CFX11_07_Solver

合集下载

7_CFX-solver

基本功能计算过程
定义运行过程（Define Run）监视计算过程（Monitor）停止及重启计算过程（Stop & Restart）完成计算并启动后处理程序
软件界面说明
计算过程
定义运行过程监视计算过程停止/重启启动后处理
计算过程
定义运行过程监视计算过程停止/重启启动后处理
软件界面说明
基本功能
管理题目计算（启动/暂停/重启）监控计算残差（已完成/正在进行的题目）调整求解内存输出结果（多种格式：CGNS / MSC Patran / Fieldview / Ensight）并行计算编辑定义文件/结果文件插值原有结果到新的定义文件/结果文件
CFX-Solver
软件界面说明
软件界面介绍
软件界面介绍
启动/监控/关闭模拟过程退出CFX-Solver程序
软件界面介绍
软件设置
软件界面介绍
工作空间属性/监控停止/重启/备份运行
界面窗口布置
残差观察重置/关闭工作空间
软件界面介绍
定义文件/结果文件管理
编辑结果文件启动CFX-Post 环境变量显示
软件界面介绍
监控动量/质量变量监控传热变量监控紊流变量输出文件
软件界面介绍
链接到Solver Manager 帮助文档
主帮助文档（包含 CFX所有帮助信息）
关于Solver Manager 帮助的使用方法
软件界面介绍
定义题目运行（def文件/初始值文件/串（并）行/高级设置）监控正在进行的计算过程（batch模式或SolverManager关闭）显示已计算完成的过程直接编辑定义文件（有限制地修改部分参数） CFX结果文件转换为其它格式将计算结果插值到另一题目中启动CFX-Post，显示题目计算结果工作空间列表

微分方程求解器solver说明

有效值：正实数或向量；
默认值：1e-6
绝对误差对应于解向量中的所有元素；向量则分别对应于解向量中的每一分量
RelTol
有效值：正实数；
默认值：1e-3
相对误差对应于解向量中的所有元素；在每步计算过程中，误差估计为：
e(k)<=max(RelTol*abs(y(k)), AbsTol(k))
NormControl
输出
odeplot
ODE的时间序列图
ode45
普通4~5阶法解ODE
odephas2
ODE的二维相平面图
ode15s
变阶法解刚性ODE
odephas3
ODE的三维相平面图
ode113
普通变阶法解ODE
odeprint
在命令窗口输出结果
表二：不同求解器的特点
Solve
ODE类型
特点
说明
ode45
非刚性
有效值：on，off
默认值：off
为on时，控制解向量范数的相对误差，使每步计算中有：norm(e)<=max(RelTol*norm(y), AbsTol)
Events
有效值：on，off
返回相应的时间记录
OutputFcn
有效值：odeplot，odephas2，odephas3，odeprint
默认值：odeplot
若无输出参数，则solver执行下面操作之一：
画出解向量中各元素随时间的变化；
画出解向量中前两个分量构成的相平面图；
画出解向量中的前三个分量构成的三维相平面图；
随计算过程，显示解向量
OutputSel
有效值：正整数向量；
默认值：[ ]
若不使用默认设置，则属性所表现的是那些正整数指定的解向量中的分量的曲线或数据。若为默认值时，则默认地按上面情形进行操作

CFX求解经验

初值：不用说了，全选Automatic，这个选项让solver自动从文件中读入初场。
有些word的公式编辑的字符没输进去，订正如下
1，第2段最后，湍流模型一般选k-epsilon，对有流动分离的场合选基于k-omega的SST模型，甚至可选雷诺应力的SSG模型，不过越复杂的模型越难收敛。
2，第3段，稳态流场时间步长估计式：delta t=L/2U。U和L分别为特征速度和特征长度。我的建议：比这个步长再稍小一些。
最后需要设定的是求解控制参数。首先是对流项离散格式的选取。CFX中提供了三个选项：一阶迎风格式、high resolution、修正格式(blend factor)。一阶格式鲁棒性最好，但求解精度稍低。二阶格式精度好，但鲁棒性及收敛速度略差。根据CFX自带文献的说法，按精度的要求，得到较好的解通常需要blend factor应在0.75以上。其次是时间步长的选取：文献提供了对流占主导地位的稳态流动的流场时间步长的估计式：；在保证收敛的情况下，大的时间步长有助于快速收敛，小的时间步对收敛速度有负面的影响。迭代的次数：文献建议，对于一般问题，选在在100～200步以内。
收敛标准：一般选RMS 10e-5可满足通常需要。
3，进行瞬态计算，将接口设为transient rotor-stator，其界面插值方式我也不太清楚，请高手指教。
时间间隔(total time)选为能使节距最大的叶片转一个节距所需的时间。确定需要计算的瞬态流场的个数，一般不少于10个，假定为n，则timesteps为total time/n 。每个时间步的迭代数(Max. Iter. Per Timestep)一般选3，提高计算精度可以通过减小时间步长达到，每个时间步的迭代数不计算中，由于各个部分流动特点或几何位置不同，在CFX中需要将其分成若干个域，对这些不同的域，用户可以根据需要对每个域设置各自的初始值以及计算时间步长。为组成整个流场，需要用域接口(domain interface)将各个域连接起来。根据域之间的相对运动情况，可将接口性质定义为none(无相对运动)、frozen rotor(静止的动叶)等等。在级的计算中，常见的是静叶与动叶之间的接口。由于我们准备先按稳态计算，故将接口性质选frozen rotor ，在有节距变化时，将对物理量沿节距分布型线进行拉伸或压缩。

cfx参数

11.2. Command-Line Options and Keywords for cfx5solve
The command-line options for cfx5solve are described below. To see command-line help, run cfx5solve -help.
Command-Line Options -file <file>
Alternative form le <file>
Usage the run from the specified CFX-Solver results file. The mesh from the CFX-Solver input file is used unless the -use-mesh-from-iv option is also specified. Only one -continue-from-file argument can be supplied. See Continuing the History in the CFX-Solver Modeling Guide for more details.
-ansys-install ation <directory>
-ansys-jobname <name>
-ansys-license <licensekey>
-ansys-restart <file>
Causes the flow solver to write a backup file every <elapsed time -bak-elapsed-t frequency> hours, minutes, -baket ime <elapsed seconds, et cetera. Elapsed time <elapsed time time must be in quotes and have units in frequency> frequency> square brackets. For example: -baket “10 [min]” or -baket “5 [hr]”. -batch Starts CFX-Solver in batch mode (that is, without starting the CFX-Solver Manager interface). Reads Command Language from the named file, and uses it to provide

CFX培训教材03求解器设置ppt课件

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求解器控制 – 收敛标准
收敛标准用于判别求解是否收敛，以及是否停止求解器的运行 – 假定最大的迭代步数未达到
残差是求解方程应达到的精度 – 求解的过程是从初始解逐渐逼近理论上的精确解，但是永远不能达到精确解 – 小的残差设置=高的方程求解精 – 高的方程精确求解≠整个求解的高精度 – 取决于方程对真实系统的描述是否合适! – 残差是表征精度高低的一个量度，其它的量度还有: • 监测点和不平衡量
设定守恒目标(Conservation Target)= 设定全局的非平衡量目标
% Imbalance Flux In Flux Out Maximum Flux
非平衡量表征流体域内所有量(质量, 动量, 能量)的守恒性
• 对收敛解Flux In=Flux Out • 建议在求解的过程中，设置守恒目标和/或守恒监测 • 有了守恒目标, 求解器必须在既满足残差目标，又满足守恒目标下才能停止求解 (假
– 也可以选择物理时间步或者直接给一个时间步
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求解器控制– 方程的分类设置
方程的分类设置(Equation Class Settings)按钮提供一个高级的选择，用于对某些方程进行特别的求解控制
• 通常，每个文件应该是空间分离的 • 最好求解器输入文件的domains与
多初值文件的domains不重叠
6
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求解器控制 – 编辑
7
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ANSYSCFX11.0双向流固耦合实现步骤（原创）

流固耦合方法要实现流固耦合首先要确定固体模型和流体模型。

本设计的流体和固体模型都是在ANSYS Workbench中建立的（也可以用其他的三维建模工具）。

建模后将流体模型输出为IGES格式，然后导入到ICEM中化分网格备用。

固体模型则直接在Workbench中的Simulation中定义固支面和流固耦合面等，并划分网格。

最后输出inp文件。

最后利用CFX进行双向流固耦合计算。

具体步骤在下面分别叙述。

流体部分1.流体模型的建立启动ANSYS Workbench，点击New geometry开启DesignModeler。

在这里可以采用多种建模方法，我用的是直接在Create下拉菜单中选择最底部的Primitives 中的bend选项，直接建立一系列的扇形环柱体。

即可组成流体域的模型，在这里不再赘述。

2.流体网格的划分建模后将流体模型输出为IGES格式，然后导入到ICEM中。

在ICEM中通过点和线处理工具删掉一些多于的线并补上必要的点（分块的时候用来固定节点）。

然后创建体，在创建的提示栏中选择所有的面。

注意体形成后要多还几个角度观察，以确定solid点在整个模型的内部。

接下来就要分块，点击blocking按钮，选择整个实体为对象创建块。

之后将块沿边界切割成若干子块，删掉不需要的子块。

然后把快上的节点固定在相应的实体的点上，把块的边界线固定在相应的实体线上。

然后在块的特征边上设定节点数，化分网格。

3.网格输出网格划分完之后，需要将网格从ICEM CFD导出到计算软件ANSYS CFX中做计算，其具体的操作步骤如下：（1）选择File > Mesh > Load from Blocking;（2）选择File > Blocking > Save Multiblock Mesh,在出来的对话框上选择V olume。

（3）选择Output > Select solver,在出来的对话框上选择计算所用的软件ANSYS CFX，点击Okay。

CFX12_04_Solver_C

– 收敛的结果与所使用的时间步无关
Initial Guess 50 iterations 100 iterations 150 iterations Final Solution
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
– 如果时间步太小，收敛速度将降低，如果时间步太小，收敛速度将降低，时间代价较大
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
4-15
April 28, 2009 Inventory #002598
Solver Settings
Solver Settings
初始化
• • • •
Training Manual
迭代求解的过程需要在计算前对所有的求解变量指定一个初始值
合理的初值可以减少求解时间
在个别情况下，在个别情况下，不合理的初值可能在计算开始的几步就导致求解失败
设置初值的3个方法设置初值的个方法: 个方法
1. 求解器自动计算初值 2. 手动输入初值 3. 以计算结果作为初值
Training Manual
Unsteady
Advection
Diffusion
Generation
• 三种可供选择的格式：High Resolution, 三种可供选择的格式： Upwind 和 Specified Blend
– 后续将有讨论
• 默认的High Resolution格式，一般不作修改默认的格式，格式
φip = φ up + β ∇φ ⋅ ∆r
– 这里 ∇φ 是变量梯度，∆r 是上游节点到插值节点的矢量是变量梯度， – 换言之 ip 点的值等于上游的值一基于梯度的修正换言之, 点的值等于up上游的值上游的值+一基于梯度的修正 – 0<β<1… 0<β<1 β<1

python 解复杂方程组复数域solve 函数

文章标题：探讨Python中解复杂方程组复数域的solve函数一、引言复杂方程组在数学和科学领域中有着广泛的应用，而Python作为一种强大的编程语言，提供了solve函数来解决复杂方程组，在复数域中尤为重要。

本文将从简单到复杂，由浅入深地探讨Python中解复杂方程组复数域的solve函数。

二、复数域的概念和应用复数是由实部和虚部组成的，通常表示为a+bi的形式，其中a和b分别为实数部分和虚数部分。

在实际问题中，很多方程组涉及到复数，比如电路分析、量子力学等。

解决复数域中的方程组对于实际问题具有重要意义。

三、Python中的solve函数Python中的solve函数是用来求解代数方程组的，它可以处理实数域和复数域中的方程组。

当方程组涉及到复数时，使用solve函数可以方便地得到方程组的解，从而进行进一步的分析和计算。

四、使用solve函数解复数域方程组的示例为了更好地理解solve函数在复数域中的应用，我们通过一个简单的示例来展示其用法。

考虑方程组：1. z + 2i = 02. 2z - 3i = 5其中z为复数，i为虚数单位。

我们可以使用solve函数来求解这个方程组，在Python中的代码如下：```pythonfrom sympy import Symbol, Eq, solvez = Symbol('z')equation1 = Eq(z + 2j, 0)equation2 = Eq(2*z - 3j, 5)solution = solve((equation1, equation2), z)print(solution)```在这段代码中，我们首先引入了Symbol、Eq和solve函数，然后定义了方程组的两个方程，最后使用solve函数求解得到了方程组的解。

在这个示例中，solve函数成功地求解了复数域中的方程组，并输出了解z的值。

五、深入理解solve函数的实现原理solve函数的实现原理涉及到复数域中方程组的求解算法，这超出了普通用户的使用范围。

7_CFX-solver

• 软件界面说明
软件界面介绍
软件界面介绍
软件界面介绍
软件界面介绍
启动/监控/关闭模拟过程
退出CFX-Solver程序
软件界面介绍
软件设置
软件界面介绍
工作空间属性/监控停止/重启/备份运行界面窗口Biblioteka 置残差观察重置/关闭工作空间
软件界面介绍
定义文件/结果文件管理
编辑结果文件启动CFX-Post 环境变量显示
• 软件界面说明
基本功能
管理题目计算（启动/暂停/重启）监控计算残差（已完成/正在进行的题目）调整求解内存输出结果（多种格式：CGNS / MSC Patran / Fieldview / Ensight）并行计算编辑定义文件/结果文件插值原有结果到新的定义文件/结果文件
CFX-Solver
• 基本功能 • 计算过程
定义运行过程（Define Run）监视计算过程（Monitor）停止及重启计算过程（Stop & Restart）完成计算并启动后处理程序
• 软件界面说明
计算过程
定义运行过程监视计算过程停止/重启
启动后处理
计算过程
定义运行过程监视计算过程停止/重启
启动后处理
软件界面介绍
软件界面介绍
软件界面介绍
工作空间属性设置（控制显示内容和方式）监控新的数据
版面布置切换工作窗口罗列载入版面布置文件停止正在进行的计算继续开始计算存储备份文件
编辑/修改运行题目的参数文件
编辑/修改已运行完毕题目的参数文件显示均方残差显示最大残差关闭工作空间
计算过程
定义运行过程监视计算过程停止/重启

Excel Solver的用法

然后点击“工具”菜单中的Solver，将Set Target Cell设为$G$22这个单元格，将By Changing Cells设为$F$8:$F9这两个单元格，即改变L和K的值，Equal To选中Min这项，其他的选项不用理会，如下图：
然后点右上角的Solver，$F$8:$F9就会改变，改变之后的值即为优化的L和K值。
Solver求解非线性回归问题的方法：
假设X和Y满足这样一个关系：Y=L(1-10-KX)，实验测得一组X和Y的值如下：
X
Y
0
0
0.54
183
0.85
225
1.50
286
2.46
380
3.56
470
5.00
544
求L和K的值。
在Excel中随便假设一组L和K的值，比如都假设为1，以这组假设的值，求出一组Y’，然后再求出一组(X-Y)2的值，再将求出的这组(X-Y)2的值用Sum函数全部加起来(下面的图中，全部加起来结果在$G$22这个单元格中)。
4、非线性回归
5、求函数在某区间内的极值
注意：Solver插件可以用于解决上面这些问题，并不是说上面这些问题Solver一定可以解决，而且有时候Solver给出的结果也不一定是最优的。
Solver安装方法：
Solver是Excel自带的插件，不需要单独下载安装。但Excel默认是不启用Solver的，启用方法：在”工具”菜单中点击“插件”，在Solver Add-In前面的方框中打勾，然后点OK，Excel会自动加载Solver，一旦启用成功，以后Sovler就会在”Excel一个功能非常强大的插件(Add-Ins)，可用于工程上、经济学及其它一些学科中各种问题的优化求解，使用起来非常方便，Solver包括（但不限于）以下一些功能：

CFX11_05_Solver Control

3/23/2007 © 2007 ANSYS, Inc. All rights reserved. CFX 11.0 ANSYS, Inc. Proprietary
Inventory #002445 5-2
Version 1.3
How to Define Solver Settings • As shown before…
High resolution Scheme
Inventory #002445 5-5
Version 1.3
Timestep
• ANSYS CFX employs the so called False Transient Algorithm. It requires timestep to simulate iteration. • In a Steady State simulation the timestep provides relaxation of the equation non-linearities • A steady-state simulation is a transient evolution of the flow from the initial guess to the steady-state conditions
Theory
• Upwind
– 1st Order Accurate, robust
Upwind Scheme
• Specified Blend Factor
– b fixed throughout the domain – Solution is not bounded (can get overshoots and undershoots)
3/23/2007 © 2007 ANSYS, Inc. All rights reserved.

CFX_教程-07

ห้องสมุดไป่ตู้
Inventory #002445 7-5
Version 1.3
定义一个模拟计算并行
本地并行
分布式并行
3/23/2007 © 2007 ANSYS, Inc. All rights reserved.
CFX 11.0 ANSYS, Inc. Proprietary
Inventory #002445 7-6
Version 1.3
CFX 求解器管理
讲座 7
3/23/2007 © 2007 ANSYS, Inc. All rights reserved.
CFX 11.0 ANSYS, Inc. Proprietary
Inventory #002445 7-1
Version 1.3
求解器管理器 • ANSYS CFX求解器管理器是一个图像化的界面用于: – 定义一个模拟计算 – 交互式的控制 ANSYS CFX求解器 – 显示已经求解过程的信息 – 导出数据
CFX 11.0 ANSYS, Inc. Proprietary
Inventory #002445 7-9
CFX求解 – 工作界面
CFX-Pre CFX-Solver CFX-Post
Version 1.3
单击创建 ‘New Monitor’ 界面
用户化界面
.out 文件
CFX 11.0 ANSYS, Inc. Proprietary
• 插值选项允许将一个由某一网格文件得出的结果强行让由另一个网格文件生成的定义文件所接受. • 使用ANSYS CFX-Solver的并行处理工程可以让你将一个大型的CFD问题分开求解,这样可以在不同的处理器上进行同时求解

CFX13_04_Solver

Training Manual
ANSYS, Inc. Proprietary © 2010 ANSYS, Inc. All rights reserved.
4-6
Release 13.0 December 2010
Solver Settings
Solver Control – Editing
• Edit the Solver Control object in the Outline tree
Training Manual
•
Edit each Domain to set initial values on a per-domain basis
– When both are defined the domain settings take precedence Solid domain must have initial conditions set on a perdomain basis
• If b = 0 we get the Upwind advection scheme, i.e. no correction
– This is robust but only first order accurate – Sometimes useful for initial runs, but usually not necessary
•
•
In some cases a poor initial guess may cause the solver to fail during the first few iterations
The initial values can be set in 3 ways: 1. Solver automatically calculates the initial values 2. Initial values are entered by the user 3. Initial values are obtained from a previous solution Initial values can be set on a per-domain basis or globally for all domains

CFX12_04_Solver

Chapter 4Solver SettingsIntroduction to CFX Introduction to CFXOverviewTraining Manual •Initialization•Solver ControlSolver ControlOutput Control•Output Control•Solver ManagerSolver ManagerNote: This chapter considers solver settings for steady-state simulations.N t Thi h t id l tti f t d t t i l tiSettings specific to transient simulation are discussed in a later chapter.InitializationTraining Manual •Iterative solution procedures require that all solution variables are assigned initial values before calculating a solution• A good initial guess can reduce the solution time•In some cases a poor initial guess may cause the solver to fail during the first few iterations•The initial values can be set in 3 ways:1.Solver automatically calculates the initial values1S l t ti ll l l t th i iti l l2.Initial values are entered by the userInitial values are obtained from a previous solution3.Initial values are obtained from a previous solution•Initial values can be set on a per-domain basis or globally for all domainsInitialization–Setting Initial ValuesTraining Manual•Insert Global Initialisationfrom the toolbar or by right-clicking on Flow Analysis 1•Edit each Domain to set initialvalues on a per-domain basisvalues on a per domain basis–When both are defined thedomain settings takeprecedenced–Solid domain must haveinitial conditions set on a per-domain basisd i b iInitialization–Setting Initial ValuesTraining Manual •The Automatic option means that theCFX-Solver will calculate an initial valuefor the solved variable unless a previousfor the solved variable unless a previousresults file is provided–Will be based on boundary conditionvalues and domain settingsThe Automatic with Value option means•The Automatic with Value option meansthat the specified value will be usedunless a previous results file is provided–Can use a constant value or an expressionCan use a constant value or an expressionInitialization–Using a Previous SolutionTraining Manual •To use a previous solution as theinitial guess enable the Initial ValuesSpecification toggle when launchingSpecification toggle when launchingthe Solver–You can provide multiple initial valuesfiles•When simulating a system you canprovide previous solutions for eachcomponent of the system as the initialcomponent of the system as the initialguess•Usually each file would correspond to aseparate region of spaceseparate region of space•It is best if domains in the Solver InputFile do not overlap with multiple initialvalues filesSolver Control –EditingTraining Manual •Edit the Solver Control object in the Outline treeSolver Control –OptionsTraining Manual •The Solver Control panel containsvarious controls that influence thebehavior of the solverbehavior of the solverp•These controls are important for theaccuracy of the solution, the stability ofthe solver and the length of time it takesto obtain a solutionto obtain a solutionTraining ManualSolver Control –Advection Scheme•The Advection Scheme refers to the way theadvection term in the transport equations ismodeled numerically modeled numerically–i.e. the term that accounts for bulk fluid motion–Often the dominant term •Three schemes are available,HighUnsteady Advection Diffusion GenerationThree schemes are available, High Resolution , Upwind and Specified Blend–Discussed in more detail next•There is rarely any reason to change from thedefault High Resolution schemeTraining ManualTraining Manual Solver Control –Advection Scheme TheoryIf =0we get the advectionφip φup βφ∇Δr⋅+=Theory Flow is misaligned with mesh 1•If β= 0 we get the Upwind advection scheme, i.e. no correction–This is robust but only first order accurateSometimes sef l for initial r ns b t–Sometimes useful for initial runs, but usually not necessaryTh S ifi d Bl d h ll tUpwind Scheme •The Specified Blend scheme allows you to specify βbetween 0 and 1 (i.e. between nocorrection up to full correction)B t thi i t t d t b b d d–But this is not guaranteed to be bounded, meaning that when the correction isincluded it can overshoot or undershootwhat is physically possible β=1.00what is physically possible •The High Resolution scheme maximizes βthroughout the flow domain while keeping High Resolution throughout the flow domain while keepingthe solution boundedSchemeSolver Control –Turbulence NumericsTraining Manual •Regardless of the Advection Schemeselection, the Turbulence equationsdefault to the First Order (Upwind)default to the First Order(Upwind)scheme–Usually this is sufficient•The High Resolution scheme can beselected for additional accuracyselected for additional accuracy–Can give better accuracy in boundarylayers on unstructured meshesSolver Control –Convergence ControlTraining Manual •The Solver will finish when it reaches Max.Iterations unless convergence is achievedsooner–If Max. Iterations is reached you may not havea converged solutionCan be useful to set Max. Iterations to a large–Can be useful to set Max.Iterations to a largenumberWhen the Solver finishes you should always•When the Solver finishes you should alwayscheck why it finished•Fluid Timescale Control sets the timescale inFluid Timescale Control sets the timescale ina steady-state simulation …Solver Control –Timescale BackgroundTraining Manual •ANSYS CFX employs the so called False Transient Algorithm – A timescale is used to move the solution towards the final answer •In a steady-state simulation the timescale provides relaxation of the qequation non-linearities•A steady-state simulation is a “transient” evolution of the flow from the initial guess to the steady-state conditionsinitial guess to the steady state conditions–Converged solution is independent of the timescale usedInitial GuessInitial Guess50 iterations100 iterations100iterations150 iterationsFi l S l tiFinal SolutionSolver Control –Timescale SelectionTraining Manual •For obtaining successfulconvergence, the selection of theconvergence,the selection of thetimescale plays an important role–If the timescale is too large, theIf th ti l i t l thconvergence becomes bouncy ormay even lead to the failure of theSolverSol er–If the timescale is too small, theconvergence will be very slow andthe solution may not be fullyaccurateSolver Control –Timescale SelectionTraining Manual •For advection dominated flow, a fraction of the fluid residence time is often a good estimate for the timescaleoften a good estimate for the timescale–A timescale of 1/3of (Length Scale / Velocity Scale) is often optimal–May need a smaller timescale for the first few iterations and for complexphysics, transonic flow,…..physics transonic flowg()g•For rotating machines, 1/ωωin rad/s) is a good choice•For buoyancy driven flows, the timescale should be based on afunction of gravity, thermal expansivity, temperature difference and function of gravity thermal expansivity temperature difference and length scale (see documentation)Solver Control –Timescale ControlTraining Manual •Timescale Control can be Auto Timescale,Physical Timescale or Local TimescaleFactor•Physical Timescale–Specify the timescale. Usually a constant butcan also be variable via an expression–Can often set a better timescale than AutoTimescale would produce –fasterconvergenceSolver Control –Timescale ControlTraining Manual •Auto Timescale–The Solver calculates a timescale based onboundary / initial conditions or current solutionand domain length scale–Use a Conservative or Aggressive estimate forthe domain length scale, or a specified value–Timescale is re-calculated and updated everyfew iterations as the flow field changes–Can set a Maximum Timescale to provide anupper limit–Tends to produce a conservative timescaleT d d i i l–Timescale factor (default = 1) is a multiplierwhich can be changed to adjust thehi h b h d t dj t thautomatically calculated timescaleTraining Manual Solver Control –Timescale Control•Local Timescale Factor–Timescale varies throughout the domainLocal Timescale =Local Mesh Length ScaleLocal TimescaleLocal Velocity Scale Smaller Timescale in high–Can accelerate convergence when vastly different local velocity scales existE g a jet entering a plenumSmaller Timescale in high velocity and/or fine mesh regions•E.g. a jet entering a plenum –Best used on fairly uniform meshes, since small element will have a small timescale which can slow convergenceL l Ti l F t i lti li f th l l ti l–Local Timescale Factor is a multiplier of the local timescale –Never use as final solution ; always finish off with a constant timescaleSolver Control –Convergence CriteriaTraining Manual •Convergence Criteria settings determinewhen the solution is considered convergedand hence when the Solver will stopand hence when the Solver will stop–Assuming Max. Iterations is not reached•Residuals are a measure of how accuratelythe set of equations have been solved–Since we are iterating towards a solution, we neverget the exact solution to the equationst th t l ti t th ti–Lower residuals mean a more accurate solution tothe set of equations (more on the next slide)Do not confuse accurately solving the equations–Do not confuse accurately solving the equationswith overall solution accuracy –the equations mayor may not be a good representation of the trueysystem!–Residuals are just one measure of accuracy andshould be combined with other measures:•Monitor Points (ch. 8) and Imbalances (below)Solver Control –Residuals TheoryTraining Manual •The continuous governing equations are discretized into a set of linear equations that can be solved. The set of linear equations can be written in the form:the form:[A] [Φ] = [b]where [A] is the coefficient matrix and [Φ] is the solution variablewhere[A]is the coefficient matrix and[]is the solution variable•If the equation were solved exactly we would have:[A] [Φ] -[b] = [0]•The residual vector [R] is the error in the numerical solution:The residual vector[R]is the error in the numerical solution:[A] [Φ] -[b] = [R]•Since each control volume has a residual we usually look at the RMSaverage or the maximum normalized residualTraining Manual Solver Control –Residuals•Residual Type–MAX: Convergence based on maximumresidual anywhere residual anywhere–RMS: Convergence based on averageresidual from all control volumes2R –Root Mean Square = n∑i i •Residual TargetF bl MAX id l–For reasonable convergence MAX residuals should be 1.0E-3, RMS should be at least1.0E-4–The targets dependent on the accuracy g p yneeded•Lower values may be needed for greateraccuracyTraining ManualSolver Control –Conservation Target•The Conservation Target sets a target for theglobal imbalances O t Fl I Fl The imbalances measure the overallFluxMaximum Out Flux In Flux Imbalance %−=•The imbalances measure the overall conservation of a quantity (mass, momentum,energy) in the entire flow domain•Clearly in a converged solution Flux In should equal Flux OutSolver Control –Elapsed Time and Interrupt ControlTraining Manual •Elapsed Time Controlp y–Can specify the maximum wall clock timefor a run–Solver will stop after this amount of timeregardless of whether it has converged•Interrupt Controlp y pp g–Can specify other criteria for stoppingthe Solver based on logical CELexpressions–When the expression returns true thesolver will stop•Any value >= 0.5 is truep–Examples•If temperature exceeds a specified valueif(areaAve(T)@wall>200[C],1,0)•If mesh quality drops below a specified value in a moving mesh case –More on logical expressions in the CEL lectureSolver Control –Solid Timescale ControlTraining Manual •This option is only available when a soliddomain is included in the simulation•The Solid Timescale should be selected suchthat it is MUCH larger than the fluid timescale(100 times larger is typical)(100times larger is typical)–the energy equation is usually very stable inthe solid zonesolid timescales are typically much larger than–solid timescales are typically much larger thanfluid timescales•The fluid timescale is estimated using Length Scale / Velocity Scale•The solid timescale is automatically calculated as function of the length scale, thermal conductivity, density and specific heat capacity–Or you can choose the Physical Timescale option and provide a timescale directlySolver Control –Equation Class SettingsTraining Manual •The Equation Class Settings tab is anadvanced option that can be used toset Solver controls on an equationspecific basisNot usually needed–Not usually needed–Will override the controls set on BasicSettings for the selected equation•Advanced Options–Advanced solver control options–Rarely neededOutput Controls –ResultsTraining Manual •The Output Control settings control the outputproduced by the Solver–The Trn Results, Trn Stats and Export tab only apply toThe Trn Results Trn Stats and Export tab only apply totransient simulations and are covered in the Transientchapter•The Results tab controls the final .res file–Generally do not use the Selected Variables (or None!)p p y goption since it probably won’t contain enoughinformation to restart the run later–Output Equation Residuals is useful if you need tocheck where convergence problems are occurring–Extra Output Variables Listcontains variables that are notwritten to the standard resultsfile• E.g. VorticityOutput Controls –BackupTraining Manual •The Backup tab controls if and whenbackup results files are automaticallywritten by the Solverwritten by the Solver•Recommend for long Solver runs in caseof power failure, network interruptions, etcof power failure network interruptions etc•Option:–Standard: Like a full results file–Essential: Allows a clean solver restart–Smallest: Can restart the solver, butthere’ll be a jump in the residuals–Selected Variables: Not recommended•Can also manually request a backup filefrom the Solver Manager at any timeFrequency of output can be adjustedOutput Controls –MonitorTraining Manual •The Monitor tab allows you to create MonitorPointsThese are used to track values of interest as–These are used to track values of interest asthe Solver runs•The Cartesian Coordinates Option is used totrack the value of a variable at a specific X, Y,Z location•The Expression Option is used to monitor thevalues of a CEL expression– E.g. Calculate the area average of Cp at theinlet boundary: areaAve(Cp)@inletinlet boundary:– E.g. Mass flow of particular fluid through anoutlet: oil.massFlow()@outlet•In steady-state simulations you should createmonitor points for quantities of interestg–One measure of convergence is when thesevalues are no longer changingSolver ManagerTraining Manual •The CFX-Solver Manager is a graphical user interface used to:–Define a run–Control the CFX-Solver interactively–View information about the emerging solutionpo t data–Export dataSolver Manager–Defining a RunTraining Manual •Define a new Solver runp•Solver Input File should be the .def file–Can also pick .res, .bak or _full.trn files to restart aprevious incomplete run•To make a physics change and restart a solution,To make a ph sics change and restart a sol tioncreate a new .def file and provide it as the SolverInput File then select the .res, .bak or _full.trn filein the Initial Values Specification section–If both files have the same physics, this is the sameas picking the .res/.bak/_full.trn file as the input fileUse Mesh From selects which mesh to use. If the•Use Mesh From selects which mesh to use.If themeshes are identical can use either option,otherwise:–If you use the Solver Input File mesh, the InitialValues solution is interpolated onto the input filesolution is interpolated onto the input file–If you use the Initial Values mesh only the physicsfrom the Solver Input File is used•Continue History From carriers over convergencehistory and iteration countersSolver Manager–Defining a Parallel RunTraining Manual •By default the Solver will run in serial– A single solver process runs on the localmachine•Set the Run Mode to one of the parallel optionsto make use of multiple cores/processorsto make use of multiple cores/processors–Requires parallel licenses–Allows you to divide a large CFD problem intosmaller partitionssmaller•Faster solution times•Solve larger problems by making use of memory(RAM) on multiple machines•The Local Parallel options should be usedwhen running on a single machinewhen running on a single machine•The Distributed Parallel options should beused when running across multiple machinesused when running across multiple machinesSolver Manager–Defining a Parallel RunTraining Manual•Serial•Local ParallelLocal Parallel•Distributed ParallelDistributed Parallel•Different communication methods are available (MPICH2, HP MPI, PVM)–See documentation “When To Use MPI or PVM” for more details, but HP MPI is recommended in most casesSolver Manager–Define Run Advanced ControlsTraining Manual•The Show Advanced Control toggle enables thePartitioner, Solver and Interpolator tabs•On the Partitioner tab you can pick differentpartitioning algorithms–Partitioning is always a serial process–Can be a problem for rge cases since youcannot distribute the memory load across multiplemachines–The default MeTiS algorithm uses more memorythan others, so if you run out of memory use adifferent method (see documentation for details)•Multidomain Option:–Independent Partitioning: Each domain ispartitioned into n partitions–Coupled Partitioning: All domains are combinedand then partitioned into n partitionsThere s a specific option for Transient Rotor Stator•There’s a specific option for Transient Rotor StatorcasesSolver Manager–Define Run Advanced ControlsTraining Manual •On the Solver tab you can select the DoublePrecision option–The solver will use more significant figures in itsThe solver will use more significant figures in itscalculations–Doubles solver memory requirementsUse when round-off error could be a problem –if–Use when round-off error could be a problem–if‘small’ variations in a variable are important,where ‘small’ is relative to the global range ofthat variable, e.g:•Many Mesh Motion cases, since the motion is oftensmall relative to the size of the domain•Most CHT cases, since thermal conductivity isvastly different in the fluid and solidvastly different in the fluid and solid•If you have a wide pressure range, but smallpressure changes are important–Small values by themselves do not need DP•The Solver estimates its memory requirements upfront•Memory Alloc Factor is a multiplier for this estimate–Use when the solver stops with an “Insufficient Memory Allocated” errorSolver Manager–Interactive Solver ControlTraining Manual •During a solution Edit Run in Progress lets you make changes on the fly –Models generally cannot be changed, but timescales, BC’s, etc canTraining ManualSolver Manager –Additional Solution Monitors•By default monitor plots are created showing the RMS residuals for each New MonitorRMS residuals for each equation solved, plus one plot for any monitor points Right-click to switch •Right-click to switch between RMS and MAX•Additional monitors can be selected showing:selected showing:–Imbalances–Boundary fluxes (FLOW)B d fRight-click –Boundary forces •Tangential (viscous)•Normal (pressure)Source terms.out fileMonitor Plot–Source terms …Training ManualSolver Manager –Additional Icons•By dragging the cursor over any icon, the feature description will appear Start a new Switch R id l Pl t SimulationMonitor Finished Run Stop CurrentResidual Plot between RMS and Finished RunRunMAXMonitor Run Save Currentin ProgressRun。

CFX翻译——精选推荐

第19章求解控制求解控件可用来在解决方案阶段设定参数来控制CFX-Solver。

本章描述如下：●基本设置标签（P145）●方程类设置标签（P147）●外部耦合标签（P148）●粒子控制（P148）●高级选项标签（P148）你可以在ANSYS的流动模型建议的设置参数解决中找到更多的帮助。

CFX-Solver建模指南。

基本设置标签基本设置标签控制遵循普通和仿真具体参数：•基本设置:普通(p145)•基本设置稳态模拟(p146)•基本设置的暂态仿真(p147)•沉浸固体控制(p147)基本设置:普通水平对流方案有关详情见方案选择水平(p333)CFX-Solver建模ANSYS向导。

紊流数值计算紊流数值选择的是一阶和高分辨率。

一阶选择使用迎风的水平对流和一阶后退欧拉瞬态方案。

高分辨率选择使用高分辨率的水平对流和高分辨率的瞬态方案。

有关详情见水平方案选择（p333）CFX-Solver建模指导，运用有限元分析软件ANSYS，对瞬态方案采用有限元软件ANSYS CFX-Solver建模指导。

注意：紊流数值计算设置将覆盖在公式类的设置标签（p147）的设置。

收敛标准有关详情见有限元软件ANSYS CFX-Solver建模指南中收敛监测和获得（p336）。

●残余类型：选择均方根或最大值。

●残余目标：指定收敛值。

●有关详情见有限元软件ANSYS CFX-Solver建模指南中残余类型和目（p337）。

●保护对象：选择性地指定分数不平衡的值，默认值是0.01。

有关详情见有限元软件ANSYS CFX-Solver建模指南中保护目标（p338）。

逝去挂钟时间控制如果要停止运行持续最长访问时长（挂钟时间）就选择最大运行时间选项。

如果你选择这个选项，流场求解将自动试图估计出完成接下来的步骤或外环的反复的时间。

估计时间是平均时间，需要解决之前的迭代（包括组装和求解线性方程的时间、辐射和粒子跟踪的时间）再加上写标准备份或暂时文件的平均时间。

python 解复杂方程组复数域solve 函数

python 解复杂方程组复数域solve 函数在科学计算领域，解决复杂方程组一直是一个具有挑战性的问题。

随着计算机技术的发展和数学算法的优化，利用Python解复杂方程组变得越来越简单。

本文将介绍如何利用Python的库和函数解决复数域的复杂方程组，并给出一个具体的示例。

1.复杂方程组简介复杂方程组是由多个含有复数未知数的方程组成的。

在实际应用中，复杂方程组的求解有助于解析物理、工程、数学等领域的问题。

由于复数的特性，求解这类方程组具有一定的难度。

2.复数域求解复杂方程组的优势复数域求解复杂方程组的优势主要体现在以下几点：- 复数域中的运算规则更加简单，有助于编写高效的算法；- 复数域中的方程组可能具有更简单的结构，便于求解；- 复数具有丰富的数学性质，有助于揭示问题的本质。

3.Python中解决复数域复杂方程组的库和方法在Python中，解决复数域复杂方程组主要依赖于NumPy和SciPy库。

以下是一个简单的示例：```pythonimport numpy as npfrom scipy.linalg import solveA = np.array([[1+2j, 3+4j], [5+6j, 7+8j]])b = np.array([1+2j, 3+4j])x = solve(A, b)print(x)```4.solve函数的使用示例及解析上述代码中，我们使用了SciPy库中的solve函数来求解复数域的线性方程组。

solve函数接受两个参数：系数矩阵A和常数向量b。

在复数域中，系数矩阵和常数向量可以是复数矩阵和向量。

解析：- 首先，我们创建了一个2x2的复数矩阵A，表示复杂方程组的系数；- 其次，创建了一个2维复数向量b，表示方程组的常数项；- 然后，调用solve函数求解方程组；- 最后，输出解向量x。

5.结论与建议利用Python的NumPy和SciPy库，我们可以轻松地解决复数域的复杂方程组。

CFX软件介绍

ANSYS CFX——流体动力学分析技术的开拓者产品关键字⏹精确的数值方法⏹快速稳健的求解技术⏹丰富的物理模型⏹旋转机械流动分析的专有特征⏹先进的网格剖分技术发展历史CFX是全球第一个通过ISO9001质量认证的大型商业CFD软件，是英国AEA Technology 公司为解决其在科技咨询服务中遇到的工业实际问题而开发，诞生在工业应用背景中的CFX一直将精确的计算结果、丰富的物理模型、强大的用户扩展性作为其发展的基本要求，并以其在这些方面的卓越成就，引领着CFD技术的不断发展。

目前，CFX已经遍及航空航天、旋转机械、能源、石油化工、机械制造、汽车、生物技术、水处理、火灾安全、冶金、环保等领域，为其在全球6000多个用户解决了大量的实际问题。

回顾CFX发展的重要里程，总是伴随着她对革命性的CFD新技术的研发和应用。

1995年，CFX收购了旋转机械领域著名的加拿大ASC公司，推出了专业的旋转机械设计与分析模块－CFX-Tascflow，CFX-Tascflow一直占据着90%以上的旋转机械CFD市场份额。

同年，CFX成功突破了CFD领域的在算法上的又一大技术障碍，推出了全隐式多网格耦合算法，该算法以其稳健的收敛性能和优异的运算速度，成为CFD技术发展的重要里程碑。

CFX 一直和许多工业和大型研究项目保持着广泛的合作，这种合作确保了CFX能够紧密结合工业应用的需要，同时也使得CFX可以及时加入最先进的物理模型和数值算法。

作为CFX的前处理器，ICEM CFD优质的网格技术进一步确保CFX的模拟结果精确而可靠。

2003年，CFX加入了全球最大的CAE仿真软件ANSYS的大家庭中。

我们的用户将会得到包括从固体力学、流体力学、传热学、电学、磁学等在内的多物理场及多场耦合整体解决方案。

CFX将永远和我们的用户伙伴一起，用最先进的技术手段，不断揭开我们身边真实物理世界的神秘面纱。

产品特色CFX是全球第一个在复杂几何、网格、求解这三个CFD传统瓶径问题上均获得重大突破的商业CFD软件。

python 解复杂方程组复数域solve 函数

python 解复杂方程组复数域solve 函数（最新版）目录1.引言：介绍 Python 解复杂方程组的需求和复数域的重要性2.复数域解法：解释复数域解复杂方程组的原理3.Python 中的 solve 函数：介绍 Python 中用于解复杂方程组的 solve 函数4.使用 solve 函数解复杂方程组：具体演示如何使用 solve 函数解复杂方程组5.总结：回顾本文内容，强调 Python 解复杂方程组的便利性和复数域的重要性正文在数学领域，解复杂方程组一直是一个具有挑战性的问题。

尤其是在实际应用中，方程组的解可能涉及到复数域。

复数域在解决许多实际问题中具有重要意义，例如电路分析、控制系统等。

Python 作为一种广泛应用于科学计算的语言，提供了强大的数学库，可以方便地处理复数域的方程组。

本文将介绍如何使用Python 中的 solve 函数在复数域中解复杂方程组。

复数域解法是解决复杂方程组的一种有效方法。

在复数域中，方程组中的系数和常数可以表示为复数。

通过引入复数概念，可以扩大方程组的解空间，使得原本在实数域中无解或无穷多解的问题得以解决。

复数域解法的原理主要基于复数的代数运算和解析几何知识。

Python 中的 solve 函数位于 scipy 库中，可以用于解线性方程组、非线性方程组以及微分方程组等。

在解复杂方程组时，我们可以将方程组表示为矩阵形式，并利用 solve 函数提供的线性代数方法求解。

对于复数域的问题，我们可以通过设置方程组的系数和常数为复数来实现。

下面是一个具体的例子，展示如何使用 solve 函数解复杂方程组：```pythonfrom scipy.linalg import solve# 定义复数域方程组A = [[1+1j, 2+2j], [3+3j, 4+4j]]B = [5+5j, 6+6j]# 使用 solve 函数求解X = solve(A, B)print(X)```运行上述代码，可以得到方程组的解。