A lattice Boltzmann based implicit immersed boundary method for fluid–structure interaction

The immersed boundary method is a practical and effective method for fluid–structure interaction problems. It has been applied to a variety of problems. Most of the time-stepping schemes used in the method are explicit, which suffer a drawback in terms of stability and restriction on the time step. We propose a lattice Boltzmann based implicit immersed boundary method where the immersed boundary force is computed at the unknown configuration of the structure at each time step. The fully nonlinear algebraic system resulting from discretizations is solved by an Inexact Newton–Krylov method in a Jacobian-free manner. The test problem of a flexible filament in a flowing viscous fluid is considered. Numerical results show that the proposed implicit immersed boundary method is much more stable with larger time steps and significantly outperforms the explicit version in terms of computational cost.     

A semi-implicit time-splitting scheme for a regional nonhydrostatic atmospheric model

In this study a semi-implicit finite difference scheme is proposed for the nonhydrostatic atmospheric model based on the Euler equations for compressible ideal gas. Fast acoustic and gravity waves are approximated implicitly, while slow inertial processes are treated explicitly. Such time approximation requires the solution of 3D elliptic equations at each time step. An efficient elliptic solver is based on decoupling in the vertical direction and splitting in the horizontal directions. Stability analysis of the scheme shows that the time step is restricted only by the maximum wind speed and does not depend on the propagation velocity of the fast waves. A specific approximation of the advection terms keeping the second order of accuracy and possessing extended stability is employed to achieve larger time steps. The performed numerical experiments show the computational efficiency of the designed scheme and accuracy of the predicted atmospheric fields.     

The sufficient condition for stability of a time varying discrete system

A sufficient condition for the stability of a time varying discrete system is established in terms of eigenvalues of the system matrix which may be symmetric or non-symmetric non-singular. This condition is useful for the synthesis of a stable time varying system, for example, the decision of convergence coefficient at each step in a successive approximation formula     

Numerical solution of incompressible Navier–Stokes equations using a fractional-step approach

A fractional step method for the solution of steady and unsteady incompressible Navier–Stokes equations is outlined. The method is based on a finite-volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (third and fifth) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when fifth-order upwind differencing and a modified production term in the Baldwin–Barth one-equation turbulence model are used with adequate grid resolution.     

混凝土浇筑过程中温度场和应力场仿真分析

在混凝土浇筑过程中,其弹性模量随时间变化.这一独特现象给混凝土结构的残余热应力应变的理论求解带来极大困难.即使使用有限元法对混凝土进行热力耦合分析,也必须解决材料弹性模量徐变的问题.采用分时间段方法对弹性模量的时变特性进行等效近似处理,在一个时间段内近似认为弹性模量为一个稳定值,并在各个时间段对混凝土进行热力耦合计算.每一时间段仿真分析时读取上个时间段的结果作为初始条件.最后提取整个龄期各测试点处的仿真温度数据,并与实测温度数据进行对比,验证温度场仿真方法的正确性.     

Approximation of discrete linear systems based on a dual criterion

A new method for approximating scalar discrete linear systems is described. The method can be classified as a time domain/frequency domain technique. Two reduced order models are obtained. One is obtained when the time domain specifications are in terms of the impulse response of the error. The other is derived when the time domain specifications are in terms of the step response of the error. The technique utilizes the input normal system representation to determine the order and the denominator polynomial of the reduced order model.     

Robust nonlinear control of a three-tank system using finite-time disturbance observers

A finite-time disturbance observer-based robust control method is proposed for output tracking of the Inteco threetank system in the presence of mismatched uncertainties. The controller is designed in a backstepping manner. At each step of the virtual controller design, a robust feedback controller with some effective nonlinear damping terms is designed so that the system states remain in the feasible domain. The nonlinear uncertainty is compensated by a finite-time disturbance observer. And to avoid the shortcoming of “explosion of terms”, the dynamic surface control technique which employs a low-pass filter is adopted at each step of the virtual controller design. Attention is paid to reducing the measurement noise effects and to initialization technique of the system states and reference output trajectory. Theoretical analysis is performed to clarify the control performance. And the theoretical results are verified based on the experimental studies on the real Inteco three-tank system.     

Conservative semi-implicit semi-Lagrangian scheme for simulation of shallow flows

A fully conservative semi-Lagrangian (SL) scheme is presented to solve for the shallow-water equations. Existing inherently conservative SL schemes only ensure the conservation of mass while momentum is not fully conserved. The gravity terms, which are mainly responsible for the wave structure in dam break flows, are then discretized by using traditional non-conservative Eulerian schemes. In the presence of large variations in water surface (e.g., dam-break type flows), such an approach leads to incorrect shock speed and highly oscillatory results. Indeed, if the conservation of the gravity terms is forced, the use of existing schemes will be restricted to small time steps. In this paper we present a fully conservative scheme which can accurately simulate the shallow flows with a large time step. In our approach, both convective and gravitational terms are treated in a conservative manner, which ensures an accurate shock speed. The fully conservation property improves considerably the performance of common SL schemes for a wide range of practical applications.     

Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations

Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of their non-linear nature and the presence of stiff source terms, especially for high charge to mass ratios and for low Larmor radii. In this article, we design entropy stable finite difference schemes for the two-fluid equations by combining entropy conservative fluxes and suitable numerical diffusion operators. Furthermore, to overcome the time step restrictions imposed by the stiff source terms, we devise time-stepping routines based on implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the two-fluid plasma equations is exploited by us to design IMEX schemes in which only local (in each cell) linear equations need to be solved at each time step. Benchmark numerical experiments are presented to illustrate the robustness and accuracy of these schemes.     

Theoretical Investigation of Time Suboptimal Control of Industrial Manipulators Along Specified Paths

A method for the time suboptimal control of an industrial manipulator from an initial position and orientation to a final position and orientation as it moves along a specified path is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives the control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in numerical examples to verify the method developed.     

Online reputation measurement of companies based on user-generated content in online social networks

Social media websites such as Facebook, Twitter, etc. has changed the way peoples communicate and make decision. In this regard, various companies are willing to use these media to raise their reputation. In this paper, a reputation management system is proposed which measures the reputation of a given company by using the social media data, particularly tweets of Twitter. Taking into account the name of the company and its' related tweets, it is determined that a given tweet has either negative or positive impact on the company's reputation or product. The proposed method is based on N-gram learning approach, which consists of two steps: train step and test step. In the training step, we consider four profiles i.e. positive, negative, neutral, and irrelevant profiles for each company. Then 80% of the available tweets are used to build the companies' profiles. Each profile contains the terms that have been appeared in the tweets of each company together with the terms' frequencies. Then in the test step, which is performed on the 20% remaining tweets of the dataset, each tweet is compared with all of the built profiles, based on distance criterion to examine how the given tweet affects a company's reputation. Evaluation of the proposed method indicates that this method has a better efficiency and performance in terms of recall and precision compared to the previous methods such as Neural Network and Bayesian method.     

Theoretical Investigation of a Time-Suboptimal Control Method for Rotational Motions of Industrial Manipulators End-Effectors

A time suboptimal control method is developed for rotational motions of industrial manipulators end-effectors. A set of nonlinear equations is obtained and linearized at each time step of the motion. A method which yields the time suboptimal joint angular velocities as functions of time is developed by considering constraints on joint velocities as well as joint and tool center point frame accelerations. The method is demonstrated on a six-degree-of-freedom elbow-type manipulator.     

Numerical solution of unsteady Navier–Stokes equations on curvilinear meshes

The objective of the present work is to extend our FDS-based third-order upwind compact schemes by Shah et al. (2009) [8] to numerical solutions of the unsteady incompressible Navier–Stokes equations in curvilinear coordinates, which will save much computing time and memory allocation by clustering grids in regions of high velocity gradients. The dual-time stepping approach is used for obtaining a divergence-free flow field at each physical time step. We have focused on addressing the crucial issue of implementing upwind compact schemes for the convective terms and a central compact scheme for the viscous terms on curvilinear structured grids. The method is evaluated in solving several two-dimensional unsteady benchmark flow problems.     

Gradient Methods for Nonstationary Unconstrained Optimization Problems

Problems of unconstrained optimization with an objective function depending on a scalar parameter (time) are considered. The solution of these problems also depends on time and any numerical method must keep track of this dependence. For the solution of such nonstationary problems, a discrete gradient method is treated, in which only one gradient step is taken for the varying function at each instant of time. Estimates of intervals (variations) between exact and approximate solutions are found and an asymptotic behavior of these estimates is defined.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 38–46.Original Russian Text Copyright © 2005 by Popkov.     

A Lagrangian meshless finite element method applied to fluid–structure interaction problems

A method is presented for the solution of the incompressible fluid flow equations using a Lagrangian formulation. The interpolation functions are those used in the meshless finite element method and the time integration is introduced in a semi-implicit way by a fractional step method. Classical stabilization terms used in the momentum equations are unnecessary due to the lack of convective terms in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplifies the connections with fixed or moving solid structures, thus providing a very easy way to solve fluid–structure interaction problems.     

Stabilization Methods for Spectral Element Computations of Incompressible Flows

A stabilization method for the spectral element computation of incompressible flow problems is investigated. It is based on a filtering procedure which consists in filtering the velocity field by a spectral vanishing Helmholtz-type operator at each time step. Relationship between this filtering procedure and SVV-stabilization method, introduced recently in [JCP, 2004, 196(2), p680], is established. A number of numerical examples are presented to show the accuracy and stabilization capability of the method.     

Mixed analytical/numerical method for flow equations with a source term

A mixed analytical/numerical approach is studied for flow problems described by partial differential equations with source terms which are analytically integrable and which may involve a time scale (S-scale) much smaller than the mean flow time scale (M-scale). A rigorous error analysis based on the modified equation is conducted for a linear model equation and it is shown, both analytically and numerically, that the mixed scheme is more accurate than a conventional numerical method. Most interestingly, the mixed approach has a good accuracy for the M-scale structure even though the time step is larger than the S-scale, while a conventional scheme fails to work in this case by producing errors of order O(1) or larger.     

基于图像亮度局部约束的总变分图像去噪法

为了解决总变分图像去噪方法易产生虚假边缘这一不足,结合总变分理论和图像亮度局部约束的优点,提出了一种新的图像去噪方法。在总变分图像去噪的数值求解过程中,利用局部均值和局部方差对迭代过程中所获得的结果进行局部约束。实验结果表明,本文方法具有良好的图像去噪能力,在高噪声水平下,其峰值信噪比(Peak signal-noise ratio,PSNR)至少提高了1dB左右,图像视觉效果也有了很大改善。     

Economic performance analysis in the design of on-line batch optimization systems

In this paper, the on-line optimization of batch reactors under parametric uncertainty is considered. A method is presented that estimates the likely economic performance of the on-line optimizer. The method of orthogonal collocation is employed to convert the differential algebraic optimization problem (DAOP) of the dynamic optimization into a nonlinear program (NLP) and determine the nominal optimum. Based on the resulting NLP, the optimization steps are approximated by neighbouring extremal problems and the average deviation from the true process optimum is estimated dependent on the measurement error and the parametric uncertainty. The true process optimum is assumed to be represented by the optimum of the process model with the true parameter values. A back off from the active path and endpoint inequality constraints is determined at each optimization step which ensures the feasible operation of the process. Based on the analysis results the optimal structure of the optimizer in terms of measured variables and estimated parameters can be determined. The method of the average deviation from optimum is developed for the fixed terminal time case and for time optimal problems. In both cases, the theory is demonstrated on an example.