非定常Stokes方程的多级增强Petrov-Galerkin低阶有限元方法

本文对非定常的Stokes方程采用等阶P1/P1元逼近,增强速度有限元空间,应用Petrov-Galerkin途径,根据多级增强空间是否与时间t有关,对时间项采用向后差分,给出了两种全离散的稳定有限元格式.并且证明了这两种格式的稳定性与收敛性.     

Coupling of two-dimensional atomistic and continuum models for dynamic crack

A concurrent multiscale method of coupling atomistic and continuum models is presented in the two-dimensional system. The atomistic region is governed by molecular dynamics while the continuum region is represented by construct- ing the mass and stiffness matrix dependent on the coarsening of the grids, which ensures that they merge seamlessly. The low-pass phonon filter embedded in the handshaking region is utilized to effectively eliminate the spurious reflection of high-frequency phonons, while keeping the low-frequency phonons transparent. These schemes are demonstrated by numerically calculating the reflection and transmission coefficient, and by the further application of dynamic crack propa- gation subjected to mode-I tensile loading.     

六硝基六氮杂异伍兹烷/2, 4, 6-三硝基甲苯共晶冲击起爆过程的分子动力学模拟

多尺度冲击技术可以准确的再现含能材料冲击起爆过程中冲击波阵面及反应区内的热力学和化学反应路径. 文本利用反应力场分子动力学(ReaxFF-MD)对六硝基六氮杂异伍兹烷/2, 4, 6-三硝基甲苯(CL20/TNT)1:1共晶沿<110>方向以6–10 km·s^-1的冲击速度进行冲击压缩模拟. 产物识别分析显示当冲击速度≥7 km·s^-1时, 冲击激发化学反应发生, 并且利用Rankine-Hugoniot守恒关系求得冲击起爆压力为24.56 GPa. 再者, 比较了冲击速度与粒子速度, 冲击速度与冲击诱发形变的关系, 当冲击速度为7–8 km·s^-1时, 冲击起爆发生, 系统经历弹- 塑性相变, 初级化学反应及次级化学反应, 并且相变与化学反应同时进行, 对于较高的冲击波速度(≥9 km·s^-1), 共晶系统内为过驱响应, 热力学参数均出现陡峭的梯度变化, 冲击波压缩材料直接阶跃至塑性变形阶段, 并且此阶段出现大量的碳原子.     

Multilevel augmentation methods for solving the Burgers' equation

In this article, multilevel augmentation method (MAM) for solving the Burgers' equation is developed. The Crank–Nicolson–Galerkin scheme of the Burgers' equation results in nonlinear algebraic systems at each time step, the computational cost for solving these nonlinear systems is huge. The MAM allows us to solve the nonlinear system at a fixed initial lower level and then compensate the error by solving a linear system at the higher level. We prove that the method has the same optimal convergence order as the projection method, while reducing the computational complexity greatly. Finally, numerical experiments are presented to confirm the theoretical analysis and illustrate the efficiency of the proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1665–1691, 2015     

Needs and Opportunities – Molecular Modeling Meets Polymer Process Modeling

Summary: A non-exhaustive and somehow arbitrary review on actual trends and remaining challenges for a model based process development is given. An example how state of the art molecular modeling methods help to provide kinetic information is explained in some detail. A brief sketch of various methods providing thermodynamic information for engineering is given, and finally, recent concurrent coupling schemes of particle based simulation and computational fluid dynamics are highlighted.     

A variational multiscale method based on bubble functions for convection-dominated convection-diffusion equation

This work presents a variational multiscale method based on polynomial bubble functions as subgrid scale and a numerical implementation based on two local Gauss integrations. This method can be implemented easily and efficiently for the convection-dominated problem. Static condensation of the bubbles suggests the stability of the method and we establish its global convergence. Representative numerical tests are presented.     

Development and application of multiscale models of acute viral infections in intervention research

The objective of this study is to advance two frontiers in multiscale modelling of acute viral infections, which are (a) the mathematical technology or technical frontier, where we present a new method for development of multiscale models of acute viral infections using influenza A virus (IAV) as a paradigm in which a new set of metrics to measure both individual level and community level infectiousness are introduced, and (b) the scientific applications frontier, where we demonstrate the implementation of multiscale modelling in evaluating the comparative effectiveness of IAV health interventions from efficacy data. The multiscale model is developed by integrating the within-host scale and the between-host scale. Using the example of IAV as a paradigm, we demonstrate the utility and process by which multiscale modelling can be used to evaluate the comparative effectiveness of health interventions that operate at different scale domains. The multiscale modelling is general enough to be applicable to other acute viral infections.     

Two-level iteration penalty and variational multiscale method for steady incompressible flows

In this paper, we study two-level iteration penalty and variational multiscale method for the approximation of steady Navier-Stokes equations at high Reynolds number. Comparing with classical penalty method, this new method does not require very small penalty parameter $\varepsilon$. Moreover, two-level mesh method can save a large amount of CPU time. The error estimates in $H^1$ norm for velocity and in $L^2$ norm for pressure are derived. Finally, two numerical experiments are shown to support the efficiency of this new method.     

Computational Materials Chemistry at the Nanoscale

In order to illustrate how atomistic modeling is being used to determine the structure, physical, and chemical properties of materials at the nanoscale, we present here the results of molecular dynamics (MD) simulations on nanoscale assemblies of such materials as carbon nanotubes, diamond surfaces, metal alloy nanowires, and ceramics. We also include here the results of nonequilibrium MD simulations on the nanorheology of a monolayer of wear inhibitor self-assembled on two metal oxide surfaces, separated by hexadecane lubricant, and subjected to steady state shear.We also present recent developments in force fields (FF) required to describe bond breaking and phase transformations in such systems. We apply these to study of plasticity in metal alloy nanowires where we find that depending on the strain rate, the wire may deform plastically (forming twins), neck and fracture, or transition to the amorphous phase.