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 new endocytic model based on the co-rotational grid method

Endocytosis plays important roles in many cellular physiological processes, such as metabolism and immune. Many theoretical models have been proposed to study the endocytic process, but little has considered the tensile deformation of the membrane and the actin forces. In this paper, a new endocytic model is proposed based on the co-rotational grid method. Our model gives a direct estimation of the in-plane strain of the plasma membrane and provides a basis for the calculation of further scission process of the vesicle. The results fit well with experimental data in the literature. Moreover, it is suggested that the active forces of actin at the endocytic site is the main mechanism driving the invagination of the plasma membrane.     

Characteristic behaviour of plasma fluctuations inside a plasma bubble in presence of a magnetic field due to the formation of a potential well

Experiments were carried out to observe the effect of a magnetic field and grid biasing voltage in presence of a plasma bubble in a magnetized, filamentary discharge plasma system. A spherical mesh grid of 80% optical transparency was negatively biased and introduced into the plasma for creating a plasma bubble. Diagnostics via an electrical Langmuir probe and a hot emissive probe were extensively used for scanning the plasma bubble. Plasma floating potential fluctuations were measured at three different positions of the plasma bubble. The instability in the pattern showed the dynamic transition from periodic to chaotic for increasing magnetic fields. Time scale analysis using continuous wavelet transform was carried out to identify the presence of non‐linearity from the contour plots. The mechanisms of the low‐frequency instabilities along with the transition to chaos could be qualitatively explained. Non‐linear techniques such as fast Fourier transform, phase space plot, and recurrence plot were used to explore the dynamics of the system appearing during plasma fluctuations. In order to demonstrate the observed chaotic phenomena in this study, characteristics of chaos such as the Lyapunov exponent were obtained from experimental time series data. The experimentally observed potential structure is confirmed with numerical analysis based on fluid hydrodynamics.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

A 3D mesh deformation technique for irregular in‐flight ice accretion

Aircraft holding around busy airports may be requested to sustain as much as 45 min of icing before landing or being diverted to another airport. In this paper, a three‐dimensional mesh deformation scheme, based on a structural frame analogy, is proposed for the numerical simulation of ice accretion during extended exposure to adverse weather conditions. The goal is to provide an approach that is robust and efficient enough to delay or altogether avoid re‐meshing while preserving (enforcing) nearly orthogonal elements at the highly distorted ice surface. Robustness is achieved by suitably modifying the axial and torsional stiffness components of the frame elements in order to handle large and irregular grid displacements typical of in‐flight icing. Computational efficiency is obtained by applying the mesh displacement to an automatically selected small subset of the entire computational domain. The methodology is validated first in the case of deformations typical of fluid‐structure interaction problems, including wing bending, a helicopter rotor in forward flight, and the twisting of a high‐lift wing configuration. The approach is then assessed for aero‐icing on two swept wings and compared against experimental measurements where available. Copyright © 2015 John Wiley & Sons, Ltd.     

基于粒子滤波的运动目标光电定位仿真研究

运动目标的光电定位不能像静止目标那样简单做均值滤波，鉴于此，引入粒子滤波算法，它不仅可以应用于线性系统，而且还适用于非线性系统。结合光电定位需求，详细推导了计算公式及初值和参数选取公式，对只含测量噪声以及含有测量和运动噪声等的海面运动目标光电无源定位算法进行了仿真计算，验证了算法的有效性，讨论了噪声强度对滤波效果的影响，滤波参数选择对滤波效果的影响，目标运动方式对滤波跟随性的影响，重采样算法对滤波效果的影响等。所得结论为:粒子滤波可用于运动目标光电定位过程，可有效降低定位误差；粒子滤波算法具有较强鲁棒性，适用于噪声较大、目标运动形态变化大等情况。     

适用于等熵流动的交错拉氏Godunov方法

为消除传统单元中心型Godunov方法在求解稀疏波问题时的非物理过热现象，发展一种适用于等熵流动的交错拉氏Godunov方法.主要的特征是采用速度与热力学变量交错分布的形式，避免在单元内进行速度平均，从而消除由于动量平均过程导致的动能耗散.与传统的von Neumann型交错网格方法相比，网格的边界通量由节点处的多维黎曼求解器提供，克服了多维人工粘性选取带来的困难.为减少多维黎曼求解器在求解稀疏波问题时的非物理熵增，给出稀疏波出现的合理判据，从而保证了热力学关系式的满足.数值实验表明：该方法能很好地消除稀疏波的过热现象，同时在求解激波问题时又能保持与传统单元中心型拉氏方法相同的激波捕捉能力.     

基于改进格林元的压裂水平井动态分析方法

以建立高效的动态分析方法为出发点，以边单元作为求解点，改进传统的格林元方法，减少未知数和求解矩阵维度；并提出基于改进格林元的加密网格加密方法，保证考虑复杂裂缝网络的压裂水平井动态模拟的早期精度.退化模型与半解析解、数值模拟结果进行对比，验证本文基于加密网格的改进格林元方法的准确性和动态分析的高效性.最后进行动态响应的敏感性分析，结果表明：①格林元方法是一种高精度的动态模拟方法，将求解节点设置在网格的边上可以提高压裂水平井动态模拟的速度；②改进格林元方法的加密基于叠加原理，不需要通过插值近似，其求解精度高.在相同加密网格条件下，基于本文改进格林元方法的加密效果比有限差分加密效果更佳；③复杂裂缝导流能力、改造区渗透率提高倍数、改造区大小等参数对压裂水平井动态特征影响较大，在动态分析和参数反演时，应着重考虑这些因素的影响.