Superconvergence of finite element method for singularly perturbed convection–diffusion equations in 1D

In this article, a singularly perturbed convection–diffusion equation is solved by a linear finite element method on a Shishkin mesh. By means of an analysis exploiting symmetries in the convective term of the bilinear form, a new superconvergence rate, which improves the existing result, is obtained.     

Diffusion of gases across lipid membranes with OmpA channel: a molecular dynamics study

Molecular transport across biological membranes occurs in a range of important chemical and biological processes. The biological membrane can usually be modelled as a phospholipid bilayer, but to correctly represent biological transport, the embedded transmembrane proteins must also be included. In previous molecular simulation studies on transport of small gas molecules in dipalmitoylphosphatidylcholine (DPPC) bilayer membrane, a coarse-grained model was used to provide direct insight into collective phenomena in biological membranes. Coarse graining allowed investigation of longer time and length scales by reducing the degrees of freedom and employing suitable potentials. In this work, membranes that include transmembrane proteins are modelled. This allows one to compare the molecular transport across a lipid membrane with and without the assistance of transmembrane channels. Outer membrane protein A (OmpA) – a porin from Escherichia coli with a small pore size – was chosen in this study because its detailed structure is known, it has high stability and is known to form a nonspecific diffusion channel that permits the penetration of various solutes. In this work the pore characteristics and interaction between lipid and protein were investigated and transport of water and other small gas molecules within the channel were studied. The MD simulation results obtained are compared with previous simulation results and available experimental data. The results obtained from this study will lead to better understanding of protein functionality and advance the development of biochips and drug delivery systems.     

共形单步交替方向隐式时域有限差分方法及其改进

提出了一种基于共形网格技术的共形单步交替方向隐式时域有限差分(CLeapfrog ADI-FDTD)方法。与常规FDTD方法相比,此方法能够减小由于目标边界不契合网格划分而引入的阶梯近似误差,提高算法计算不规则目标时的精度;同时算法稳定性更强,计算效率更高。由于引入共形技术后显著降低了原差分法的无条件稳定性,本文利用增长矩阵本征值方法理论分析了算法的稳定性,然后采用了一种改进的共形面积计算方法,在此基础上提出了一种稳定性更高的改进的共形单步交替方向隐式时域有限差分(ICLeapfrog ADI-FDTD)方法。数值算例验证了ICLeapfrog ADI-FDTD是一种具有高稳定性和高精度的高效算法。     

大气模式下多脉冲激光推进的数值模拟

研究了大气模式激光推进中多脉冲推进的冲量耦合系数低于单脉冲推进的冲量耦合系数的机理。将飞行器设为可动模型,利用商业软件FLUENT的动网格方法对多脉冲推进进行了数值模拟,解决了已往分段计算中忽略后期流场信息造成的偏差大的问题。结果表明：多脉冲推进的平均冲量耦合系数随脉冲数的增多而降低,但是下降趋势渐缓,计算结果与实验相符;气体开始逃逸之后的后期流场与飞行器的相互作用对推进性能的影响不能忽略。     

基于目标三角面元模型生成FDTD共形网格的方法

提出了一种基于目标三角面元数据的FDTD共形网格生成方法,该方法通过投影求交计算得到目标表面各三角面元与网格线的交点,将每条网格线与三角面元的交点按坐标进行排序,根据交点的坐标及其编号的奇偶性确定FDTD共形网格的位置,并生成相应的共形FDTD计算所需的元段长度。结合处理理想导体曲面的CFDTD方法修正共形网格上的磁场递推式。数值结果证实了共形网格生成方法的正确性和在提高FDTD方法计算精度方面的有效性。     

用于ALE有限元模拟的网格更新方法

任意拉格朗日欧拉法(ALE)可以通过定义参考网格的运动,实现自由液面跟踪,完成液体晃动的数值计算. 综合用于更新网格节点的3种基本计算方法,将多方向更新网格速度的技术应用于任意拉格朗日欧拉网格节点的速度计算. 给出了水平圆柱形贮箱和椭圆形贮箱内液体晃动算例,实现了多方向更新网格运动与晃动流场计算的耦合,使ALE方法能胜任复杂几何边界下的自由液面流动的数值模拟.      

Self-assembly mechanism of PEG-b-PCL and PEG-b-PBO-b-PCL amphiphilic copolymer micelles in aqueous solution from coarse grain modeling

We followed the self-assembly of high-molecular weight MePEG- b -PCL (poly(methyl ethylene glycol)-block-poly(ε-caprolactone)) diblock and MePEG- b -PBO- b -PCL (poly(methyl ethylene glycol)-block-poly(1,2-butylene oxide)-block-poly(ε-caprolactone)) into micelles using molecular dynamics simulation with a coarse grain (CG) force field based on quantum mechanics (CGq FF). The triblock polymer included a short poly(1,2-butylene oxide) (PBO) at the hydrophilic-hydrophobic interface of these systems. Keeping the hydrophilic length fixed (MePEG₄₅), we considered 250 chains in which the hydrophobic length changed from PCL₄₄ or PBO₆- b -PCL₄₃ to PCL₆₂ or PBO₉- b -PCL₆₁. The polymers were solvated in explicit water for 2 μs of simulations at 310.15 K. We found that the longer diblock system undergoes a morphological transition from an intermediate rod-like micelle to a prolate-sphere, while the micelle formed from the longer triblock system is a stable rod-like micelle. The two shorter diblock and triblock systems show similar self-assembly processes, both resulting in slightly prolate-spheres. The dynamics of the self-assembly is quantified in terms of chain radius of gyration, shape anisotropy, and hydration of the micelle cores. The final micelle structures are analyzed in terms of the local density components. We conclude that the CG model accurately describes the molecular mechanisms of self-assembly and the equilibrium micellar structures of hydrophilic and hydrophobic chains, including the quantity of solvent trapped inside the micellar core.     

Penalty Virtual Element Method for the 3D Incompressible Flow on Polyhedron Mesh

In this paper, a penalty virtual element method (VEM) on polyhedral mesh for solving the 3D incompressible flow is proposed and analyzed. The remarkable feature of VEM is that it does not require an explicit computation of the trial and test space, thereby bypassing the obstacle of standard finite element discretizations on arbitrary mesh. The velocity and pressure are approximated by the practical significative lowest equal-order virtual element space pair (Xh,Qh) which does not satisfy the discrete inf-sup condition. Combined with the penalty method, the error estimation is proved rigorously. Numerical results on the 3D polygonal mesh illustrate the theoretical results and effectiveness of the proposed method.     

成品油管道顺序输送二维模型优化求解

将一种简化的自适应网格应用于顺序输送二维混油模型的计算中,网格的疏密程度由速度和浓度梯度控制且用动网格取代传统的固定网格。混油模型中采用混掺长度理论计算速度场和扩散系数,并考虑了油品黏度变化对混油的影响。提高传统数值解法的精度,减少计算量,使之适应于长输管线顺序输送的混油数值计算。通过在计算机上的数值模拟实验,证明了该方法的有效性,分析了雷诺数、输送顺序对混油的影响并得到混油随输送距离的变化规律。     

基于数据重建的三角网格模型简化优化方法

由CT切片数据重建得到的三角网格模型常存在数据量大、狭长三角形多等问题,针对这些问题,研究了一种保持特征的高质量三角网格模型的简化优化方法。该方法分为网格简化和网格优化两个阶段。首先,采用基于曲面变化的二次误差度量计算边折叠代价,并按代价值的大小进行迭代的折叠简化,可较好地保持模型表面的特征;其次,通过二阶加权伞算子对简化模型中局部存在的狭长三角形进行优化处理,改善三角网格模型的质量。实验结果表明,该方法能够较好地保持特征区域的细节信息,并可靠地生成高质量、低几何误差的简化模型。