Applying Periodic Boundary Conditions to Predict Open Water Propeller Performance

Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different advance coefficients of DTMB 4119, 4382, and 4384 propellers were calculated.The pressure coefficient distribution of the DTMB 4119 propeller at different sections was also physically tested.Comparisons indicated good agreement between the results of experiments and the simulation.It showed that the periodic boundary condition can be used to rationally predict the open water performance of a propeller.By analyzing the three established modes for the computation, it was shown that using the spline curve method to divide the grids can meet the calculation's demands for precision better than using the rake cutting method.

A study on periodic boundary condition in direct numerical simulation for gas–solid flow

Direct numerical simulation(DNS) of gas–solid flow at high resolution has been carried out by coupling the lattice Boltzmann method(LBM) for gas flow and the discrete element method(DEM) for solid particles. However,the body force periodic boundary condition(FPBC) commonly used to cut down the huge computational cost of such simulation has faced accuracy concerns. In this study, a novel two-region periodic boundary condition(TPBC) is presented to remedy this problem, with the flow driven in the region with body force and freely evolving in the other region. With simulation cases for simple circulating fluidized bed risers, the validity and advantages of TPBC are demonstrated with more reasonable heterogeneity of the particle distribution as compared to the corresponding case with FPBC.

A Molecular Dynamics Simulation for Periodic Boundary Condition in the Bending Process of Ag／Ni Composite Interfaces

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Periodic Boundary Conditions for Finite-Differentiation-Method Fast-Fourier-Transform Micromagnetics

We describe an accurate periodic boundary condition （PBC） called the symmetric PBC in the calculation of the magnetostatie interaction field in the finite-differentiation-method fast-Fourier-transform （FDM-FFT） micromagneties. The micromagnetic cells in the regular mesh used by the FDM-FFT method are finite-sized elements, but not geometrical points. Therefore, the key PBC operations for FDM-FFT methods are splitting and relocating the micromagnetic cell surfaces to stay symmetrically inside the box of half-total sizes with respect to the origin. The properties of the demagnetizing matrix of the split micromagnetic cells are discussed, and the sum rules of demagnetizing matrix are fulfilled by the symmetric PBC.

ANALYSIS OF OPEN MICROSTRIP STRUCTURES BY USING DIAKOPTIC METHOD OF LINES COMBINED WITH PERIODIC BOUNDARY CONDITIONS

This paper presents the analysis of open microstrip structures by using diakoptic method of lines (ML) combined with periodic boundary conditions (PBC). The parameters of microstrip patch are obtained from patch current excited by plane wave. Impedance matrix elements are computed by using fast Fourier transform(FFT), and reduced equation is solved by using diakoptic technique. Consequently, the computing time is reduced significantly. The convergence property of simulating open structure by using PBC and the comparison of the computer time between using PBC and usual absorbing boundary condition (ABC) show the validity of the method proposed in this paper. Finally, the resonant frequency of a microstrip patch is computed. The numerical results obtained are in good agreement with those published.

Effects of Periodic Boundary Condition on Traffic Waves

In this paper, we use the speed-gradient model proposed by Jiang et al. [Transp. Res. B 36 （2002） 405] to study the effect of boundary condition on shock and rarefaction wave. Our numerical results show that this model can reproduce the evolution of the two traffic waves, which further proves that this model can be used to perfectly explore the consequences caused by various boundary conditions.

Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

Existence and Uniqueness of Almost Periodic Solution for a Mathematical Model of Tumor Growth

This article is concerned with a mathematical model of tumor growth governed by 2nd order diffusion equation . The source of mitotic inhibitor is almost periodic and time-dependent within the tissue. The system is set up with the initial condition C(r, 0) = C0(r) and Robin type inhomogeneous boundary condition . Under certain conditions we show that there exists a unique solution for this model which is almost periodic.

Factors influencing electromagnetic scattering from the dielectric periodic surface

The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’ s principle and Floquet’s theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.

Existence of Periodic Solutions of Nonlinear Systems with Nonlinear Boundary Conditions

In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions.By constructing the Poincare operator,we obtain the existence of Wp2β-periodic weak solutions under some reasonable assumptions.

Second-Order Two-Scale Analysis Method for the Heat Conductive Problem with Radiation Boundary Condition in Periodical Porous Domain

In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale,the cell problem,effective material coefficients,homogenization problem,first-order correctors and second-order correctors are obtained successively.The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition.The error estimation is also obtained for the original solution and the SOTS’s approximation solution.Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.

SPECTRAL METHOD FOR ZAKHAROV EQUATION WITH PERIODIC BOUNDARY CONDITIONS

This paper describes the spectral method for numerically solving Zakharov equation with periodicboundary conditions. This method is spectral method for spatial variable and difference method fortime variable. We make error estimation of approximate solution and prove the convergence of spectralmethod. We had given the convergence rate. Also, we prove the stability of approximate method forinitial values.

Exact Boundary Conditions for PeriodicWaveguides Containing a Local Perturbation

We consider the solution of the Helmholtz equation−
u(x)−n(x)2ω2u(x)=f(x),x=(x,y),in a domain which is infinite in x and bounded in y.We assume that f(x)is supported in 0:={x∈|a−<x<a+}and that n(x)is x-periodic in\0.We show how to obtain exact boundary conditions on the vertical segments,􀀀−:={x∈|x=a−}and􀀀+:={x∈|x=a+},that will enable us to find the solution on 0∪􀀀+∪􀀀−.Then the solution can be extended in in a straightforward manner from the values on􀀀−and􀀀+.The exact boundary conditions as well as the extension operators are computed by solving local problems on a single periodicity cell.

统计物理学中关于平动运动边界条件的教学实践

热力学统计物理教材中求解平动运动粒子的波函数时,对于边界条件往往任意选择无限深势阱模型和周期性边界条件中的一种。由于两种边界条件下求解得到的单位能量间隔中量子态数是完全一致的,因此边界条件的具体形式不会影响统计物理研究问题的结果。然而,边界条件的选择对于学生理解上下游特定课程的具体内容是有一定影响的,部分课程中存在着不同的概念应用,本文建议在热力学统计物理课程中还是应该将两种不同边界条件的适用范围给以详细说明。

简单立方点阵结构静态平压性能分析

为了提高简单立方(SC)点阵结构的平压力学性能,在ABAQUS中对SC单胞建立了周期边界约束方程,并通过ESO算法对周期边界条件下的SC单胞进行了拓扑优化设计。随后对优化SC单胞的等效弹性模量进行了求解,发现优化SC单胞的等效弹性模量明显优于传统SC单胞,从外部去除单胞材料可使优化单胞等效压缩模量提高27.14%,从内部去除单胞材料可使单胞等效剪切模量提高46.18%。最后将优化SC单胞从单胞层面扩展到宏观结构中,探究了三类SC点阵结构的静态平压性能。研究表明,周期边界条件与ESO相结合的拓扑优化方法,可使SC结构静态平压时的抵抗力得到明显提升。相比传统SC点阵结构,优化后的SC点阵结构抵抗力提高了20%以上。

人字形板式换热器耦合传热特性分析

以人字形波纹板式换热器为基础,建立了完整的三板双流道耦合传热模型,并进行了数值分析。结果表明:在单边流动方式下流体出现了流量分配不均的情况,在导流区较为严重,流速与流量分布规律相同,在换热区靠近触点的位置流速更大。对计算模型施加展向周期性边界条件,发现波纹板的温度分布、总传热系数与常见的单元传热相比,误差更小。因此,在进行板式换热器模拟计算时,需要考虑耦合传热。同时分析了局部努塞尔数和二次流强度的变化趋势,发现在主流方向上,局部努塞尔数和二次流强度的变化趋势基本相同,在触点位置都出现了剧烈的变化,增强了换热,因此在设计板式换热器时,可以考虑通过适当改变结构以增加触点个数来增强换热。

RRS-PBC: a molecular approach for periodic systems

Technically, when dealing with a perfect crystal, methods （PBC） in conjunction with plane-wave basis sets are widely in k-（reciprocal） space that impose periodic boundary conditions used. Chemists, however, tend to think of a solid as a giant mole- cule, which offers a molecular way to describe a solid by using a finite cluster model （FCM）. However, FCM may fail to sim- ulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space infor- mation of a perfect crystalline solid out of a reduced real space （RRS） of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.

计及周期/半周期性边界条件的永磁电机子域模型

该文提出的表贴磁极永磁电机考虑周期/半周期性边界条件的子域模型,为舰船大容量直驱多相永磁推进电机的设计优化提供一种快速、高效的工具。介绍周期性边界条件和半周期性边界条件的原理及实现方法,并将其应用到基于等效面电流的子域模型中求解电机气隙磁场,而后通过有限元仿真验证了解析计算的准确性。对比3种求解域下子域模型中谐波系数矩阵的维数和求解速度,表明考虑周期/半周期性边界条件的子域模型在保证结果精度的前提下,能大幅降低矩阵维数,并显著减少求解时间。对实验样机进行空载和负载实验,空载反电势与负载转矩实验结果与解析结果吻合较好,进一步说明了周期/半周期性边界条件下所用子域模型的正确性。

Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.