0%

laplacianFoam

Posted on In

背景介绍

导热问题，常发生在固体加热，此时由于介质均一，热量的传递仅由热扩散作用决定，因而可忽略对流的影响。

算法解析

基础知识

N-S方程：
$$
\rho(\frac{\partial \mathbf u}{\partial t}+\mathbf u \cdot\nabla\mathbf u)=-\nabla p+\mu\nabla^2\mathbf u\tag{1}
$$

$$
\nabla\cdot\mathbf u=0\tag{2}
$$

温度方程：
$$
\frac{\partial(\rho T)}{\partial t}+\nabla(\rho\mathbf U T)=\nabla\cdot(\frac{\lambda}{c_p}\nabla T)+S_T\tag{3}
$$

控制方程

在本文中，考虑非稳态导热问题，控制方程如下：
$$
\frac{\partial T}{\partial t}=\nabla\cdot(\frac \lambda {\rho c_p}) \tag{4}
$$

问题1：什么情况下散度加梯度等于拉普拉斯

代码解析

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
\*---------------------------------------------------------------------------*/

#include "fvCFD.H"       //这个之前看过
#include "simpleControl.H"     //SIMPLE控件类，用于为SIMPLE循环提供收敛信息检查

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

int main(int argc, char *argv[])
{
    #include "setRootCase.H"       //设置算例的根目录

    #include "createTime.H"        //创建时间对象
    #include "createMesh.H"        //创建网格对象
    //include "createFields.H"
    Info<< "Reading field T\n" << endl;

    volScalarField T
    (
        IOobject
        (
            "T",
            runTime.timeName(),
            mesh,
            IOobject::MUST_READ,
            IOobject::AUTO_WRITE
        ),
        mesh
    );


    Info<< "Reading transportProperties\n" << endl;

    IOdictionary transportProperties
    (
        IOobject
        (
            "transportProperties",
            runTime.constant(),
            mesh,
            IOobject::MUST_READ_IF_MODIFIED,
            IOobject::NO_WRITE
        )
    );


    Info<< "Reading diffusivity DT\n" << endl;

    dimensionedScalar DT
    (
        transportProperties.lookup("DT")
    );


    simpleControl simple(mesh);

    // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

    Info<< "\nCalculating temperature distribution\n" << endl;

    while (simple.loop())
    {
        Info<< "Time = " << runTime.timeName() << nl << endl;

        while (simple.correctNonOrthogonal())	//Non-orthogonal corrector loop，解释如下
        {
            solve
            (
                fvm::ddt(T) - fvm::laplacian(DT, T)
            );
        }

        #include "write.H"

        Info<< "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
            << "  ClockTime = " << runTime.elapsedClockTime() << " s"
            << nl << endl;
    }

    Info<< "End\n" << endl;

    return 0;
}


// ************************************************************************* //

correctNonorthogonal

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
inline bool Foam::solutionControl::correctNonOrthogonal()
 {
     corrNonOrtho_++;
 
     if (debug)
     {
         Info<< algorithmName_ << " correctNonOrthogonal: corrNonOrtho = "
             << corrNonOrtho_ << endl;
     }
 
     if (corrNonOrtho_ <= nNonOrthCorr_ + 1)
     {
         return true;
     }
     else
     {
         corrNonOrtho_ = 0;
         return false;
     }
 }