corrective algorithms in density approximation and solid boundary treatment (SBT). In density approximation, the moving least squares (MLS) approach is applied to re‐initialize density every several steps to obtain smoother and more stable pressure fields. An improved coupled dynamic SBT algorithm is implemented to obtain stable pressure values near solid wall areas and, thus, to minimize possible numerical oscillations brought in by the solid boundaries. Three representative numerical examples, including a benchmark test for hydrostatic pressure, a dam breaking problem and a liquid sloshing problem, are comparatively analyzed with ISPH and IWCSPH. It is demonstrated that the present IWCSPH is more attractive than ISPH in modeling free surface incompressible flows as it is more accurate and more stable with comparable or even less computational efforts. Copyright © 2013 John Wiley & Sons, Ltd.     

Keller–Osserman estimates and removability result for the anisotropic porous medium equation with gradient absorption term

We study “large” nonnegative solutions for a class of quasilinear equations model of which is We give a sufficient condition on the exponents and for the removability of isolated singularities.     

Bi2O3/FAp,a sustainable catalyst for synthesis of dihydro-[1,2,4]triazolo[1,5-a]pyrimidine derivatives through green strategy

The bismuth loaded on fluorapatite (Bi₂O₃/FAp) proved to be an excellent catalyst for the synthesis of novel dihydro-[1,2,4]triazolo[1,5-a]pyrimidine derivatives via a three-component reaction involving the mixture of 1H-1,2,4-triazol-5-amine, ethyl cyanoacetate or ethyl acetoacetate, and different benzaldehydes in ethanol at room temperature. The catalyst material was characterized by X-ray diffraction, Brunauer–Emmett–Teller surface area analysis, Fourier-transform infrared, scanning electron microscopy, energy-dispersive X-ray spectroscopy, and transmission electron microscopy techniques. The efficacy of Bi₂O₃/FAp as a heterogeneous catalyst was evaluated with the loading of different wt% of bismuth on FAp. The 2.5% bismuth on FAp performed extremely well as a catalyst with a high yield of products (92%–96%) in a short reaction time (25–35 min). The catalyst was recovered by simple filtration. It showed undiminished activity up to five runs. Simple work-up, room temperature reaction, short reaction time, high yields, no column chromatography, and good reusability of catalyst are the merits of the proposed protocol. In addition, this process offers 100% carbon efficiency and 98% atom economy with noteworthy fiscal and environmental benefits.     

Accuracy of high‐order density‐based compressible methods in low Mach vortical flows

At low Mach numbers, Godunov‐type approaches, based on the method of lines, suffer from an accuracy problem. This paper shows the importance of using the low Mach number correction in Godunov‐type methods for simulations involving low Mach numbers by utilising a new, well‐posed, two‐dimensional, two‐mode Kelvin–Helmholtz test case. Four independent codes have been used, enabling the examination of several numerical schemes. The second‐order and fifth‐order accurate Godunov‐type methods show that the vortex‐pairing process can be captured on a low resolution with the low Mach number correction applied down to 0.002. The results are compared without the low Mach number correction and also three other methods, a Lagrange‐remap method, a fifth‐order accurate in space and time finite difference type method based on the wave propagation algorithm, and fifth‐order spatial and third‐order temporal accurate finite volume Monotone Upwind Scheme for Conservation Laws (MUSCL) approach based on the Godunov method and Simple Low Dissipation Advection Upstream Splitting Method (SLAU) numerical flux with low Mach capture property. The ability of the compressible flow solver of the commercial software, ANSYS FLUENT , in solving low Mach flows is also demonstrated for the two time‐stepping methods provided in the compressible flow solver, implicit and explicit. Results demonstrate clearly that a low Mach correction is required for all algorithms except the Lagrange‐remap approach, where dissipation is independent of Mach number. © 2013 Crown copyright. International Journal for Numerical Methods in Fluids. © 2013 John Wiley & Sons, Ltd.     

用于液体激光介质的Nd~(3+)离子掺杂氟化镧纳米颗粒的制备与性能表征

设计并合成了掺杂不同Nd3+离子浓度的氟化镧纳米颗粒,并用油酸进行了表面修饰,使得这类纳米颗粒可分散于常见的有机溶剂中形成透明、均一、稳定的溶液。对纳米颗粒的结构、晶相以及发光性能进行了表征。固体和溶液材料在1 060 nm都有强的发射峰,说明纳米晶格可有效地保护Nd3+离子免受外界环境对发光的猝灭影响。纳米颗粒有机溶液的吸收损耗和散射损耗测试结果表明,其总损耗系数能够满足激光介质材料的损耗要求,为该材料的实用化打下了基础。     

求解定常不可压Stokes方程的两层罚函数方法

借助于两套有限元网格空间提出了一种求解定常不可压Stokes方程的两层罚函数方法.该方法只需要求解粗网格空间上的Stokes方程和细网格空间上的两个易于求解的罚参数方程（离散后的线性方程组具有相同的对称正定系数矩阵）.收敛性分析表明粗网格空间相对于细网格空间可以选择很小，并且罚参数的选取只与粗网格步长和问题的正则性有关.因此罚参数不必选择很小仍能够得到最优解.最后通过数值算例验证了上述理论结果，并且数值对比可知两层罚函数方法对于求解定常不可压Stokes方程具有很好的效果.     

Preparation of free‐standing silicone particles in aqueous heterogeneous system

To prepare cross‐linked silicone (silicone rubber) particles in an aqueous medium, we investigated two synthesis methods involving a miniemulsion system. The first method was based on cationic ring‐opening polymerization of cyclic siloxane, which is a common synthetic route for linear silicone oil and uses octamethylcyclotetrasiloxane (D₄) as the monomer and dimeric D₄ (bis‐D₄) as the cross‐linker. Although this method produces silicone particles, the particles do not remain in the particulate state after drying because of low cross‐linking density. The polymerization mechanism of this method was also investigated, which proceeds under the ring‐opening reaction of D₄ in monomer droplets and upon polycondensation of hydrolyzed D₄, which occurs in the water phase (ie, outside the monomer droplets). This mechanism implied that introducing the cross‐linking structure into particles is difficult because of the low solubility of bis‐D₄ in water. To overcome these difficulties, we demonstrated a second method of preparing silicone particles based on the thiol‐Michael addition reaction between thiol‐terminated silicone oil and triacrylate in miniemulsion systems. Transmission electron microscopy images indicated that the silicone particles obtained in the particulate state upon drying and the aggregates of these particles showed elasticity.     

Stability of algebraic multigrid for Stokes problems

An investigation is made of the performance of algebraic multigrid (AMG) solvers for the discrete Stokes problem. The saddle‐point formulations are based on the direct enforcement of the fundamental conservation laws in discrete spaces and subsequently stabilised with the aid of a regular splitting of the diffusion operator. AMG solvers based on an independent coarsening of the fields (the unknown approach) and also on a common coarsening (the point approach) are investigated. Both mixed‐order and equal‐order interpolations are considered. The dependence of convergence on the ‘degree of coarsening’ is investigated by studying the ‘convergence versus coarsening’ characteristics and their variation with mesh resolution. They show a consistency in shape, which reveals two distinct performance zones, one convergent the other divergent. The transition from the convergent to the divergent zones is discontinuous and occurs at a critical coarsening factor that is largely mesh independent. It signals a breakdown in the stability of the smoothing at the coarser levels of coarse grid approximation. It is shown that the previously observed, mesh‐dependent, scaling of convergence factors, which had suggested inconsistencies in the coarse grid approximation, is not a reliable marker of inconsistency. It is an indirect consequence of the breakdown in the stability of smoothing. For stable smoothing, reduction factors are shown to be largely mesh independent. The ability of mixed‐order interpolation to permit stable smoothing and therefore to deliver mesh‐independent convergence is explained. Two expedient options are suggested for obtaining mesh‐independent convergence for those AMG codes that are based on an equal‐order interpolation. Copyright © 2012 John Wiley & Sons, Ltd.     

Global persistence of geometrical structures for the Boussinesq equation with no diffusion

Our main aim is to investigate the temperature patch problem for the two-dimensional incompressible Boussinesq system with partial viscosity: the initial temperature is the characteristic function of some simply connected domain with 𝒞^1,𝜀 Hölder regularity. Although recent results ensure that the 𝒞¹ regularity of the patch persists for all time, whether higher order regularity is preserved has remained an open question. In the present paper, we give a positive answer to that issue. We also study the higher dimensional case, after prescribing an additional smallness condition involving critical Lebesgue or weak-Lebesgue norms of the data, so as to get a global-in-time statement. All our results stem from general properties of persistence of geometrical structures (of independent interest), that we establish in the first part of the paper.