概要
- コードのテストなどに使用する「適当な」非構造格子の生成方法です。
- ParaViewから出力する簡易なフォーマットを使用します。
- 汎用の格子フォーマット入出力を持っていない人でもパースしやすいです。
- 利益があるかもしれない人の例
- P○intwiseとか使える環境無いし手元のコードには汎用格子フォーマットの入出力無いし書くのも興味無いけど適当な非構造格子で自分のコードをテストしたい
準備
- ParaViewを用意します
- sudo apt update
- sudo apt install paraview -y
- 端末で"paraview"を実行してGUIが立ち上がる事を確認します
分割元の適当な格子を用意する
外枠となる格子が必要です。中の分割は何でも可ですが、最終的に作成したい「適当な格子」と同等な密度にしておく必要があります。
ここでは以下のようなデータ(original.tec)を元の格子とします。
手元では2次元のTecplot形式を使用しました。
original.tec
VARIABLES=X,Y
ZONE I= 25 ,J= 20 ,F=POINT
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元の格子データにいい感じに擾乱を入れる
このステップはオプションです。
元のデータに適当な擾乱を入れることで最終的な格子に「それっぽい」非構造感が出ます。
ここでは以下のように格子点を移動させました。
格子点の移動
w1 = 1.5d0
w2 = 0.5d0
do loop = 1, 3
do k = 2, kmax-1
do i = 2, imax-1
if(mod(k,2).eq.0) then
x(i,k) = (w1*x(i,k) + w2*x(i,k+1)) / (w1 + w2)
y(i,k) = (w1*y(i,k) + w2*y(i,k+1)) / (w1 + w2)
end ifif(mod(i,3).eq.0) then
x(i,k) = (w1*x(i,k) + w2*x(i,k+1)) / (w1 + w2)
y(i,k) = (w1*y(i,k) + w2*y(i,k+1)) / (w1 + w2)
end ifif(mod(i,2).eq.0 .and. mod(k,5).eq.0) then
x(i,k) = (w1*x(i,k) + w2*x(i+1,k)) / (w1 + w2)
y(i,k) = (w1*y(i,k) + w2*y(i+1,k)) / (w1 + w2)
end ifif(mod(i,3).eq.0 .and. mod(k,2).eq.0) then
x(i,k) = (w1*x(i,k) + w2*x(i+1,k)) / (w1 + w2)
y(i,k) = (w1*y(i,k) + w2*y(i+1,k)) / (w1 + w2)
end ifif(mod(i,2).eq.0) then
x(i,k) = (w1*x(i,k) + w2*x(i,k-1)) / (w1 + w2)
y(i,k) = (w1*y(i,k) + w2*y(i,k-1)) / (w1 + w2)
end if
end do
end do
end do
original.tecに対して適用すると以下のようなデータになります。
perturbed.tec
VARIABLES=X,Y
ZONE I=25,J=20,F=POINT
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ParaViewでDelaunay 2Dフィルターを適用し非構造格子を生成する
上で作成したデータをParaViewで読んだ後、Delaunay 2Dフィルターを適用します。
各フィルターは[Filters]->[Search]で検索出来ます。
この時、右下の凸角のような箇所に元の形状には無いセルが生成されてしまう事があります。
CFDなどで使用する際には困るので少し修正を加えます。
Extract Selectionフィルターで不要なセルを削除する
Select Cells Onなどで余分なセルを選択します。
[Edit]->[Find Data]を開き[Invert selection]のチェックボックスを入れて必要なセルだけが選択された状態にします。
Extract Selectionフィルターを適用し必要なセルだけを抽出します。
作成した非構造格子を出力する
Extract Selectionフィルターを選択した状態でSpreadSheet Viewを開きます。
- 節点の情報を出力します
- AttributeをPoint Dataにします
- Toggle column visibilityで以下にチェックを入れます
- vtkOriginalPointIds
- Points
- vtkOriginalPointIds列が昇順になっていることを確認します
- Export Spreadsheetで出力します
- 手元ではpoint.tsvとしました
※PointIDではなくvtkOriginalPointIdsにする必要があります。
- セルの情報を出力します
- ArrtibuteをCell Dataにします
- Toggle cell connectivity visibilityを選択しておきます
- Toggle column visibilityで以下にチェックを入れます
- Cell ID
- Cell Type
- Point Index 0〜2
- Export Spreadsheetで出力します
- 手元ではcell.tsvとしました
※出力したCell Type IDはすべて5になっているはずです。これはVTKフォーマットのcell typeでは5が三角形に対応するためです。
参考1：PENGUINITIS - VTK ファイルフォーマット
参考2：http://www.princeton.edu/~efeibush/viscourse/vtk.pdf (Figure 2)
出力した結果をパースする
出力した結果に非構造格子の構成に必要な情報が揃っているので手元のコードでパースします。
point.tsv
Points_0 Points_1 Points_2 vtkOriginalPointIds
-0.15 0 0 0 ←節点ID=0の座標は(-0.15, 0, 0)
-0.1125 0 0 1...
cell.tsv
Cell Type Point Index 0 Point Index 1 Point Index 2 Cell ID
5 63 38 14 0 ←セルID=0を構成する節点IDは63, 38, 14
5 46 20 21 1...
節点ID(vtkOriginalPointIds)、セルID(Cell ID)はどちらも0から数えます。
