1 OpenFOAM ॳڃฤ — ΩϟϏςΟྲྀΕ — ʦஶʧӉ஦ʹೖͬͨΧϚΩϦ ٕज़ॻయʢ2023 ೥Նʣ৽ץ 2023 ೥ 7 ݄ 15 ೔ɹ ver 1.0

2 ˙໔੹ ຊॻ͸৘ใͷఏڙͷΈΛ໨తͱ͍ͯ͠·͢ɻ ຊॻͷ಺༰Λ࣮ߦɾద༻ɾӡ༻ͨ͜͠ͱͰԿ͕ى͖Α͏ͱ΋ɺͦΕ͸࣮ߦɾద༻ɾӡ༻ͨ͠ਓࣗ਎ͷ੹೚Ͱ͋ Γɺஶऀ΍ؔ܎ऀ͸͍͔ͳΔ੹೚΋ෛ͍·ͤΜɻ ˙঎ඪ ຊॻʹొ৔͢ΔγεςϜ໊΍੡඼໊͸ɺؔ܎֤ࣾͷ঎ඪ·ͨ͸ొ࿥঎ඪͰ͢ɻ ·ͨຊॻͰ͸ɺ™ɺ®ɺ© ͳͲͷϚʔΫ͸লུ͍ͯ͠·͢ɻ

3 ͸͡Ίʹ ຊॻΛखʹऔ͍͖ͬͯͨͩɼ͋Γ͕ͱ͏͍͟͝·͢ɽ ຊॻ͸ɼOpenFOAM ೖ໳ॻͱॳ৺ऀͷͨΊͷୈҰาͱͯ͠Θ͔Γ΍͘͢ղઆͨ͠ຊͰ͢ɽ ຊॻͷ໨త ຊॻͷ໨త͸ɼOpenFOAM ͷجૅతͳ࢖͍ํΛ਎ʹ͚ͭΔ͜ͱͰ͢ɽOpenFOAM ͸ιϧό͝ ͱʹνϡʔτϦΞϧ͕༻ҙ͞Ε͓ͯΓɼ ɺͦͪΒΛࣗ਎ͷղੳͨ͠Ϟσϧʹमਖ਼ͯ͠࢖͏͜ͱʹͳ Γ·͢ɽ͔͠͠ɼOpenFOAM ॳ৺ऀʹͱ͍͖ͬͯͳΓࣗ਎ͷղੳΛ͢Δͱ͍͏͜ͱ͸೉͘͠ɼͨ ͍͍ͯͷ৔߹͸νϡʔτϦΞϧΛோΊͯΈͯɼઃఆํ๏Λ஌Δ͜ͱ͔Β࢝Ί·͢ɽͦͯ͠ઃఆํ๏ Λཧղͯࣗ͠਎ͷΦϦδφϧͷղੳ΁ͱਐΉ৔߹͕΄ͱΜͲͰ͢ɽ ͨͩ͠ɼOpenFOAM ΍ͦͷଞιϑτ΢ΣΞͷΠϯετʔϧํ๏ʹ͍ͭͯ͸ຊॻͰ͸ѻ͍· ͤΜɽ ຊॻͷର৅ಡऀ ຊॻͰ͸࣍ͷΑ͏ͳਓΛର৅ͱ͍ͯ͠·͢ɻ • ྲྀମղੳΛ͜Ε͔Β͸͡ΊΔਓ • OpenFOAM ʹ͍ͭͯڵຯ͕͋Δਓ • ࣗ୐ͰγϛϡϨʔγϣϯ͢Δ͜ͱʹϫΫϫΫ͢Δਓ લఏͱ͢Δ஌ࣝ ຊॻΛಡΉʹ͋ͨΓɺ࣍ͷΑ͏ͳ஌͕ࣝඞཁͱͳΓ·͢ɻ • Linux ʹ͍ͭͯͷجૅ஌ࣝ • ྲྀମྗֶͷجૅ஌ࣝ ࢖༻͢Διϑτ΢ΣΞͷόʔδϣϯ ຊॻͰ࢖༻͢Δͷ͸ιϑτ΢ΣΞ͸ҎԼͱͳΓ·͢ɽ • OpenFOAM v2212 (WSL2) • ParaView 5.11 (WindowsɺMac) WSL2 ͷ Ubuntu2204 ʹ OpenFOAM ΛΠϯετʔϧͯ͠࢖༻͍ͯ͠Δ͜ͱΛ૝ఆ͍ͯ͠· ͢ɽParaView ͸ Windows ΋͘͠͸ Mac ʹΠϯετʔϧ͓ͯ͠࢖͍͍ͩ͘͞ɽ ໰͍߹Θͤઌ ຊॻʹؔ͢Δ࣭໰΍͓໰͍߹Θͤ͸ɺ࣍ͷϖʔδ·Ͱ͓ئ͍͠·͢ɽਖ਼ޡදͱαϯϓϧίʔυ΋ ͜͜ʹ͋Γ·͢ɽ • ϒϩά URL : https://takun-physics.net/ • Twitter: https://twitter.com/t_kun_kamakiri – i –

4 ͸͡Ίʹ ँࣙ ຊॻ͸ XXXX ࢯͱ XXXX ࢯʹϨϏϡʔ͍͖ͯͨͩ͠·ͨ͠ɽ͜ͷ৔ΛआΓͯײँ͠·͢ɻ͋ Γ͕ͱ͏͍͟͝·ͨ͠ɽ – ii –

5 ໨࣍ ͸͡Ίʹ i ୈ 1 ষ ΩϟϏςΟྲྀΕ 1 1.1 શମͷྲྀΕ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 ιϧόͷબ୒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 ࢧ഑ํఔࣜ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 νϡʔτϦΞϧΛίϐʔ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 ղੳର৅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 ϝογϡ࡞੒ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.1 blockMesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3.2 chekMesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.3 ڥք৚݅ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.4 ෺ੑ஋ͷઃఆ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.5 εΩʔϜ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.6 ୅਺ιϧό . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.7 ܭࢉ੍ޚ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.4 ܭࢉ࣮ߦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5 ݁Ռॲཧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5.1 ྲྀ଎ίϯλ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5.2 ྲྀ଎ϕΫτϧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.5.3 ྲྀઢ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6 ֬ೝࣄ߲ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6.1 ࿈ଓࣜͷޡࠩͷ֬ೝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6.2 ࢒ࠩͷ֬ೝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6.3 y+ ͷ֬ೝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 ͋ͱ͕͖ / ͓ΘΓʹ 28 – iii –

6 ୈ 1 ষ ΩϟϏςΟྲྀΕ ͜ͷষͰ͸νϡʔτϦΞϧͷΩϟϏςΟྲྀΕͷઃఆํ๏Λ֬ೝ͍͖ͯ͠·͢ɽΩϟϏςΟྲྀ Ε͸ 2 ࣍ݩͷඇѹॖྲྀΕΛԾఆ͓ͯ͠Γɼܭࢉෛՙ͕ܰ͘Ϟσϧͷઃఆ߲໨΋ଟ͘ͳ͍ͨΊ OpenFOAM ॳ৺ऀʹ͸ͱ͖ͬͭ΍͍͢ྫ୊Ͱ͢ɽνϡʔτϦΞϧͷத਎Λ֬ೝ͍ͯ͘͜͠ͱͰɼ ࣗ਎ͷઃఆϑΝΠϧͷํ๏ΛֶΜͰ͍͘͜ͱʹͳΓ·͢ɽ 1.1 શମͷྲྀΕ ·ͣ͸ղੳΛ࣮ߦ͢Δ·ͰͷશମͷྲྀΕΛԡ͓͖͑ͯ͞·͠ΐ͏ɽ • ιϧόͷબ୒ • νϡʔτϦΞϧΛίϐʔ • ϝογϡੜ੒ (blockMesh) • ղੳઃఆ (OpenFOAM ͷઃఆϑΝΠϧ) • ܭࢉ࣮ߦ (OpenFOAM) • ղੳ݁ՌͷՄࢹԽ ΦϦδφϧͷܗঢ়Λղੳ͍ͨ͠৔߹͸ղੳ༻ͷϞσϧ࡞੒ͷ޻਺΋͋Γ·͕͢ɼࠓճ͸ blockMesh ͰϝογϡΛอ࣋ͨ͠ܗঢ়Λ࡞੒͢ΔͷͰղੳϞσϧ࡞੒ͷ޻਺͸͜͜Ͱ͸ൃੜ ͠·ͤΜɽ 1.1.1 ιϧόͷબ୒ ࠓճղੳΛ͢ΔΩϟϏςΟྲྀΕ͸ɼ୯૬ྲྀΕͰԹ౓มԽͱີ౓มԽ͕ແࢹͰ͖ΔඇѹॖྲྀΕͱԾ ఆͯ͠ղੳΛߦ͍·͢ɽඇѹॖྲྀΕʹ͸୅දతͳ΋ͷͱͯ͠දͷΑ͏ͳιϧό͕͋Γ·͢ɽ ˝ ද 1.1: ඇѹॖੑྲྀΕͷιϧόʣ ιϧό ༻్ icoFoam ඇఆৗ૚ྲྀղੳιϧό simpleFoam ఆৗཚྲྀղੳιϧό (SIMPLE ๏) pisoFoam ඇఆৗཚྲྀղੳιϧό (PISO ๏) pimpleFoam ඇఆৗཚྲྀղੳιϧό (PISO ͱ SIMPLE Λ૊Έ߹Θͤͨ PIMPLE ๏) ඇఆৗͰཚྲྀϞσϧΛ࢖Θͳ͍ղੳιϧόͱͯ͠ icoFoam Λ࢖͏͜ͱʹ͠·͢ɽ – 1 –

7 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.2 νϡʔτϦΞϧΛίϐʔ 1.1.2 ࢧ഑ํఔࣜ ࣜ 1.1: ࿈ଓͷࣜ ∇ · u = 0 ࣜ 1.2: ӡಈྔอଘͷࣜ ∂u ∂t + ∇ · (uu) − ∇ · (ν∇u) = ∇p • u : ྲྀ଎ϕΫτϧ • p : ѹྗ 1.2 νϡʔτϦΞϧΛίϐʔ icoFoam ͷνϡʔτϦΞϧʹ 2 ࣍ݩղੳ༻ͷΩϟϏςΟྲྀΕ͕༻ҙ͞Ε͍ͯ·͢ɽҎԼͷίϚ ϯυͰϑΥϧμ࡞੒ͱνϡʔτϦΞϧͷίϐʔ͠·͢ɽ ˝ νϡʔτϦΞϧͷίϐʔ $ mkdir -p tutorial $ cd tutorial/ $ cp -r $FOAM_TUTORIALS/incompressible/icoFoam/cavity/cavity . $ cd cavity/ • ϑΥϧμͷ࡞੒ (-p Φϓγϣϯ͸్தϑΝΠϧ΋࡞੒) • tutorial ϑΥϧμʹҠಈ • cavity νϡʔτϦΞϧΛίϐʔ • cavity ϑΥϧμʹҠಈ ϑΥϧμߏ੒Λ֬ೝ͍ͨ͠৔߹͸ tree ίϚϯυͰ֬ೝΛߦ͏͜ͱ͕Ͱ͖·͢ɽ ˝ ϑΥϧμߏ੒ͷ֬ೝ $ tree . ᵓᴷᴷ 0 ᴹ ᵓᴷᴷ U ᴹ ᵋᴷᴷ p ᵓᴷᴷ constant ᴹ ᵋᴷᴷ transportProperties ᵋᴷᴷ system – 2 –

8 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ᵓᴷᴷ PDRblockMeshDict ᵓᴷᴷ blockMeshDict ᵓᴷᴷ controlDict ᵓᴷᴷ decomposeParDict ᵓᴷᴷ fvSchemes ᵋᴷᴷ fvSolution tree ίϚϯυ͕Πϯετʔϧ͞Ε͍ͯͳ͍৔߹͸ tree ίϚϯυͰΤϥʔʹͳΔͷͰඞཁʹԠ͡ ͯΠϯετʔϧͯ͠Έ͍ͯͩ͘͞ɽΤϥʔ͕ग़ͯ΋߄ͯͯ͸͍͚·ͤΜɽ 1.2.1 ղੳର৅ ΩϟϏςΟྲྀΕ͸ۭಎ΍͘΅ΈͳͲͷ಺෦ྲྀΕͰ޻ֶతʹ΋਎ۙͳྲྀΕݱ৅Ͱ͢ɽਤͷΑ͏ʹ্ ໘ͷΈʹ଎౓نఆ͞Εͨ৚݅ʹΑΓղੳΛߦ͍·͢ɽ ˛ ਤ 1.1: ΩϟϏςΟྲྀΕͷղੳ 1.3 ϝογϡ࡞੒ ϝογϡ࡞੒͸ blockMesh Ͱߦ͍·͢ɽblockMesh ϝογϡ͸ʮsystem/blockMeshDictʯʹ ϝογϡσʔλ࡞੒༻ͷઃఆΛೖྗ͠ϝογϡ࡞੒Λߦ͏͜ͱ͕Ͱ͖·͢ɽ 1.3.1 blockMesh ˝ blockMeshDict /*--------------------------------*- C++ -*------------------------------› ›----*\ – 3 –

9 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ | ========= | › › | | \\ / F ield | OpenFOAM: The Open Source CFD Toolbox › › | | \\ / O peration | Version: v2212 › › | | \\ / A nd | Website: www.openfoam.com › › | | \\/ M anipulation | › › | \*-----------------------------------------------------------------------› ›----*/ FoamFile { version 2.0; format ascii; class dictionary; object blockMeshDict; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * › ›* * // scale 0.1; vertices ( (0 0 0) //0 (1 0 0) //1 (1 1 0) //2 (0 1 0) //3 (0 0 0.1) //4 (1 0 0.1) //5 (1 1 0.1) //6 (0 1 0.1) //7 ); blocks ( hex (0 1 2 3 4 5 6 7) (20 20 1) simpleGrading (1 1 1) ); edges ( – 4 –

1 0 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ); boundary ( movingWall { type wall; faces ( (3 7 6 2) ); } fixedWalls { type wall; faces ( (0 4 7 3) (2 6 5 1) (1 5 4 0) ); } frontAndBack { type empty; faces ( (0 3 2 1) (4 5 6 7) ); } ); // **********************************************************************› ›*** // blockMeshDict ͷઆ໌͸ޙ΄Ͳ͢Δͱͯ͠ɼ·ͣ͸ blockMesh Λ࣮ߦͯ͠Έ·͠ΐ͏ɽ blockMesh ͷ࣮ߦ͸ҎԼͷίϚϯυͰߦ͍·͢ɽ ˝ blockMesh $ blockMesh blockMesh ࣮ߦޙʹ͸ҎԼͷΑ͏ͳϩά͕ग़ྗ͞Ε·͕͢ɼΤϥʔͷจࣈ͕ແ͚Ε͹ਖ਼ৗʹ࣮ ߦ͞Ε͍ͯ·͢ɽ – 5 –

1 1 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ˝ blockMesh ࣮ߦޙͷϩά ... (লུ) ... ---------------- Mesh Information ---------------- boundingBox: (0 0 0) (0.1 0.1 0.01) nPoints: 882 nCells: 400 nFaces: 1640 nInternalFaces: 760 ---------------- Patches ---------------- patch 0 (start: 760 size: 20) name: movingWall patch 1 (start: 780 size: 60) name: fixedWalls patch 2 (start: 840 size: 800) name: frontAndBack End blockMesh ͸ OpenFOAM ͷϝογϟʔʹ͋ͨΔ snappyHexMesh ͷϕʔεͱͳΔϝογϡ࡞ ੒༻ʹ࢖ΘΕΔ͜ͱ΋͋Γ·͢͠ɼࠓճͷΑ͏ʹ؆୯ͳܗঢ়ͷ৔߹͸ blockMesh ͷΈͰ 6 ໘ମ ϝογϡͷΈͷϝογϡ࡞੒͢Δ͜ͱ΋Ͱ͖·͢ɽ blockMesh Λ࣮ߦ͢Δͱʮconstant/polyMeshʯʹϝογϡ৘ใ͕ग़ྗ͞Ε·͢ɽ scale scale ͸ϝογϡͷੇ๏ʹର͢ΔεέʔϦϯά܎਺Ͱ͢ɽ͜͜Ͱ͸ޙͰઆ໌͢Δ vertices Ͱ͸η ϯνϝʔτϧͱͯ͠ੇ๏Λఆٛ͢ΔͨΊ 0.1 ഒͷεέʔϧΛߦ͏͜ͱͰɼϝʔτϧܥͱͯ͠ϝο γϡσʔλΛ࡞੒͢Δ͜ͱʹͳΓ·͢ɽ ˝ scale scale 0.1; OpenFOAM ͸ SI ୯ҐܥͰܭࢉ͢ΔͨΊɼ௕͞ʹରͯ͠͸ϝʔτϧܥͰܭࢉΛߦ͏͜ͱʹͳΓ ·͢ɽ͔͠͠ɼϞσϧ࡞੒ͷࡍʹ͸ϛϦϝʔτϧ΍ηϯνϝʔτϧͰ࡞੒ͨ͠ํ͕Θ͔Γ΍͍͢ έʔε΋͋Γ·͢ɽ vertices vertices Ͱ͸ϒϩοΫͷ௖఺ͷ࠲ඪΛఆٛ͠ɼ্͔Βॱ൪ʹ௖఺ʹ൪߸ׂ͕Γ౰ͯΒΕ·͢ɽ – 6 –

1 2 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ΩϟϏςΟྲྀΕͷ৔߹͸ 6 ໘ମͰ 0~7 ·ͰਤͷΑ͏ʹ௖఺ʹׂΓ౰ͯΒΕ·͢ɽ ˝ vertices vertices ( (0 0 0) //0 (1 0 0) //1 (1 1 0) //2 (0 1 0) //3 (0 0 0.1) //4 (1 0 0.1) //5 (1 1 0.1) //6 (0 1 0.1) //7 ); ˛ ਤ 1.2: ௖఺ͷఆٛ blocks blocks ͰϒϩοΫͷܗঢ়Λఆٛ͠·͢ɽhex ͱࢦఆ͠ vertices Ͱఆٛͨ͠௖఺ 0~7 ͔ΒͳΔ 6 ໘ମͷϝογϡΛ࡞੒͠·͢ɽ – 7 –

1 3 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ˝ blocks blocks ( hex (0 1 2 3 4 5 6 7) (20 20 1) simpleGrading (1 1 1) ); (20 20 1) Ͱ͸ x1,x2,x3 ํ޲ͷ෼ׂ਺Λࢦఆ͍ͯ͠·͢ɽsimpleGrading (1 1 1) Ͱ͸ϒ ϩοΫͷลͷͷϝογϡαΠζͷ֦େൺ཰Λ༩͑Δ͜ͱ͕Ͱ͖·͢ɽࠓճ͸ x1,x2,x3 ํ޲͸ۉ౳ ʹ෼ׂ͞ΕΔઃఆͱ͍ͯ͠·͢ɽ ˛ ਤ 1.3: ֦େൺ཰ͷઃఆ boundary boundary ͸ڥքͷ໊લͱλΠϓΛఆٛ͠·͢ɽfaces ʹ͸ vertices Ͱఆٛͨ͠௖఺ͷ൪߸Λࢦ ఆ͠໘Λఆ͍ٛͯ͠·͢ɽfixedWalls ΍ frontAndBack ͷΑ͏ʹɼෳ਺ͷ໘Λఆٛ͢Δ͜ͱͰά ϧʔϓԽ͢Δ͜ͱ΋Ͱ͖·͢ɽ ˝ boundary boundary ( movingWall { type wall; faces ( (3 7 6 2) ); } fixedWalls { type wall; faces ( (0 4 7 3) (2 6 5 1) (1 5 4 0) ); – 8 –

1 4 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ } frontAndBack { type empty; faces ( (0 3 2 1) (4 5 6 7) ); } ); ˛ ਤ 1.4: ֦େൺ཰ͷઃఆ ͜͜Ͱ͸ type ͸ patch,wall,empty Λ࢖͓ͬͯΓҙຯ͸දͷͱ͓ΓͰ͢ɽ 1.3.2 chekMesh ϝογϡ඼࣭Λ֬ೝ͠·͢ɻ 1.3.3 ڥք৚݅ ڥք৚݅ͷઃఆ͸ 0 ϑΥϧμʹ֨ೲ͞Ε͍ͯ·͢ɽࠓճ͸ U ͱ p ͷϑΝΠϧ͕ղੳʹඞཁͰ͢ ͷͰɼͦΕͧΕ֬ೝͯ͠Έ·͢ɽ – 9 –

1 5 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ˝ ද 1.2: ڥքͷछྨ छྨ ༻్ patch Ұൠతͳύονʢྲྀೖޱ΍ྲྀग़ޱʣ wall น໘ʢཚྲྀͷนؔ਺ʹ࢖༻ʣ empty 2 ࣍ݩܗঢ়ͷલޙͷ໘ symmetryPlane ରশ໘ wedge ࣠ରশܗঢ়ͷͨΊͷɼ͘͞ͼܕͷલޙ cyclic पظڥք໘ • U ϑΝΠϧ : ྲྀ଎ϕΫτϧ • p ϑΝΠϧ : ѹྗ ڥք৚݅͸දͷ௨Γʹઃఆ͍ͯ͠·͢ɽ ˝ ද 1.3: ڥք৚݅ͷࢦఆ ڥք໘ͷ໊લ ڥք৚݅ U p movingWall ྲྀଋنఆ type fixedValue; type zeroGradient; value uniform (1 0 0); fixedWalls ׈Γແ͠ type noSlip; type noSlip; frontAndBack 2 ࣍ݩղੳ type empty; type empty; ˝ 0/U dimensions [0 1 -1 0 0 0 0]; internalField uniform (0 0 0); boundaryField { movingWall { type fixedValue; value uniform (1 0 0); } fixedWalls { type noSlip; } frontAndBack { type empty; – 10 –

1 6 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ } } ˝ 0/p dimensions [0 2 -2 0 0 0 0]; internalField uniform 0; boundaryField { movingWall { type zeroGradient; } fixedWalls { type zeroGradient; } frontAndBack { type empty; } } dimensions dimensions ͸෺ཧྔͷ୯ҐΛࣔ͠·͢ɽ[kg(࣭ྔ) m(௕͞) s(࣌ؒ) K(έϧϏϯ) mol(෺࣭ྔ) A(ిྲྀ) cd(ޫ౓)] ͷ৐਺Λҙຯ͍ͯ͠·͢ɽOpenFOAM Ͱ͸෺ཧతʹҙຯͷ͋Δʢ୯Ґ͕߹ͬ ͍ͯΔ͜ͱʣԋࢉͷΈΛߦ͏Α͏ʹ࣮૷͞Ε͍ͯΔͨΊ, ୯Ґ͕ਖ਼͘͠ઃఆ͞Ε͍ͯΔඞཁ͕͋Γ ·͢ɽ • ྲྀ଎ͷ৔߹ɿ[LT−1] ͳͷͰ [m/s] ͱͳ͍ͬͯ·͢ɽ ˝ U ͷ dimensions dimensions [0 1 -1 0 0 0 0]; • ѹྗͷ৔߹ɿ[L2T−2] ͳͷͰ [m2/s2 ͱͳ͍ͬͯ·͢ɽ ˝ p ͷ dimensions dimensions [0 2 -2 0 0 0 0]; ѹྗ͸௨ৗύεΧϧͷ୯ҐΛ࣋ͪ·͢ɽͭ·Γ୯Ґ໘ੵ౰ͨΓͷྗͱͯ͠ [Pa] = [N/m2] = – 11 –

1 7 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ [kg/ms2] ͱͳ͍ͬͯΔඞཁ͕͋Δ͸ͣͰ͢ɽ͔͠͠ɼOpenFOAM ͷඇѹॖιϧόͷѹྗ͸ີ౓ Ͱׂͬͨ΋ͷͱͯ͠ఆٛ͞Ε͍ͯΔͷͰɼີ౓ͷ୯Ґ [kg/m3] ͰׂΒΕ͍ͯΔͱ͍͏͜ͱʹ஫ҙ ͢Δඞཁ͕͋Γ·͢ɽ internalField internalField ͸ϝογϡηϧ಺෦ঢ়ଶͷ෺ཧྔͷ஋Ͱ͢ɽuniform ͱ͢Δ͜ͱͰ಺෦஋͸ಉ͡ ஋ʹઃఆ͞Ε͍ͯ·͢ɽ ˝ U ͷ internalField internalField uniform (0 0 0); ˝ p ͷ internalField internalField uniform 0; ྲྀ଎͸ 3 ࣍ݩϕΫτϧͰ (0 0 0) ͷॳظ಺෦ঢ়ଶΛ༩͍͑ͯ·͢ɽѹྗʹؔͯ͠͸Ұ༷ʹ 0 Λ༩ ͍͑ͯ·͢ɽඇѹॖԾఆʹؔͯ͠ӡಈྔอଘଇͷࣜʹ͸ ∇p ͱ͍͏ඍ෼߲͔͠ͳ͍ͨΊɼѹྗͷ૬ ର஋͕ҙຯΛ࣋ͪ·͢ɽ0 ͱ͢Δ͜ͱͰେؾѹج४ʢήʔδѹʣͱ͢Δ͜ͱ͕Ͱ͖·͢ɽ internalField boundaryField ˛ ਤ 1.5: internalField ͱ boundaryField boundaryField boundaryField ʹ͸ڥք໘Ͱͷ৚݅Λઃఆ͠·͢ɽ U ϑΝΠϧͷ movingWall ͸ྲྀ଎Λ༩͑ΔͷͰ type fixedValue ͱͯ͠Ұ༷ʹ (1 0 0) ͷྲྀ଎ Λ༩͍͑ͯ·͢ɽfixedWalls ͸น৚݅ͱͯ͠ྲྀ଎͸ 0 Λ༩͍͑ͯ·͢ɽfrontAndBack ͸ type empty ͱͯ͠ڥք໘ͷ๏ઢํ޲ͷܭࢉ͸ߦΘͳ͍ઃఆͱ͍ͯ͠·͢ɽ ˝ U ͷ boundaryField boundaryField { – 12 –

1 8 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ movingWall { type fixedValue; value uniform (1 0 0); } fixedWalls { type noSlip; } frontAndBack { type empty; } } p ϑΝΠϧͷ movingWall ͸ type zeroGradient ͱͯ͠ޯ഑ͳ͠ͷ৚݅Λࢦఆ͠·͢ɽfixed- Walls ͷน৚݅Λ༩͑ͯΔ৔߹ͷѹྗ͸ type zeroGradient ͱͯ͠ޯ഑ͳ͠ͷ৚݅Λࢦఆ͠·͢ɽ frontAndBack ͸ U ಉ༷ type empty ͱͯ͠ڥք໘ͷ๏ઢํ޲ͷܭࢉ͸ߦΘͳ͍ઃఆͱ͍ͯ͠ ·͢ɽ ˝ p ͷ boundaryField boundaryField { movingWall { type zeroGradient; } fixedWalls { type zeroGradient; } frontAndBack { type empty; } } – 13 –

1 9 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ 1.3.4 ෺ੑ஋ͷઃఆ ෺ੑ͸ constant/transportProperties ϑΝΠϧʹΑΓߦ͍·͢ɽnu ͸ಈ೪ੑ܎਺Ͱ͢ɽಈ೪ੑ ܎਺ͷ୯Ґ͸ [m/s2] Ͱ͢ɽ ˝ constant/transportProperties nu 0.01; 1.3.5 εΩʔϜ ඍ෼ΛͲͷΑ͏ʹ཭ࢄԽ͢Δ͔Λબ୒͢Δͷ͕཭ࢄԽεΩʔϜͰ͢ɽ཭ࢄԽεΩʔϜ͸ sys- tem/fvSchemes Ͱઃఆ͠·͢ɽ཭ࢄԽεΩʔϜͷબ୒͸ඇৗʹ೉͍͠ͷͰ࠷ॳ͸νϡʔτϦΞϧ ͷσϑΥϧτઃఆͰղੳΛਐΊͯྑ͍Ͱ͢ɽ ˝ system/fvSchemes ddtSchemes { default Euler; } gradSchemes { default Gauss linear; grad(p) Gauss linear; } divSchemes { default none; div(phi,U) Gauss linear; } laplacianSchemes { default Gauss linear orthogonal; } interpolationSchemes { default linear; } snGradSchemes { – 14 –

2 0 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ default orthogonal; } ཭ࢄԽεΩʔϜͷબ୒ʹΑͬͯ͸݁Ռ͕େ͖͘มΘΔ͜ͱ΋͋ΔͷͰৄ͘͠આ໌͓͖ͯ͠·͢ɽ ddtSchemes ddtSchemes ͸࣌ؒඍ෼ͷ཭ࢄԽεΩʔϜͰ͢ɽ ˝ ddtSchemes ddtSchemes { default Euler; } Euler ͱ͍ͯ͠ΔͨΊ࣌ؒඍ෼߲ʹؔͯ͠͸ 1 ࣍ਫ਼౓ͷ཭ࢄԽख๏Λͱ͍ͬͯ·͢ɽ ˝ ද 1.4: ࣌ؒඍ෼ ddtSchemes ख๏ Euler Euler ๏ (1 ࣍ਫ਼౓) backward ޙୀࠩ෼ (2 ࣍ਫ਼౓) CrankNicolson Crank-Nicolson ๏ (2 ࣍ਫ਼౓) steadyState ఆৗղੳ gradSchemes gradSchemes Ͱ͸ޯ഑ʹؔ͢Δ཭ࢄԽεΩʔϜΛઃఆ͠·͢ɽޯ഑͸ྫ͑͹ѹྗ߲ͷ −∇p ͳ Ͳ͕ͦΕʹ͋ͨΓ·͢ɽ ˝ gradSchemes gradSchemes { default Gauss linear; grad(p) Gauss linear; } default ͸ Gauss linear ͱ͓ͯ͠Γɼѹྗʹؔͯ͠΋ Gauss linear ͷઢܗิؒΛࢦఆ͍ͯ͠ ·͢ɽ divSchemes divSchemes Ͱ͸ൃࢄʹର͢Δ཭ࢄԽεΩʔϜΛࢦఆ͠·͢ɽྫ͑͹ରྲྀ߲͸ ∇(ρuu) ͷܗΛ͠ ͍ͯ·͢ɽphi ͸ϑϥοΫε ψ = ρu Ͱ͢ɽ – 15 –

2 1 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ˝ ද 1.5: ࣌ؒඍ෼ gradSchemes ख๏ Gauss linear ઢܗิؒ Gauss midPoint ࢉज़ฏۉ Gauss pointLinear ఺ͷ஋͔Βิؒ leastSquares ࠷খೋ৐๏ ˝ divSchemes divSchemes { default none; div(phi,U) Gauss linear; } ରྲྀ߲ͷεΩʔϜ͸બ୒ΛޡΔͱ਺஋֦ࢄ͕ੜͨ͡Γɼղ͕ৼಈͯ͠ෆ҆ఆͳڍಈΛࣔͨ͠Γ͠ ·͢ɽ ˝ ද 1.6: ࣌ؒඍ෼ gradSchemes ख๏ upwind 1 ࣍ਫ਼౓෩্ࠩ෼ linear ઢܗิؒ (த৺ࠩ෼ɺ2 ࣍ਫ਼౓) linearUpwind ઢܗ෩্ࠩ෼ (2 ࣍ਫ਼౓෩্ࠩ෼) QUICK QUICK εΩʔϜ (2 ࣍ਫ਼౓) Minmod minmod ੍ݶؔ਺ (2 ࣍ਫ਼౓ TVD) SuperBee superbee ੍ݶؔ਺ (2 ࣍ਫ਼౓ TVD) vanLeer van Leer ੍ݶؔ਺ (2 ࣍ਫ਼౓ TVD) vanAlbada van Albada ੍ݶؔ਺ (2 ࣍ਫ਼౓ TVD) limitedLinear ઢܗิؒʹ TVD ੍ݶΛ͚ͭͨ΋ͷ ରྲྀ߲ͷ཭ࢄԽεΩʔϜʹ͸େ͖͘෼͚ͯҎԼͷΑ͏ͳಛ௃͕͋Γ·͢ɽ • 1 ࣍ਫ਼౓ɿ҆ఆͳղʹͳΓ΍͍͕͢਺஋֦ࢄ͕େ͖͍ • ߴ࣍ਫ਼౓ɿෆ࿈ଓղΛγϟʔϓʹଊ͑΍͍͕͢਺஋ৼಈ͕େ͖͘ෆ҆ఆʹͳΓ΍͍͢ ·ͣ͸҆ఆʹղ͖͍ͨ৔߹͸ 1 ࣍ਫ਼౓෩্ࠩ෼Λ࢖͑͹ྑ͍Ͱ͢ɽղΛγϟʔϓʹଊ͍͑ͨͷ Ͱ͋Ε͹ TVD εΩʔϜΛ࢖͏͜ͱ΋ࢹ໺ʹೖΕ·͢ɽ2 ࣍ਫ਼౓ TVD εΩʔϜ͸ɼෆ࿈ଓղΛ γϟʔϓʹଊ͑ͳ͕Δߴ࣍ਫ਼౓Λҡ࣋͠ͳ͕ΒৼಈΛ཈͑ΔΑ͏ʹ޻෉͕͞Ε͍ͯ·͢ɽ laplacianSchemes laplacianSchemes Ͱ͸ϥϓϥγΞϯʹର͢Δ཭ࢄԽεΩʔϜΛઃఆ͠·͢ɽྫ͑͹ ∇ · (ρ∇u) ͷ߲ʹ౰ͨΓ·͢ɽີ౓͕Ұఆͷ৔߹͸ඍ෼ͷ֎ʹग़ͯ͠ ρ∇2u ͱͳΓ·͢ɽ – 16 –

2 2 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ ˝ laplacianSchemes laplacianSchemes { default Gauss linear orthogonal; } ˝ ද 1.7: ࣌ؒඍ෼ gradSchemes ख๏ orthogonal ௚ަલఏ uncorrected ඇ௚ަิਖ਼ͳ͠ corrected ཅతඇ௚ަิਖ਼ limited0ʙ1 ༗ݶඇ௚ަิਖ਼ (0:uncorrected,1:corrected) ࠓճͷϝογϡ͸ 6 ໘ମͰ௚ަ֨ࢠͷΈͰ͢ͷͰ orthogonal ͰΑ͍Ͱ͢ɽ interpolationSchemes interpolationSchemes Ͱ͸ gradSchemes Ͱઃఆͨ͠΋ͷͱಉ͡ηϧͷք໘ͷิؒεΩʔϜͰΑ ͍Ͱ͢ɽجຊతʹ͸ linear ͰΑ͍Ͱ͢ɻ ˝ interpolationSchemes interpolationSchemes { default linear; } snGradSchemes snGradSchemes ͸ͱ߹Θ͓͚ͤͯ͹Α͍Ͱ͢ɽ ˝ snGradSchemes snGradSchemes { default orthogonal; } 1.3.6 ୅਺ιϧό ୅਺ํఔࣜͷιϧό͸ʮsystem/fvSolutionʯͰఆٛ͠·͢ɽ୅਺ιϧόͷબ୒΋جຊతʹ͸ νϡʔτϦΞϧΛͦͷ··࢖͏ͱ͜Ζ͔Β͸͡ΊΕ͹Α͍Ͱ͢ɽ ˝ system/fvSolution – 17 –

2 3 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ solvers { p { solver PCG; preconditioner DIC; tolerance 1e-06; relTol 0.05; } pFinal { $p; relTol 0; } U { solver smoothSolver; smoother symGaussSeidel; tolerance 1e-05; relTol 0; } } PISO { nCorrectors 2; nNonOrthogonalCorrectors 0; pRefCell 0; pRefValue 0; } solvers Ͱ֤ม਺ (U,p) ୅਺ํఔࣜͷιϧόΛࢦఆ͠·͢ɽ࢒͕ࠩ tolerance ΑΓ΋খ͘͞ͳΔ ͔ɺॳظ࢒ࠩʹର͢Δൺ͕ relTol ΑΓ΋খ͘͞ͳΔͱܭࢉ͕ऴྃ͢Δɽඇఆৗͷ৔߹͸ relTol0 ʹ ͯ͠ tolerance Λे෼খ͘͞ͱΔΑ͏ʹ͢ΔͱΑ͍Ͱ͢ɽ PISO ͸ѹྗɾ଎౓࿈੒ख๏ͷҰछͰ͋Δ PISO ๏ͷઃఆͰ͢ɽnNonOrthogonalCorrectors ͸ ඇ௚ަੑิਖ਼ͷϧʔϓճ਺Ͱɼඇ௚ަੑ͕େ͖͍৔߹͸ 1 Ҏ্ʹ͢ΔͱΑ͍Ͱ͢ɽࠓճͷέʔε͸ ѹྗنఆͷڥք৚͕݅ͳ͍ͨΊɼج४ѹྗΛࢦఆ͢Δඞཁ͕͋Γ·͢ɽpRefCell ͸ج४ѹྗΛࢦ ఆ͢Δ֨ࢠ൪߸Λࢦఆ͠ɼpRefValue Ͱج४ѹྗΛࢦఆ͠·͢ɽ – 18 –

2 4 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.3 ϝογϡ࡞੒ 1.3.7 ܭࢉ੍ޚ ܭࢉ࣌ؒ΍࣌ؒࠁΈͳͲΛग़ྗ͢Δઃఆ͸ʮsystem/controlDictʯͰߦ͍·͢ɽ ˝ system/controlDict application icoFoam; startFrom startTime; startTime 0; stopAt endTime; endTime 0.5; deltaT 0.005; writeControl timeStep; writeInterval 20; purgeWrite 0; writeFormat ascii; writePrecision 6; writeCompression off; timeFormat general; timePrecision 6; runTimeModifiable true; ֤߲໨ͷҙຯ͸ҎԼͷ௨ΓͰ͢ɽ • application ܭࢉͰ࢖༻͢Διϧόʢࠓճ͸ icoFoam) • startFrom ܭࢉ։࢝ઃఆʢstartTime Ͱࢦఆ͔ͨ࣌ؒ͠Β։࢝ɼlatestTime ͱ͢Δͱ࠷৽ͷ ܭࢉ్த͔Βܭࢉ։࢝ʣ • startTime ܭࢉ։࢝࣌ؒͷࢦఆ • stopAt ܭࢉऴྃઃఆʢendTime Ͱࢦఆͨ࣌ؒ͠Ͱऴྃ) • endTime ܭࢉऴྃ࣌ؒͷࢦఆ • deltaT ࣌ؒࠁΈ (Ϋʔϥϯ਺ࢦఆͷ৔߹͸ॳظͷ࣌ؒࠁΈɼఆৗղੳͷ৔߹͸ 1 ͱͯ͠ – 19 –

2 5 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.4 ܭࢉ࣮ߦ ͓͘) • writeControl ܭࢉͷग़ྗઃఆ (timeStep ͸࣌ؒεςοϓͷճ਺͝ͱʹग़ྗɼrunTime ͸͋ Δ࣌ؒܦա͝ͱʹग़ྗʣ • writeInterval ग़ྗִؒͷࢦఆʢtimeStep ͷ৔߹εςοϓ਺ɼrunTime ͷ৔߹͸ඵ਺) • purgeWrite ग़ྗͷ਺ (0 ͱ͍ͯ͠Δͱશͯग़ྗ) • writeFormat ग़ྗͷܗࣜ (binary ͔ ascii) • writePrecision ग़ྗσʔλͷਫ਼౓ • writeCompression ग़ྗσʔλΛѹॖ͢Δ͔Ͳ͏͔ͷઃఆ (off ͸ѹॖແ͠ɼon ͸ѹॖ) • timeFormat ࣌ؒͷॻࣜ • timePrecision ࣌ࠁͷܻ਺ͷઃఆ • runTimeModifiable ιϧό࣮ߦ࣌ʹ controlDict ΛಡΈ௚͔͢Ͳ͏͔ͷࢦఆ ඞཁʹԠͯ͡ઃఆΛม͍͑ͯͩ͘͞ɽ Ҏ্Ͱ֤ઃఆͷ֬ೝΛऴ͑·ͨ͠ͷͰܭࢉΛ࣮ߦ͠·͢ɽ 1.4 ܭࢉ࣮ߦ ܭࢉͷ࣮ߦʹ͸ରԠͨ͠ιϧόͷίϚϯυΛ࣮ߦ͠·͢ɽܭࢉ͸਺ेඵͰऴΘΔͨΊࠓճͷέʔ εͰ͸ฒྻܭࢉΛߦ͓ͬͯΓ·ͤΜɽ ˝ ιϧόͷ࣮ߦ icoFoam icoFoam ͷ࣮ߦޙɼಛʹΤϥʔແ͘ਖ਼ৗʹܭࢉ͕ਐΜͰ͍Δ৔߹͸ҎԼͷΑ͏ͳϩά͕ग़ྗ͞Ε ·͢ɽ ˝ icoFoam ࣮ߦޙͷϩά ... (লུ) Time = 0.5 Courant Number mean: 0.222158 max: 0.852134 smoothSolver: Solving for Ux, Initial residual = 2.3091e-07, Final resid› ›ual = 2.3091e-07, No Iterations 0 smoothSolver: Solving for Uy, Initial residual = 5.0684e-07, Final resid› ›ual = 5.0684e-07, No Iterations 0 DICPCG: Solving for p, Initial residual = 8.63844e-07, Final residual = › ›8.63844e-07, No Iterations 0 time step continuity errors : sum local = 8.8828e-09, global = 4.94571e-1› – 20 –

2 6 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.5 ݁Ռॲཧ ›9, cumulative = 1.10417e-17 DICPCG: Solving for p, Initial residual = 9.59103e-07, Final residual = › ›9.59103e-07, No Iterations 0 time step continuity errors : sum local = 9.66354e-09, global = 1.13175e-› ›18, cumulative = 1.21735e-17 ExecutionTime = 0.43 s ClockTime = 2 s End ͪ͜Β͸ܭࢉ্͕ख͍͔͘ͳ͔ͬͨͱ͖ʹॏཁͳϩάʹͳΓ·͢ɽղੳઃఆ͕߹͍ͬͯΔ͕ɼ਺ ஋ܭࢉ্ͷܭࢉΤϥʔͷ৔߹͸ϩάͷதͷ஋͕ҟৗͳ஋Λ͍ࣔͯ͠ͳ͍͔Λ֬ೝ͢Δ͜ͱͰΤϥʔ ՕॴΛಛఆ͢Δ͜ͱ͕Ͱ͖·͢ɽ ྫ͑͹ҎԼͷ஋͕े෼খ͘͞ͳ͍ͬͯΔ͜ͱΛ֬ೝ͠·͢ɽ • Ux,Uy,Uz,p ͷॳظ࢒ࠩ Solving for Ux, Initial residual = 2.3091e-07 ͱॻ͍͍ͯΔ෦෼͕ x ํ޲ͷ଎౓ͷॳظ࢒ࠩɽಉ ༷ʹ Uy,Uz,p ΋֬ೝ • ࿈ଓࣜͷޡࠩ time step continuity errors : sum local = 9.66354e-09, global = 1.13175e-18, cumulative = 1.21735e-17 ܭࢉ͕ഁ୼͍ͯ͠Δ৔߹͸ͪ͜Βͷ஋͕ҟৗʹେ͖͍஋Λ͍ࣔͯ͠Δ͜ͱ͕͋Γ·͢ɽ 1.5 ݁Ռॲཧ OpenFOAM ͷ݁Ռ͸ՄࢹԽιϑτͷ ParaView Λ࢖͍·͢ɽ֦ுࢠʮ.foamʯͷۭϑΝΠϧΛ ࡞ΓʢϑΝΠϧ໊͸ԿͰ΋Α͍ʣParaView ͰಡΈࠐΉ͜ͱͰ OpenFOAM ͷ݁ՌΛಡΈࠐΉ͜ͱ ͕Ͱ͖·͢ɽҎԼͷίϚϯυͰ post.foam ͱ͍͏ۭϑΝΠϧΛ࡞Γ·͢ɽ ˝ ۭϑΝΠϧͷ࡞੒ touch post.foam ParaVIew Λىಈͯ͠ post.faom ΛಡΈࠐΈ·͢ɽಡΈࠐΜͩঢ়ଶ͸ѹྗͷίϯλΛ͍ࣔͯ͠ ·͢ɽ – 21 –

2 7 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.5 ݁Ռॲཧ ˛ ਤ 1.6: ParaView ʹΑΔϑΝΠϧͷಡΈࠐΈ ˛ ਤ 1.7: post.foam ಡΈࠐΈ௚ޙ – 22 –

2 8 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.5 ݁Ռॲཧ ΩϟϏςΟྲྀΕͷղੳͰ͸ѹྗͱྲྀ଎Λ෺ཧྔͱͯ͠ѻͬͨͨΊσϑΥϧτͰ͜ΕΒͷ෺ཧྔΛ දࣔ͢Δ͜ͱ͕Ͱ͖·͢ɽ͜͜Ͱ͸ྲྀ଎ΛϝΠϯʹྲྀ଎ίϯλɼྲྀ଎ϕΫτϧɼྲྀઢΛ ParaView ͰՄࢹԽ͍͖ͯ͠·͢ɽ 1.5.1 ྲྀ଎ίϯλ ྲྀ଎ͷίϯλ͸ྲྀ଎ͷେ͖͞ͷ౳஋ઢΛ৭෼͚ͯ͠දࣔͨ͠΋ͷͰ͢ɽಡΈࠐΜͩ௚ޙ͸ѹྗͷ ίϯλ͕දࣔ͞Ε͍ͯΔͷͰྲྀ଎ίϯλʹ੾Γସ͑·͢ɽ ˛ ਤ 1.8: ྲྀ଎ίϯλͷදࣔ σϑΥϧτͷ৭߹͍͔Β͓޷Έͷ৭߹͍ʹมߋ͢Δʹ͸ʮEdit Color Mapʯ͔Β৭ͷબ୒Λߦ ͍·͢ɽࠓճ͸খ͍͞஋͔Βେ͖͍஋΁ͷมԽΛ੨͔Β੺Ͱදࣔͤ͞ΔʮBlue to Red Rainbowʯ Λબ୒͍ͯ͠·͢ɽ – 23 –

2 9 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.5 ݁Ռॲཧ ˛ ਤ 1.9: Edit Color Map ʹΑΔ৭ͷબ୒ σϑΥϧτͰ͸৭͸ 256 ஈ֊ʹ෼͚ΒΕ͍ͯΔͷͰʮColor DiscretizationʯͰ 10 ஈ֊ʹมߋ͠ ͍ͯ·͢ɽ͜ΕʹΑΓ৭ͷ۠෼͚͕͸͖ͬΓͨ͠ͱࢥ͍·͢ɽ – 24 –

3 0 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.5 ݁Ռॲཧ ˛ ਤ 1.10: Color Discretization ʹΑΔ৭෼͚ͷ਺ͷࢦఆ ৭߹͍ʹܾ·Γ͸ͳ͍Ͱ͕͢ɼղੳ݁ՌΛݟͳ͕Βٞ࿦Λ͢ΔࡍʹΘ͔Γ΍͍͢৭߹͍ʹ͢Δͷ ͕Α͍Ͱ͢ɽ͜ͷ͋ͨΓ͸ݸਓͷ޷ΈʹΑΓ·͢ɽ 1.5.2 ྲྀ଎ϕΫτϧ ࣍ʹྲྀ଎ϕΫτϧΛදࣔ͠·͢ɽϕΫτϧදه͸ Glyph ʹΑΓߦ͍·͢ɽ – 25 –

3 1 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.5 ݁Ռॲཧ ˛ ਤ 1.11: Glyph ͷબ୒ ͪ͜Β΋ Glyph ͷσϑΥϧτදه͸ѹྗʹରͯ͠Ͱ͢ͷͰɼ৭͸ʮSolid Colorʯʹ੾Γସ͑· ͢ɽϕΫτϧͷ໼ҹͷେ͖͞ʹ͸ྲྀ଎ͷେ͖͞ʹԠͯ͡εέʔϧมߋͯ͠ݟ΍͍ͯ͘͢͠·͢ɽ – 26 –

3 2 ୈ 1 ষ ΩϟϏςΟྲྀΕ 1.6 ֬ೝࣄ߲ ˛ ਤ 1.12: ϕΫτϧදهͷௐ੔ 1.5.3 ྲྀઢ ࠷ޙʹྲྀઢΛදࣔͤ͞·͢ɽྲྀઢ͸ྲྀ଎ϕΫτϧΛઢͰͭͳ͍ͩ΋ͷͰ͢ɽ·ͨ͸࣭ྔͷͳཻ͍ ࢠ͕৐ͬͨي੻ͱͱΒ͑Δ͜ͱ΋Ͱ͖·͢ɽ 1.6 ֬ೝࣄ߲ 1.6.1 ࿈ଓࣜͷޡࠩͷ֬ೝ 1.6.2 ࢒ࠩͷ֬ೝ 1.6.3 y+ ͷ֬ೝ – 27 –

3 3 ͋ͱ͕͖ / ͓ΘΓʹ ͍͔͕ͩͬͨͰ͠ΐ͏͔ɻײ૝΍࣭໰͸ਵ࣌ड͚͚͍ͭͯ·͢ɻ ஶऀ঺հ Χ΢ϓϥϯػؔۃ౦ࢧ෦ (@_kauplan) ʠ৆ຯظݶ͕ 1 ೥ʹ΋ຬͨͳ͍Α͏ͳπʔϧ΍ϑϨʔϜϫʔΫʹৼΓճ͞ΕΔͷΛڐͯ͠ ͓͚Δ΄Ͳɺզʑͷਓੜ͸௕͘͸ͳ͍ɻ ʡ • https://kauplan.org/ •ʰύϯϓΩϯɾγβʔζʱਪ͠ •ʰϫʔϧυɾτϦΨʔʱਪ͠ •ʰϓϦϯηεɾϓϦϯγύϧʱਪ͠ طץҰཡ •ʰSQL ߴ଎Խ in PostgreSQLʱ ʢٕज़ॻయ 2ʣ •ʰΦϒδΣΫτࢦ޲ݴޠղମ৽ॻʱ ʢٕज़ॻయ 3ʣ •ʰjQuery ͩͬͯෳࡶͳΞϓϦ࡞ΕΔ΋Μʂ ʱ ʢٕज़ॻయ 4ʣ •ʰShell εΫϦϓτͰαʔόઃఆΛࣗಈԽ͢Δຊʱ ʢٕज़ॻయ 5ʣ •ʰRuby ͷΤϥʔϝοηʔδ͕ಡΈղ͚ΔΑ͏ʹͳΔຊʱ ʢٕज़ॻయ 6ʣ •ʰΘ͔ΓΈ SQLʱ ʢٕज़ॻయ 7ʣ •ʰPython ͷࠇຐज़ʱ ʢٕज़ॻయ 8ʣ •ʰΧ΢ϓϥϯϨϙʔτ vol.01ʱ ʢٕज़ॻయ 10ʣ – 28 –

3 4 OpenFOAM ॳڃฤ ΩϟϏςΟྲྀΕ 2023 ೥ 7 ݄ 15 ೔ɹ ver 1.0 ʢٕज़ॻయʣ ஶɹऀ Ӊ஦ʹೖͬͨΧϚΩϦ ൃߦऀ ΧϚΩϦ ࿈བྷઌ https://takun-physics.net/ https://twitter.com/t_kun_kamakiri ҹ࡮ॴ ˓˓ҹ࡮ॴ © 2023 Ӊ஦ʹೖͬͨΧϚΩϦ (powered by Re:VIEW Starter)