From 9b52b301fc9823c8cd8b1b6b275c940a24972291 Mon Sep 17 00:00:00 2001 From: JLiu_93 Date: Tue, 27 Apr 2021 17:04:04 +0800 Subject: [PATCH 1/8] add 42.pimpleFoam.md. --- 42.pimpleFoam.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 42.pimpleFoam.md diff --git a/42.pimpleFoam.md b/42.pimpleFoam.md new file mode 100644 index 0000000..e69de29 -- Gitee From 29073460e1e96e2611db191bbf37b994a05134c4 Mon Sep 17 00:00:00 2001 From: JLiu_93 Date: Wed, 28 Apr 2021 21:50:33 +0800 Subject: [PATCH 2/8] update 42.pimpleFoam.md. --- 42.pimpleFoam.md | 150 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 150 insertions(+) diff --git a/42.pimpleFoam.md b/42.pimpleFoam.md index e69de29..6bdb735 100644 --- a/42.pimpleFoam.md +++ b/42.pimpleFoam.md @@ -0,0 +1,150 @@ +### 42 $\textit{pimpleFoam}$ + +$\textit{pimpleFoam}$ 是一个使用PIMPLE算法的瞬态不可压缩求解器。PIMPLE算法是PISO和SIMPLE的组合。该求解器在文件$\text{pimpleFoam.C}$中描述如下。 + +``` +使用PIMPLE(合并的PISO-SIMPLE)算法对不可压缩的流进行求解的大时间步长瞬态求解器。 + +湍流模型是通用的,即可以选择层流、RAS或LES。 +``` + +#### 42.1 控制方程 + +##### 42.1.1 连续性方程 + +一般的连续性方程具有以下形式: + +

+$$ +\frac{\partial\rho}{\partial t} + \nabla \cdot (\rho \mathbf{u}) = 0 +\tag{64} +$$ +

+ +我们假设流体不可压缩:$\rho = const$ + +

+$$ +\nabla \cdot \mathbf{u} = 0 +\tag{65} +$$ +

+ +或者使用其他形式 + +

+$$ +div(\mathbf{u}) = 0 +\tag{66} +$$ +

+

+$$ +\frac{u_i}{x_i} = 0 +\tag{67} +$$ +

+ +##### 42.1.2 动量方程 + +从纳维-斯托克斯方程出发,得出$\text{pimpleFoam}$的动量方程。 + +

+$$ +\frac{\partial \rho \mathbf{u}}{\partial t} + \nabla (\rho \mathbf{u} \mathbf{u}) + \nabla \cdot \tau = -\nabla p + \mathbf{g}= 0 +\tag{68} +$$ +

+ +我们假设密度为常数,方程两边同除以$\rho$ + +

+$$ +\frac{\partial \mathbf{u}}{\partial t} + \nabla (\mathbf{u} \mathbf{u}) + \frac{1}{\rho}\nabla \cdot \tau = -\frac{\nabla p}{\rho} + \frac{\mathbf{g}}{\rho} +\tag{69} +$$ +

+ +最后一项定义成一般源项 + +

+$$ +\frac{\partial \mathbf{u}}{\partial t} + \nabla (\mathbf{u} \mathbf{u}) + \frac{1}{\rho}\nabla \cdot \tau = -\frac{\nabla p}{\rho} + \mathbf{Q} +\tag{70} +$$ +

+ +切向应力和压力用新符号表示:$\frac{\tau}{\rho} = \mathbf{R}^{eff}\text{ und } \frac{p}{\rho}=p$ + +

+$$ +\frac{\partial \mathbf{u}}{\partial t} + \nabla (\mathbf{u} \mathbf{u}) + \nabla \cdot \mathbf{R}^{eff} = -\frac{\nabla p}{\rho} + \mathbf{Q} +\tag{71} +$$ +

+ +Boussinesq假说允许我们给切向应力加上雷诺应力。这个切向应力—也就是同时包含切向应力与雷诺应力—这里被写做$\mathbf{R}^{eff}$,也就是有效应力张量。 RAS和LES湍流模型都基于Boussinesq假设。 + +

+$$ +\mathbf{R}^{eff} = -\nu^{eff}(\nabla \mathbf{u} + (\nabla \mathbf{u})^T) +\tag{72} +$$ +

+ +

+$$ +R_{ij}^{eff} = -\nu^{eff}(\frac{u_i}{x_j} + \frac{u_j}{x_i}) +\tag{73} +$$ +

+ +$\tau$的迹满足不可压缩流的连续性方程 + +

+$$ +tr(\mathbf{R}^{eff}) = -2\nu^{eff}(\frac{u_i}{x_i})=0 +\tag{74} +$$ +

+ +

+$$ +\frac{u_i}{x_i} = \nabla \cdot \mathbf{u} =0 +\tag{75} +$$ +

+ +因此,我们可以用$\mathbf{R}^{eff}$偏应力部分替代$\mathbf{R}^{eff}$ + +

+$$ +\mathbf{R}^{eff} = \underbrace{dev(\mathbf{R}^{eff})}_{deviatoric\ part} + \underbrace{\frac{1}{3} tr (\mathbf{R}^{eff})\mathbf{I}}_{hydrostatic\ part} +\tag{76} +$$ +

+ +

+$$ +dev(\mathbf{R}^{eff}) = \mathbf{R}^{eff} - \frac{1}{3} \underbrace{tr (\mathbf{R}^{eff})}_{=0}\mathbf{I} +\tag{77} +$$ +

+ +动量方程可以被改写为 + +

+$$ +\frac{\partial \mathbf{u}}{\partial t} + \nabla (\mathbf{u} \mathbf{u}) + \underbrace{\nabla \cdot (dev(\mathbf{R}^{eff}))}_{=div(dev(\mathbf{R}^{eff}))} = -\frac{\nabla p}{\rho} + \mathbf{Q} +\tag{78} +$$ +

+ +带入方程72,最终可以得到 + +

+$$ +\frac{\partial \mathbf{u}}{\partial t} + \nabla (\mathbf{u} \mathbf{u}) + \nabla \cdot (dev(-\nu^{eff}(\nabla \mathbf{u} + (\nabla \mathbf{u})^T)))= -\frac{\nabla p}{\rho} + \mathbf{Q} +\tag{79} +$$ +

-- Gitee From 518402f1d965408f95327010c091897195fb6075 Mon Sep 17 00:00:00 2001 From: JLiu_93 Date: Wed, 28 Apr 2021 22:51:09 +0800 Subject: [PATCH 3/8] update 42.pimpleFoam.md. --- 42.pimpleFoam.md | 67 +++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 66 insertions(+), 1 deletion(-) diff --git a/42.pimpleFoam.md b/42.pimpleFoam.md index 6bdb735..9f39328 100644 --- a/42.pimpleFoam.md +++ b/42.pimpleFoam.md @@ -119,7 +119,7 @@ $$

$$ -\mathbf{R}^{eff} = \underbrace{dev(\mathbf{R}^{eff})}_{deviatoric\ part} + \underbrace{\frac{1}{3} tr (\mathbf{R}^{eff})\mathbf{I}}_{hydrostatic\ part} +\mathbf{R}^{eff} = \underbrace{dev(\mathbf{R}^{eff})}_{偏应力张量} + \underbrace{\frac{1}{3} tr (\mathbf{R}^{eff})\mathbf{I}}_{静水应力张量} \tag{76} $$

@@ -148,3 +148,68 @@ $$ \tag{79} $$

+ +##### 42.1.3 实现 + +动量方程实现在$\text{UEqn.H}$这个文件中。方程79的前两项可以很容易的在代码列表263中读出。 + +其中第一项是动量的局部导数—由于流体不可压缩,密度不包含在项内—位于列表263的第5行。这里,源代码中的指令与数学符号的读法非常一致。 + +

+$$ +\frac{\partial \mathbf{u}}{\partial t}\qquad \Leftrightarrow\qquad \text{fvm::ddt(U)} +$$ +

+ +方程79的第二项描述了动量的对流输运。标识符$\text{phi}$不应该导致混淆。为了方便从源代码中读取方程,这里可以用$\text{U}$代替$\text{phi}$,其并不改变方程的含义。源代码中为什么使用$\text{phi}$与求解过程有关。关于$\text{phi}$的详细讨论见第63节。 + +

+$$ +\underbrace{\nabla(\mathbf{u}\mathbf{u})}_{div (\mathbf{u}\mathbf{u})} \qquad \Leftrightarrow \qquad \text{fvm::div(phi, U)} +$$ +

+ +第三项代表的是动量扩散传输项。动量扩散传输是由层流黏度和湍流引起的。因此,由湍流模型处理这个项。见代码列表263的第7行。 + +

+$$ +\underbrace{\nabla\cdot(dev(\mathbf{R}^{eff}))}_{=div(dev(\mathbf{R}^{eff})} \qquad \Leftrightarrow \qquad \text{turbulence->divDevReff(U)} +$$ +

+ +方程79的右边两项分别代表压力梯度和源项。 + +

+$$ +\underbrace{-\nabla p}_{=-grad p} \qquad \Leftrightarrow \qquad \text{-fvc::grad(p))} +$$ +

+ +

+$$ +\mathbf{Q} \qquad \Leftrightarrow \qquad \text{sources(U)} +$$ +

+ +``` +tmp UEqn +( + fvm::ddt(U) + + fvm::div(phi , U) + + turbulence ->divDevReff(U) +); + +UEqn().relax(); + +sources.constrain(UEqn()); + +volScalarField rAU (1.0/ UEqn().A()); + +if (pimple.momentumPredictor ()) +{ + solve(UEqn() == -fvc::grad(p) + sources(U)); +} +``` +列表 263:$\text{pimpleFom}$的$\text{UEqn.H}$文件 + + -- Gitee From b5efac9691a2eeba1d1e9c2554fb268bd16b2663 Mon Sep 17 00:00:00 2001 From: JLiu_93 Date: Wed, 28 Apr 2021 22:52:19 +0800 Subject: [PATCH 4/8] update 42.pimpleFoam.md. --- 42.pimpleFoam.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/42.pimpleFoam.md b/42.pimpleFoam.md index 9f39328..ac67910 100644 --- a/42.pimpleFoam.md +++ b/42.pimpleFoam.md @@ -181,7 +181,7 @@ $$

$$ -\underbrace{-\nabla p}_{=-grad p} \qquad \Leftrightarrow \qquad \text{-fvc::grad(p))} +\underbrace{-\nabla p}_{=-grad\ p} \qquad \Leftrightarrow \qquad \text{-fvc::grad(p))} $$

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update 42.pimpleFoam.md. --- 42.pimpleFoam.md | 101 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 101 insertions(+) diff --git a/42.pimpleFoam.md b/42.pimpleFoam.md index ac67910..1a00ddf 100644 --- a/42.pimpleFoam.md +++ b/42.pimpleFoam.md @@ -213,3 +213,104 @@ if (pimple.momentumPredictor ()) 列表 263:$\text{pimpleFom}$的$\text{UEqn.H}$文件 +#### 42.2 PIMPLE 算法 - 内部机制是怎样的? + +这一节我们将要讨论$\text{pimpleFoam}$和$\text{twoPhaseEulerFoam}$, 即两种使用PIMPLE算法的求解器,是如何工作的。代码列表264展示了$\text{pimpleFoam}$的主循环。 + +第一条指令表示循环所有的时间步。接着是三个$\text{#include}$开头的指令,其主要关于时间步控制。时间步增加以后($\text{runTime ++;}$), PIMPLE循环开始了。 + +在这个循环里, 首先动量方程被解出($\text{#include "UEqn.H"}$),然后进入压力修正循环($\text{#include "pEqn.H"}$)。最终,如果有湍流方程的话,PIMPLE循环会对该方程解($\text{turbulence ->correct ();}$)。在每个时间步的结尾数据都会被写出。 + + +``` +while (runTime.run()) +{ + #include "readTimeControls.H" + #include "CourantNo.H" + #include "setDeltaT.H" + + runTime ++; + +// --- 压力-速度 PIMPLE 修正循环 + while (pimple.loop()) + { + #include "UEqn.H" + + // --- Pressure corrector loop + while (pimple.correct ()) + { + #include "pEqn.H" + } + + if (pimple.turbCorr ()) + { + turbulence ->correct (); + } + } + + runTime.write (); +} +``` + +图105展示了PIMPLE算法的流程图。这个算法在每个时间步都会被执行。如果PIMPLE循环只被执行一次,这个算法就和PISO算法基本一致。我们可以从代码列表271得到这个结论。 + +![](images/fig105.png) + +图105:PIMPLE算法流程图 + +##### 42.2.1 $\text{readTimeControl.H}$ + +在代码列表264第三行中,$\text{readTimeControl.H}$被包含在使用了$\text{#include}$的预处理器宏的源码中。这是一种非常常见的方法,可以使OpenFOAM的代码具有结构和秩序。重复使用的代码被写在一个单独的文件中。然后用$\text{#include}$宏把这个文件包含起来。因此,代码的重复就可以避免了。$\text{readTimeControl.H}$文件可能被包含在每个能够使用可变时间步长的求解器中。如果这段代码没有被另外写到一个单独的文件中,这段代码就会在每个可变时间步长的求解器中被发现。维护这段代码,会很累人而且容易出错。 + +代码列表265显示了$\text{readTimeControl.H}$的内容。第一条指令从$\text{controlDict}$中读取$\text{adjustTimeStep}$参数。如果没有参数($\text{"adjustTimeStep"}$),那么就会使用默认值。因此,省略$\text{controlDict}$中的参数$\text{adjustTimeStep}$将导致时间步长固定。这是一个非常直接的例子,即只用源代码来确定求解器的行为。在这种情况下,源文件的名称以及变量和函数的名称是不言而喻的。在其他情况下,我们必须深入研究代码,以了解某个命令的作用。 + +##### 42.2.2 $\text{pimpleControl}$ + +检查文件$\text{pimpleControl.H}$和$\text{pimpleControl.C}$将加强我们对$\text{pimpleFoam}$内部原理的理解。 + +###### 求解控制 + +代码列表266和277展示了$\text{pimpleControl.H}$和$\text{pimpleControl.C}$的部分源码。代码列表266显示了$\text{pimpleControl.H}$中保护数据的声明。 + + +``` + // 受保护数据 + // 求解控制 + //- PIMPLE最大修正数 + label nCorrPIMPLE_; + + //- PISO最大修正数 + label nCorrPISO_; + + //- 当前PISO修正器 + label corrPISO_; + + //- 标记在最后迭代中是否需要求解湍流 + bool turbOnFinalIterOnly_; + + //- 收敛标记 + bool converged_; +``` + +代码列表266:$\text{pimpleControl.H}$中受保护数据 + + +``` +void Foam:: pimpleControl ::read() +{ + solutionControl ::read(false); + + // 读入求解控制 + const dictionary& pimpleDict = dict(); + + nCorrPIMPLE_ = pimpleDict.lookupOrDefault