MPI+OpenMP混合求解偏微分方程

差分方法是求解偏微分方程的最主要工具之一,并行求解差分方程可以快速解决工程问题。研究了基于MPI与OpenMP混合的并行计算方法 ,基于该方法测试了稳态传热问题的计算,结果表明,混合并行模式对于提高计算速度有加大的帮助。     

传热与流动的数值计算与彩色图象显示

本文介绍了在应用计算机进行传热与流动过程数值模拟与彩色图象显示方面的一些初步结果,其中包括一维稳态热传导、一维不稳态热传导、二维稳态热传导、二维充分发展通道内的传热与流动、扩散火焰的发展以及流体中夹带颗粒运动的数值分析与显示等。     

基于微分方程对称的分布参数系统稳态控制

应用对称群理论中经典对称, 以无穷小生成元为分析工具, 考虑分布参数系统的控制问题已有研究, 在此基础上, 本文给出利用微分方程对称实现分布参数系统稳态控制的方法. 通过求解微分方程的对称, 借助其和无穷小生成元之间的关系, 研究给出符合控制目标稳态要求的分布参数系统边界控制条件. 针对两个例子,说明了利用微分方程对称实现分布参数系统稳态控制的过程, 设计了边界控制条件, 进行了仿真说明. 相较基于经典对称获得分布参数系统无穷小生成元的过程, 利用微分方程对称, 避免了空间延拓过程, 并可能获得与其不同的无穷小生成元形式.     

基于COM的Matlab在中药分析中的应用

介绍了利用MatLab软件中的数据分析工具开发的中药生产数据分析平台的设计和实现。该平台用C#语言搭建，采用COM组件的形式将MatLab软件的数据分析工具和图形工具动态加载到分析系统中。平台根据实际生产过程中的大量数据，从相关性、变异性等多个方面对其分析，并通过具体数据和图形两种方式显示分析结果，从而起到指导生产和改进模型的作用。     

用Mathematica解热量传递过程中的数学问题

本文建议用数学软件Mathematica计算热量传递过程,包括用符号运算功能推导保温层临界直径,用曲线拟合法处理传热实验数据,用积分法求取传热系数为温度函数时的换热面积,用Solve等命令求解换热和保温过程所产生的非线性方程,用DSolve命令求解非稳态传热过程产生的微分方程等等。同时绘制出有关函数图形,准确、形象地展示计算过程和结果,方便教师讲解和学生理解,避免复杂、繁琐、耗时的手工计算,提高学生利用计算机解决热量传递问题的能力。     

基于MATLAB随机种群模型数值模拟方法的应用研究

随机微分方程被广泛地应用在生物的各个领域。通常情况下,随机种群模型很难找到解析解,因而数值模拟是研究这类模型数值解的一个有效的工具。为此,运用MATLAB软件,对随机两种群模型和带Markovian转换的随机种群模型进行数值模拟,展示数值模拟的过程,从而给出MATLAB软件求解这类数值模拟的一般方法。     

利用正交脉冲函数求解液压机器人模型参照自适应控制及其微机实现

本文采用 Block Pulse Functions(BPF)将模型参考自适应控制的时变调节器微分方程转化为代数方程,从而简化了方程求解和微机控制过程。实验结果表明,采用 BPF 求解的模型参考自适应微机-单自由度液压机械手控制系统动态响应快、稳态定位精确及抗干扰性能好。     

二维稳态传热问题的计算机仿真

热量传输现象在工程技术领域中广泛存在,对二维稳态传热情形下温度场分布的研究有重要现实意义。对于复杂几何形状的物体和非线性的边界条件,分析解法显得无能为力;相比之下,建立在有限元基础上的数值计算是有效和准确的。在传热和流体流动问题的数值计算方面,SIMPLE算法被广泛采用。通过VC和Matlab的混合编程用SIMPLE算法实现了对二维稳态传热问题的计算仿真,描述了温度场的分布。     

化工过程仿真培训系统中的换热器模型

本文讨论了化工过程仿真培训系统中的换热器的动态模型，着重比较了两种稳态模拟与动态补偿相结合的仿真算法－基于平均传热温差和基于传热单元数的仿真算法。分析了基于平均传热温差的仿真算法存在的问题，讨论了基于传热单元数的仿真算法中有关参数的确定方法，最后给出仿真实例。     

软件集成环境下的精馏塔动态仿真

化工过程动态仿真的关键问题是物性数据的计算及非线性微分方程和代数方程的求解，商品化的过程稳态模拟软件能够精确计算纯组分及混合物的物性，而MATLAB/SIMULINK具有强大计算及仿真功能。该文通过将Matlab／Simulink与Aspen Plus模拟软件物性和热力学数据库集成，对精馏塔进行了动态仿真研究。文中阐述了软件集成的方法，建立了精馏塔的通用动态数学模型，在Simulink中以S-函数的方式进行了实现。通过软件集成进行过程的仿真研究，充分利用了现有软件的优势，减少了编程工作量，提高了开发效率。     

Multi-time-scale heat transfer modeling of turbid tissues exposed to short-pulsed irradiations

A combined hyperbolic radiation and conduction heat transfer model is developed to simulate multi-time-scale heat transfer in turbid tissues exposed to short-pulsed irradiations. An initial temperature response of a tissue to an ultrashort pulse irradiation is analyzed by the volume-average method in combination with the transient discrete ordinates method for modeling the ultrafast radiation heat transfer. This response is found to reach pseudo steady state within 1 ns for the considered tissues. The single pulse result is then utilized to obtain the temperature response to pulse train irradiation at the microsecond/millisecond time scales. After that, the temperature field is predicted by the hyperbolic heat conduction model which is solved by the MacCormack's scheme with error terms correction. Finally, the hyperbolic conduction is compared with the traditional parabolic heat diffusion model. It is found that the maximum local temperatures are larger in the hyperbolic prediction than the parabolic prediction. In the modeled dermis tissue, a 7% non-dimensional temperature increase is found. After about 10 thermal relaxation times, thermal waves fade away and the predictions between the hyperbolic and parabolic models are consistent.     

基于阵列传感器的数据中心温度场可视化系统设计

针对数据中心温度场无法实时监控的问题,采用阵列传感器采集数据,以计算流体动力学和传热学为基础,构建数据中心温度场可视化系统。详细介绍了该系统的组成和实现方法。通过分析机柜表面的温度场分布,建立热传导方程式,采用有限差分法进行求解,计算结果作为边界条件,结合k-ε模型对三维温度场进行数值模拟。根据温度场模型计算结果,采用OpenGL工具开发了温度场可视化系统。     

Buoyancy convection in a cavity with mutually orthogonal heated plates

Buoyancy driven convection in a square cavity induced by two mutually orthogonal arbitrarily placed heated thin plates is studied numerically under isothermal and isoflux boundary conditions. The flow is assumed to be two-dimensional. The coupled governing equations were solved by the finite difference method using the Alternating Direction Implicit technique and Successive Over Relaxation method. The steady state results are depicted in terms of streamline and isotherm plots. It is found that the resulting convection pattern is stronger for the isothermal boundary condition. A better overall heat transfer can be achieved by placing one of the plates far away from the center of the cavity for isothermal boundary condition and near the center of the cavity for isoflux boundary condition.     

Convective heat transfer analysis by the finite element method

A numerical procedure based on the finite element method is developed for the analysis of general two-dimensional problems in free/forced convection heat transfer. The dicretization of the field equations through use of the Galerkin method is described. Solution methods for both types of steady state convection are presented.The utility and accuracy of the described method is demonstrated through the solution of diverse examples illustrating both forced and free convection analysis. The use of temperature-dependent material properties and the inclusion of solid body conduction effects are also demonstrated.     

Transient state analysis of separated flow around a sphere

Transient state solutions of the Navier-Stokes equations were obtained for incompressible flow around a sphere accelerating from zero initial velocity to its terminal free falling velocity. By assuming rotational symmetry about the axis in the direction of motion, the Navier-Stokes equations and the continuity equation were simplified in terms of vorticity and stream function. The instantaneous acceleration of the falling sphere was calculated by considering the difference between the gravitational force and the drag force in a transient state. A set of implicit finite difference equations was developed. In order to obtain accurate information around the body, an exponential transformation along the radial direction was used to provide finer meshes in the vicinity of the surface of the sphere. The vorticity equation was solved by an alternating direction implicit (ADI) method while the stream function equation was solved by a successive over-relaxation (SOR) method. Simultaneous solutions were obtained. Transient state solutions were compared with steady state solutions for Reynolds numbers up to 300. Separations first occurred at a Reynolds number 20 for steady state flows and at Reynolds numbers 22·46 and 28·24 for transient state flows with terminal Reynolds numbers of 100 and 300, respectively. Separation angles, sizes of separation regions, and drag coefficents were calculated for both steady and unsteady states. Good agreement was obtained with existing experimental data in the steady state.     

A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

A topology optimization method for fluid flow using transient information is proposed. In many conventional methods, the design domain is updated using steady state information which is obtained after solving the flow field equations completely. Hence we must solve the flow field at each iterative which leads to high computational cost. In contrast, the proposed method updates the design domain using transient information of flow field. Hence the flow field is solved only once. The flow field is solved by lattice Boltzmann method (LBM). It is found that, by using LBM, the flow field is stably computed even though the design domain drastically changes during the computation. The design domain is updated according to sensitivity analysis. In many conventional methods, the sensitivity of objective functionals under lattice Boltzmann equations is obtained using additional adjoint equations. However, in the proposed method, the sensitivity is explicitly formulated and computed without using adjoint variables. In this paper, we show some numerical examples for low Reynolds number flows. The results demonstrate good convergence property in small computation time.     

动载下轴向槽道热管传热分析

研究超音速飞机气动加热管温度优化控制问题,热管是超音速战斗机机翼热防护中减少机翼与背景环境温差的传热元件,而目前关于动载下热管传热流动特性的研究报道较少.为了建立热传导的控制数学模型,在分析热管工作机制的基础上,建立了轴向槽道热管液相和气相传热流动数学模型.通过有限体积法分别计算出气液相模型,利用不可压缩层流模型推导出了稳态下热管中两相的壁面温度分布情况,了解到旋转产生的离心力对气相的传热影响很小,对液相区的影响较大.通过仿真比较,仿真温度分布和的实验数据基本一致,满足工程要求.为热管在机翼热防护中的优化传热奠定基础.     

MHD flow of radiative micropolar nanofluid in a porous channel: optimal and numerical solutions

The flow of a radiative and electrically conducting micropolar nanofluid inside a porous channel is investigated. After implementing the similarity transformations, the partial differential equations representing the radiative flow are reduced to a system of ordinary differential equations. The subsequent equations are solved by making use of a well-known analytical method called homotopy analysis method (HAM). The expressions concerning the velocity, microrotation, temperature, and nanoparticle concentration profiles are obtained. The radiation tends to drop the temperature profile for the fluid. The formulation for local Nusselt and Sherwood numbers is also presented. Tabular and graphical results highlighting the effects of different physical parameters are presented. Rate of heat transfer at the lower wall is seen to be increasing with higher values of the radiation parameter while a drop in heat transfer rate at the upper wall is observed. Same problem has been solved by implementing the numerical procedure called the Runge–Kutta method. A comparison between the HAM, numerical and already existing results has also been made.

     

Computer simulation of the temperature and electromagnetic field in an inductively heated semiconductor

The electromagnetic and temperature fields in an inductively heated semiconductor interact with each other in a sophisticated way through the heat dependence of the material parameters and the heat source density determined by the eddy currents. The paper deals with a computer analysis of the interacting fields taking into account the nonlinear temperature dependence of the material parameters. The basic electromagnetic and heat conduction equations are discussed, and a transformation will be introduced for the calculation of the electromagnetic field outside the material. The nonlinear equation system resulting from discretization is solved by an iterative method, whose relaxation factor is optimized during the iteration. Experiences gained in the course of the numerical calculations are reported, and results of a calculation performed with specific physical data are described.