Interface‐fitted moving mesh method for axisymmetric two‐phase flow in microchannels

A boundary‐fitted moving mesh scheme is presented for the simulation of two‐phase flow in two‐dimensional and axisymmetric geometries. The incompressible Navier‐Stokes equations are solved using the finite element method, and the mini element is used to satisfy the inf‐sup condition. The interface between the phases is represented explicitly by an interface adapted mesh, thus allowing a sharp transition of the fluid properties. Surface tension is modelled as a volume force and is discretized in a consistent manner, thus allowing to obtain exact equilibrium (up to rounding errors) with the pressure gradient. This is demonstrated for a spherical droplet moving in a constant flow field. The curvature of the interface, required for the surface tension term, is efficiently computed with simple but very accurate geometric formulas. An adaptive moving mesh technique, where smoothing mesh velocities and remeshing are used to preserve the mesh quality, is developed and presented. Mesh refinement strategies, allowing tailoring of the refinement of the computational mesh, are also discussed. Accuracy and robustness of the present method are demonstrated on several validation test cases. The method is developed with the prospect of being applied to microfluidic flows and the simulation of microchannel evaporators used for electronics cooling. Therefore, the simulation results for the flow of a bubble in a microchannel are presented and compared to experimental data.     

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

振型归一化对梁结构柔度曲率损伤指标的影响

结构柔度矩阵需由质量矩阵归一化振型获得,而质量矩阵归一化振型难以直接测得,限制了柔度曲率类损伤指标的应用。为分析振型归一化方法对梁结构柔度曲率类损伤指标的影响,根据梁结构的刚度、弯矩和位移曲率的关系,建立了均布荷载作用下结构损伤前后位移曲率与损伤程度的理论表达式,实现定量分析均匀荷载面曲率结构损伤程度。提出P-范数振型归一化方法,通过均匀荷载面曲率指标推导了振型质量矩阵归一化系数差x_α与损伤程度的关系。以三跨连续梁算例对理论进行了验证,结果表明,损伤程度定量指标效果良好,不同P-范数振型归一化方法下,损伤程度的偏差可由2x_α估算;2-范数振型归一化方法的损伤识别结果与质量矩阵振型归一化结果最接近,故当无法获得质量矩阵归一化振型时,可采用2-范数归一化振型代替。     

One-dimensional displacement of active matter on curved substrates

We analytically find the diffusion of overdamped active Brownian particles (ABPs) constrained to move along curved one-dimensional channels. The autonomous motion of these particles is achieved by a projection of their internal propulsion force along the channels' long section. In particular, the diffusion of ABPs moving on one-dimensional channels with a form of a circle, an ellipse, and a limacon of second order is analysed. To characterise the effect of substrate's geometry and self-propulsion on their diffusion, analytical expressions for the ABPs short- and long-time variances, as well as their steady angular probability density functions are offered. Curvature effects are found to reduce the time an ABP reaches its steady state. Our theoretical results are validated using Brownian dynamics simulations. This model may be relevant for experiments dealing with catalytic driven systems, bacteria, and tumour cell dispersion in one-dimensional channels.     

薄板弯曲分析的节点积分高阶无网格法

采用高阶无网格法求解薄板弯曲问题，在已发展的线性曲率光顺方案的基础上，通过引入泰勒展开技术，建立了能够精确再现纯弯曲和线性弯曲模式的节点积分方法。与之相比，目前无网格薄板分析主要采用的节点积分方法仅能精确再现纯弯曲模式。数值结果表明，本文方法可精确通过纯弯曲和线性弯曲试验，且能得到光滑、无振荡的弯矩场。与标准的高斯积分方法和目前已存在的节点积分方法相比，本文方法在计算精度、效率以及弯矩分布等方面均展现出显著优势。     

Binary hairy nanoparticles: Recent progress in theory and simulations

Binary polymer brushes, including mixed homopolymer brushes and diblock copolymer brushes, are an attractive class of environmentally responsive nanostructured materials. Owing to microphase separation of the two chemically distinct components in the brush, multifaceted nanomaterials with functionalized and patterned surfaces can be obtained. This review summarizes recent progress on the theory and simulations related to binary polymer brushes grafted to flat, spherical, and cylindrical substrates, with a focus on patterned morphologies of multifaceted hairy nanoparticles, an intriguing class of hybrid nanostructured particles (e.g., nanospheres and nanorods). In particular, powerful field theory and particle-based simulations suitable for revealing novel structures on these patterned surfaces, including self-consistent field theory and dissipative particle dynamics simulations, are emphasized. The unsolved yet critical issues in this research field, such as dynamic response of binary polymer brushes to environmental stimuli and the hierarchical self-assembly of binary hairy nanoparticles, are briefly discussed. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1583–1599     

Analysis of a meshless solver for high Reynolds number flow

In this paper, the extension of an upwind least‐square based meshless solver to high Reynolds number flow is explored, and the properties of the meshless solver are analyzed both theoretically and numerically. Existing works have verified the meshless solver mostly with inviscid flows and low Reynolds number flows, and in this work, we are interested in the behavior of the meshless solver for high Reynolds number flow, especially in the near‐wall region. With both theoretical and numerical analysis, the effects of two parameters on the meshless solver are identified. The first one is the misalignment effect caused by the significantly skewed supporting points, and it is found that the meshless solver still yields accurate prediction. It is a very interesting property and is opposite to the median‐dual control volume based vertex‐centered finite volume method, which is known to give degraded result with stretched triangular/tetrahedral cells in the near‐wall region. The second parameter is the curvature, and according to theoretical analysis, it is found in the region with both large aspect ratio and curvature, and the streamwise residual is less affected; however, the wall‐normal counterpart suffers from accuracy degradation. In this paper, an improved method that uses a meshless solver for the streamwise residual and finite difference for wall‐normal residual is developed. This method is proved to be less sensitive to the curvature and provides improved accuracy. This work presents an understanding of the meshless solver for high Reynolds number flow computation, and the analysis in this paper is verified with a series of numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.