メッシュ作成事例 / 日本アムスコ

はじめに

OpenFOAMにはいくつかのメッシュ作成・編集ツールが含まれます。これらのツールを利用したメッシュ分割方法を紹介します。ここでは、以下の図のような配管を例題とし、OpenFOAM-4.1を使います。

形状

作業ディレクトリの作成

まず最初に作業用ディレクトリを作成します。

実行方法

$ mkdir -p $FOAM_RUN/emsco-jp/mixingChamber/{0,constant,system}
$ cd $FOAM_RUN/emsco-jp/mixingChamber

合流部分のメッシュ作成

合流部分のメッシュを作成します。

system/blockMesh

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      blockMeshDict;
}

convertToMeters 1.;

vertices
(
    (   -200.           0.         -50.)
    (   -100.           0.        -100.)
    (-17.6777           0.        -100.)
    (      0.           0.        -100.)
    (   -200.           0.     -33.5355)
    (   -100.           0.     -67.0711)
    (-17.6777           0.     -67.0711)
    (      0.           0.         -70.)
    (   -200.           0.     -8.83883)
    (   -100.           0.     -17.6777)
    (-17.6777           0.     -17.6777)
    (      0.           0.         -25.)
    (   -200.           0.           0.)
    (   -100.           0.           0.)
    (    -25.           0.           0.)
    (   -200.      27.5803     -27.9628)
    (   -100.      55.1606     -55.9255)
    (-17.6777      55.1606     -55.9255)
    (      0.      53.4276      -59.798)
    (   -200.      32.7797     -8.83883)
    (   -100.      65.5594     -17.6777)
    (-17.6777      65.5594     -17.6777)
    (      0.      64.4433         -25.)
    (   -200.      33.3333           0.)
    (   -100.      66.6667           0.)
    (    -25.      66.6667           0.)
    (   -200.      35.7299     -34.9768)
    (   -100.      71.4598     -69.9536)
    (-17.6777      71.4598     -69.9536)
    (      0.      68.3983     -72.9498)
    (   -200.      49.2125     -8.83883)
    (   -100.      98.4251     -17.6777)
    (-17.6777      98.4251     -17.6777)
    (      0.      96.8246         -25.)
    (   -200.          50.           0.)
    (   -100.         100.           0.)
    (    -25.         100.           0.)
    (      0.           0.           0.)
    (      0.           0.         -15.)
    (-12.5713           0.     -12.5713)
    (    -15.           0.           0.)
    (      0.      66.6667           0.)
    (      0.      65.8703         -15.)
    (-12.5713      66.1078     -12.5713)
    (    -15.      66.6667           0.)
    (      0.         100.           0.)
    (      0.      98.8686         -15.)
    (-12.5713      99.2067     -12.5713)
    (    -15.         100.           0.)
    (      0.         300.           0.)
    (      0.         300.         -15.)
    (-12.5713         300.     -12.5713)
    (    -15.         300.           0.)
    (      0.         300.         -25.)
    (-17.6777         300.     -17.6777)
    (    -25.         300.           0.)
);

blocks
(
    hex (  4   0  26  15   5   1  27  16) (  4   8  16) simpleGrading (  1   1   1)
    hex (  5   1  27  16   6   2  28  17) (  4   8  10) simpleGrading (  1   1   1)
    hex (  6   2  28  17   7   3  29  18) (  4   8   3) simpleGrading (  1   1   1)
    hex (  8   4  15  19   9   5  16  20) (  6   8  16) simpleGrading (  1   1   1)
    hex (  9   5  16  20  10   6  17  21) (  6   8  10) simpleGrading (  1   1   1)
    hex ( 10   6  17  21  11   7  18  22) (  6   8   3) simpleGrading (  1   1   1)
    hex ( 12   8  19  23  13   9  20  24) (  3   8  16) simpleGrading (  1   1   1)
    hex ( 13   9  20  24  14  10  21  25) (  3   8  10) simpleGrading (  1   1   1)
    hex ( 19  15  26  30  20  16  27  31) (  6   4  16) simpleGrading (  1   1   1)
    hex ( 20  16  27  31  21  17  28  32) (  6   4  10) simpleGrading (  1   1   1)
    hex ( 21  17  28  32  22  18  29  33) (  6   4   3) simpleGrading (  1   1   1)
    hex ( 23  19  30  34  24  20  31  35) (  3   4  16) simpleGrading (  1   1   1)
    hex ( 24  20  31  35  25  21  32  36) (  3   4  10) simpleGrading (  1   1   1)
    hex ( 37  38  39  40  41  42  43  44) (  3   3   8) simpleGrading (  1   1   1)
    hex ( 38  11  10  39  42  22  21  43) (  2   3   8) simpleGrading (  1   1   1)
    hex ( 39  10  14  40  43  21  25  44) (  2   3   8) simpleGrading (  1   1   1)
    hex ( 41  42  43  44  45  46  47  48) (  3   3   4) simpleGrading (  1   1   1)
    hex ( 42  22  21  43  46  33  32  47) (  2   3   4) simpleGrading (  1   1   1)
    hex ( 43  21  25  44  47  32  36  48) (  2   3   4) simpleGrading (  1   1   1)
    hex ( 45  46  47  48  49  50  51  52) (  3   3  24) simpleGrading (  1   1   1)
    hex ( 46  33  32  47  50  53  54  51) (  2   3  24) simpleGrading (  1   1   1)
    hex ( 47  32  36  48  51  54  55  52) (  2   3  24) simpleGrading (  1   1   1)
);

edges
(
    arc   0  26 (   -200.      19.3799     -46.0914)
    arc   1  27 (   -100.      38.7598     -92.1828)
    arc   2  28 (-17.6777      38.7599      -92.183)
    arc   3  29 (      0.      36.7765     -92.9919)
    arc   4  15 (   -200.      14.0688     -32.1284)
    arc   5  16 (   -100.      28.1377     -64.2568)
    arc   6  17 (-17.6777      28.1377     -64.2568)
    arc   7  18 (      0.      27.1965     -67.4267)
    arc  15  19 (   -200.      30.8521     -18.5835)
    arc  16  20 (   -100.      61.7043     -37.1671)
    arc  17  21 (-17.6777      61.7042     -37.1671)
    arc  18  22 (      0.      60.0609     -42.7552)
    arc  19  23 (   -200.      33.1947     -4.42807)
    arc  20  24 (   -100.      66.3896     -8.85616)
    arc  26  30 (   -200.      44.4365     -22.9216)
    arc  27  31 (   -100.       88.873     -45.8431)
    arc  28  32 (-17.6777       88.873     -45.8431)
    arc  29  33 (      0.      86.0201     -50.9956)
    arc  30  34 (   -200.      49.8027     -4.43692)
    arc  31  35 (   -100.      99.6055     -8.87384)
    arc  11  10 (-9.56709           0.      -23.097)
    arc  10  14 ( -23.097           0.     -9.56709)
    arc  38  39 (-6.40188           0.     -14.3873)
    arc  39  40 (-14.3873           0.     -6.40188)
    arc  41  42 (      0.      66.4674     -7.51056)
    arc  42  22 (      0.       65.246     -20.0127)
    arc  45  46 (      0.      99.7167      -7.5213)
    arc  46  33 (      0.      97.9743     -20.0261)
    arc  53  54 (-9.56709         300.      -23.097)
    arc  54  55 ( -23.097         300.     -9.56709)
    arc  50  51 (-6.40188         300.     -14.3873)
    arc  51  52 (-14.3873         300.     -6.40188)

    spline   6   7 ((-13.3898           0.     -68.4441)
                    (-8.97586           0.     -69.3334)
                    (-4.50057           0.     -69.8366))
    spline  17  18 ((-13.5157      54.3837     -57.6997)
                    (  -9.115      53.8465       -58.89)
                    (-4.58527      53.5316      -59.574))
    spline  28  29 ((-13.5188      70.0816     -71.3339)
                    (-9.11908      69.1344     -72.2527)
                    (-4.58804      68.5809     -72.7781))
    spline  22  21 ((-4.88586      64.5289     -24.5179)
                    (-9.57849      64.7719     -23.0923)
                    (-13.8964      65.1341     -20.7819))
    spline  21  25 ((-20.7819      65.9834     -13.8965)
                    (-23.0923      66.3425     -9.57842)
                    (-24.5179      66.5824     -4.88576))
    spline  42  43 ((-3.21621      65.8866     -14.8464)
                    (-6.40285      65.9342     -14.3871)
                    (-9.53071      66.0098     -13.6263))
    spline  43  44 ((-13.6252      66.3454      -9.5346)
                    (-14.3862      66.5217     -6.40754)
                    (-14.8461      66.6301     -3.21924))
    spline  43  21 ((-13.8488      65.9881     -13.8488)
                    (-15.1257      65.8569     -15.1257)
                    ( -16.402      65.7139      -16.402))
    spline  33  32 ((-4.89486      96.9482     -24.5161)
                    (-9.59032      97.2984     -23.0873)
                    (-13.9039      97.8178      -20.777))
    spline  32  36 ((-20.7769      99.0287     -13.9039)
                    (-23.0875      99.5391     -9.59004)
                    (-24.5162      99.8801     -4.89446))
    spline  46  47 ((-3.21688      98.8918     -14.8463)
                    (-6.40384      98.9597     -14.3869)
                    (-9.53149      99.0673     -13.6261))
    spline  47  48 ((-13.6238      99.544      -9.53933)
                    (-14.3851      99.7941     -6.41328)
                    (-14.8458      99.948      -3.22296))
    spline  47  32 ((-13.8498      99.0363     -13.8498)
                    ( -15.127      98.8492      -15.127)
                    (-16.4031      98.6455     -16.4031))
);

defaultPatch
{
    name wall;
    type wall;
}

boundary
(
    inlet1
    {
        type patch;
        faces
        (
            (  0   4  15  26)
            (  4   8  19  15)
            ( 15  19  30  26)
            (  8  12  23  19)
            ( 19  23  34  30)
        );
    }
    inlet2
    {
        type patch;
        faces
        (
            ( 49  50  51  52)
            ( 50  53  54  51)
            ( 51  54  55  52)
        );
    }
    outlet
    {
        type patch;
        faces
        (
        );
    }
    xsymm
    {
        type symmetryPlane;
        faces
        (
            (  3  29  18   7)
            (  7  18  22  11)
            ( 18  29  33  22)
            ( 37  38  42  41)
            ( 38  11  22  42)
            ( 41  42  46  45)
            ( 42  22  33  46)
            ( 45  46  50  49)
            ( 46  33  53  50)
        );
    }
    ysymm
    {
        type symmetryPlane;
        faces
        (
            (  0   1   5   4)
            (  1   2   6   5)
            (  2   3   7   6)
            (  4   5   9   8)
            (  5   6  10   9)
            (  6   7  11  10)
            (  8   9  13  12)
            (  9  10  14  13)
            ( 37  40  39  38)
            ( 38  39  10  11)
            ( 39  40  14  10)
        );
    }
    zsymm
    {
        type symmetryPlane;
        faces
        (
            ( 12  13  24  23)
            ( 13  14  25  24)
            ( 23  24  35  34)
            ( 24  25  36  35)
            ( 40  37  41  44)
            ( 14  40  44  25)
            ( 44  41  45  48)
            ( 25  44  48  36)
            ( 48  45  49  52)
            ( 36  48  52  55)
        );
    }
);

mergePatchPairs
(
);

system/controlDict

FoamFile
{
    version 2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}

deltaT          1;

writeInterval   1;

実行方法
```
$ blockMesh > log.blockMesh
```
実行結果

鏡面コピー(1)

x=0の平面で鏡面コピーします。

system/mirrorMeshDict.1

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      mirrorMeshDict;
}

planeType pointAndNormal;

pointAndNormalDict
{
    basePoint       (0 0 0);
    normalVector    (1 0 0);
}

planeTolerance 1.e-3;

実行方法

$ cp system/mirrorMeshDict.1 system/mirrorMeshDict
$ mirrorMesh -overwrite > log.mirrorMesh.1

実行結果

鏡面コピー(2)

同様に、y=0の平面とz=0の平面で鏡面コピーします。

system/mirrorMeshDict.2

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      mirrorMeshDict;
}

planeType pointAndNormal;

pointAndNormalDict
{
    basePoint       (0 0 0);
    normalVector    (0 1 0);
}

planeTolerance 1.e-3;

system/mirrorMeshDict.3

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      mirrorMeshDict;
}

planeType pointAndNormal;

pointAndNormalDict
{
    basePoint       (0 0 0);
    normalVector    (0 0 1);
}

planeTolerance 1.e-3;

実行方法

$ cp system/mirrorMeshDict.2 system/mirrorMeshDict
$ mirrorMesh -overwrite > log.mirrorMesh.2
$ cp system/mirrorMeshDict.3 system/mirrorMeshDict
$ mirrorMesh -overwrite > log.mirrorMesh.3

実行結果

パッチの分割

x=0の平面で鏡面コピーしたときに、太いパイプの入り口条件(inlet1)が本来は出口である反対にも設定されています。パッチを2つに分割して、出口側のパッチをoutletに修正します。

system/topoSetDict.1

FoamFile
{
    version    2.0;
    format     ascii;
    class      dictionary;
    location   "system";
    object     topoSetDict;
}

actions
(
    {
        name    f0;
        type    faceSet;
        action  new;
        source  patchToFace;
        sourceInfo
        {
            name    "inlet1";
        }
    }
    {
        name    f0;
        type    faceSet;
        action  delete;
        source  normalToFace;
        sourceInfo
        {
            normal  (1 0 0);
            cos     0.01;
        }
    }
    {
        name    f1;
        type    faceSet;
        action  new;
        source  patchToFace;
        sourceInfo
        {
            name    "inlet1";
        }
    }
    {
        name    f1;
        type    faceSet;
        action  delete;
        source  normalToFace;
        sourceInfo
        {
            normal  (-1 0 0);
            cos     0.01;
        }
    }
);

system/createPatchDict

FoamFile
{
    version    2.0;
    format     ascii;
    class      dictionary;
    location   "system";
    object     createPatchDict;
}

pointSync false;

patches
(
    {
        name    "inlet1";
        patchInfo
        {
            type    patch;
        }
        constructFrom set;
        set     f0;
    }
    {
        name    "outlet";
        patchInfo
        {
            type    patch;
        }
        constructFrom set;
        set     f1;
    }
);

実行方法

$ topoSet -dict system/topoSetDict.1 > log.topoSet.1
$ createPatch -overwrite > log.createPatch

パッチ分割前(blue: inlet1)
パッチ分割後(blue: inlet1, red: outlet)

余分な領域の削除

y=0の平面で鏡面コピーしたときに細いパイプが上下の2つできています。必要な領域だけを残して、余分な領域を削除します。

system/topoSetDict.2

FoamFile
{
    version    2.0;
    format     ascii;
    class      dictionary;
    location   "system";
    object     topoSetDict;
}

actions
(
    {
        name    c0;
        type    cellSet;
        action  new;
        source  cylinderToCell;
        sourceInfo
        {
            p1      ( 200.001 0. 0.);
            p2      (-200.001 0. 0.);
            radius  100.001;
        }
    }
    {
        name    c0;
        type    cellSet;
        action  add;
        source  cylinderToCell;
        sourceInfo
        {
            p1      (0.      0. 0.);
            p2      (0. 300.001 0.);
            radius  50.001;
        }
    }
);

system/fvSchemes

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSchemes;
}

gradSchemes
{
}

divSchemes
{
}

laplacianSchemes
{
}

system/fvSolution

FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      fvSolution;
}

// このファイルはヘッダ情報のみ

実行方法

$ topoSet -dict system/topoSetDict.2 > log.topoSet.2
$ subsetMesh c0 -patch wall -overwrite > log.subsetMesh

実行結果

直線押し出し(1)

入り口側を300mmだけ−x方向に押し出します。

system/extrudeMeshDict.1

FoamFile
{
    version    2.0;
    format     ascii;
    class      dictionary;
    location   "system";
    object     extrudeMeshDict;
}

constructFrom mesh;

sourceCase "$FOAM_CASE";

sourcePatches
(
    inlet1
);

exposedPatchName inlet1;

flipNormals false;

extrudeModel linearDirection;

nLayers 40;

expansionRatio 1;

linearDirectionCoeffs
{
    direction (-1 0 0);
    thickness 300;
}

mergeFaces false;

実行方法

$ cp system/extrudeMeshDict.1 system/extrudeMeshDict
$ extrudeMesh > log.extrudeMesh.1

実行結果

直線押し出し(2)

同様に、出口側を300mmだけ+x方向に押し出します。

system/extrudeMeshDict.2

FoamFile
{
    version    2.0;
    format     ascii;
    class      dictionary;
    location   "system";
    object     extrudeMeshDict;
}

constructFrom mesh;

sourceCase "$FOAM_CASE";

sourcePatches
(
    outlet
);

exposedPatchName outlet;

flipNormals false;

extrudeModel linearDirection;

nLayers 40;

expansionRatio 1;

linearDirectionCoeffs
{
    direction (1 0 0);
    thickness 300;
}

mergeFaces false;

実行方法

$ cp system/extrudeMeshDict.2 system/extrudeMeshDict
$ extrudeMesh > log.extrudeMesh.2

実行結果

回転押し出し

出口側を90degだけ回転させながら、押し出します。

system/extrudeMeshDict.3

FoamFile
{
    version    2.0;
    format     ascii;
    class      dictionary;
    location   "system";
    object     extrudeMeshDict;
}

constructFrom mesh;

sourceCase "$FOAM_CASE";
sourcePatches
(
    outlet
);
exposedPatchName outlet;

flipNormals false;

extrudeModel sector;

nLayers 40;

expansionRatio 1;

sectorCoeffs
{
    axisPt  (500 -200 0.);
    axis    (0 0 -1);
    angle   90;
}

mergeFaces false;

実行方法

$ cp system/extrudeMeshDict.3 system/extrudeMeshDict
$ extrudeMesh > log.extrudeMesh.3

実行結果

直線押し出し(3)

出口側を300mmだけ−y方向に押し出します。

system/extrudeMeshDict.4

FoamFile
{
    version    2.0;
    format     ascii;
    class      dictionary;
    location   "system";
    object     extrudeMeshDict;
}

constructFrom mesh;

sourceCase "$FOAM_CASE";

sourcePatches
(
    "outlet"
);

exposedPatchName outlet;

flipNormals false;

extrudeModel linearDirection;

nLayers 40;

expansionRatio 1;

linearDirectionCoeffs
{
    direction (0 -1 0);
    thickness 300;
}

mergeFaces false;

実行方法

$ cp system/extrudeMeshDict.4 system/extrudeMeshDict
$ extrudeMesh > log.extrudeMesh.4

実行結果

スケール

ここまで長さの単位としてミリメートルを使ってきましたが、OpenFOAMではメートル単位を使います。長さの単位を変更するために1000分の1倍にスケールします。

実行方法

$ transformPoints -scale '(0.001 0.001 0.001)' > log.transformPoints

メッシュ品質のチェック

メッシュ品質をチェックします。メッシュ品質に問題がなければ、メッシュの完成です。

実行方法
```
$ checkMesh
```

実行結果

/*---------------------------------------------------------------------------*\
| =========                 |                                                 |
| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
|  \\    /   O peration     | Version:  4.1                                   |
|   \\  /    A nd           | Web:      www.OpenFOAM.org                      |
|    \\/     M anipulation  |                                                 |
\*---------------------------------------------------------------------------*/
Build  : 4.1
Exec   : checkMesh
Date   : Mar 09 2017
Time   : 19:14:28
Host   : "?????"
PID    : 16049
Case   : /home/?????/OpenFOAM/?????-4.1/run/emsco-jp/mixingChamber
nProcs : 1
sigFpe : Enabling floating point exception trapping (FOAM_SIGFPE).
fileModificationChecking : Monitoring run-time modified files using timeStampMaster
allowSystemOperations : Allowing user-supplied system call operations

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Create time

Create polyMesh for time = 0

Time = 0

Mesh stats
    points:           133833
    faces:            384052
    internal faces:   367436
    cells:            125248
    faces per cell:   6
    boundary patches: 4
    point zones:      0
    face zones:       0
    cell zones:       0

Overall number of cells of each type:
    hexahedra:     125248
    prisms:        0
    wedges:        0
    pyramids:      0
    tet wedges:    0
    tetrahedra:    0
    polyhedra:     0

Checking topology...
    Boundary definition OK.
    Cell to face addressing OK.
    Point usage OK.
    Upper triangular ordering OK.
    Face vertices OK.
    Number of regions: 1 (OK).

Checking patch topology for multiply connected surfaces...
    Patch               Faces    Points   Surface topology
    inlet1              560      595      ok (non-closed singly connected)
    inlet2              84       97       ok (non-closed singly connected)
    wall                15412    15491    ok (non-closed singly connected)
    outlet              560      595      ok (non-closed singly connected)

Checking geometry...
    Overall domain bounding box (-0.5 -0.5 -0.1) (0.75 0.3 0.1)
    Mesh has 3 geometric (non-empty/wedge) directions (1 1 1)
    Mesh has 3 solution (non-empty) directions (1 1 1)
    Boundary openness (-1.6261e-16 9.69057e-17 7.57401e-16) OK.
    Max cell openness = 2.68995e-16 OK.
    Max aspect ratio = 4.55121 OK.
    Minimum face area = 9.44458e-06. Maximum face area = 8.18832e-05.  Face area magnitudes OK.
    Min volume = 6.28078e-08. Max volume = 6.47251e-07.  Total volume = 0.019845.  Cell volumes OK.
    Mesh non-orthogonality Max: 41.0009 average: 9.71381
    Non-orthogonality check OK.
    Face pyramids OK.
    Max skewness = 0.530471 OK.
    Coupled point location match (average 0) OK.

Mesh OK.

End

自動化

最後に、ここまでの手順を自動化します。

Allrun

#!/bin/sh

cd ${0%/*} || exit 1

blockMesh > log.blockMesh

for i in 1 2 3
do
    cp system/mirrorMeshDict.$i system/mirrorMeshDict
    mirrorMesh -overwrite > log.mirrorMesh.$i
done

topoSet -dict system/topoSetDict.1 > log.topoSet.1
createPatch -overwrite > log.createPatch

topoSet -dict system/topoSetDict.2 > log.topoSet.2
subsetMesh c0 -patch wall -overwrite > log.subsetMesh

for i in 1 2 3 4
do
    cp system/extrudeMeshDict.$i system/extrudeMeshDict
    extrudeMesh > log.extrudeMesh.$i
done

transformPoints -scale '(0.001 0.001 0.001)' > log.transformPoints

実行方法
```
$ chmod 755 Allrun
$ ./Allrun
```