  %XLOGLQJ&XEH0HWKRG ߦࠃࠆᄢⷙᮨᵹ૕⸃ᨆ࠺࡯࠲ߩ࿶❗ᴺߩ㐿⊒ဈ੗⃍ᄥ㇢ 1‫ޔ‬ᄢᨋ⨃ 2‫ޔ‬૒‫ᧁޘ‬ᄢテ 3‫ޔ‬ਛᯅ๺ඳ 41 ᧲ർᄢቇᄢቇ㒮Ꮏቇ⎇ⓥ⑼‫ޔ‬2 ᧲ർᄢቇᵹ૕⑼ቇ⎇ⓥᚲ
3 ㊄ᴛᎿᬺᄢቇ⥶ⓨࠪࠬ࠹ࡓᎿቇ⑼‫ޔ‬4 ቝቮ⥶ⓨ⎇ⓥ㐿⊒ᯏ᭴ ᰴ਎ઍߩᢙ୯ᵹ૕ജቇࠍ⋡ᜰߒߡឭ᩺ߐࠇߚᚻᴺ Building-Cube Method ࠍㅢߓ‫ޔ‬ታ↪⊛ߥᄢⷙᮨࠪࡒࡘ࡟࡯࡚ࠪࡦ߳ߩขࠅ⚵ߺࠍ⥶ⓨಽ㊁ࠍਛᔃߦㅴ߼ߡ޿ࠆ‫৻ߩߘޕ‬ᣇߢᄢⷙᮨ⸘▚߆ࠄ ᓧ ࠄ ࠇ ࠆ಴ ജ ࠺ ࡯࠲ߩ ⢈ ᄢ ൻ ߇ᣂ ߚ ߥ ⺖㗴ߣ ߒ ߡ 㗼 ࿷ൻ ߒ ߟ ߟ޽ࠆ ‫ ᧄߢ ߎ ߘ ޕ‬Ⓜ ߢߪ
Building-Cube Method ߩ⋥੤ᩰሶ᭴ㅧߣ↹௝╓ภൻᚻᴺࠍ⚵ߺวࠊߖߚ࠺࡯࠲࿶❗ᴺࠍ⚫੺ߒ‫ޔ‬ߘࠇߦࠃࠅᓧࠄࠇߚ࿶❗⚿ᨐߦߟ޿ߡㅀߴࠆ‫ޕ‬ ✜⸒ ੹ᣣߩᢙ୯ᵹ૕ജቇ (Computational Fluid Dynamics: CFD) ߪታ㛎ߣਗࠎߢ࠷࡯࡞ߣߒߡߩ࿾૏ࠍ⏕┙ߒߡ߅ࠅ‫ޔ‬ߘߩ↪ㅜߦᔕߓߡႺ⇇ㆡวᩰሶ߽ߒߊߪ㕖᭴ㅧᩰሶ߇ࠃߊ↪޿ࠄࠇߡ޿ࠆ‫ޕ‬ߒ߆ߒㄭᐕߢߪ⸘▚ᯏߩ㜞ᕈ⢻ൻߦ઻޿‫ޔ‬CFD ߩ㤡᣿ᦼߦ↪޿ࠄࠇߚ⋥੤ᩰሶᴺ߇ౣ߮ᵈ⋡ࠍ㓸߼ߡ޿ࠆ‫⋥ޕ‬੤ᩰሶᴺߪㆊ෰ߦ‛૕Ⴚ⇇ߢߩ♖ᐲߥߤߩℂ↱ߢ↪޿ࠄࠇߥߊߥߞߚ߽ߩߩ‫ᧄޔ‬ᚻᴺߦߪ⥄േᩰሶ↢ᚑ‫ޔ‬㜞ᰴ♖ᐲ⸃ᴺߣ޿ߞߚ․㐳ߪ߽ߣࠃࠅ‫▚⸘ޔ‬᭴ㅧ߇࿶ୟ⊛ߦࠪࡦࡊ࡞ߦߢ߈ࠆߣ޿߁ᄢ߈ߥ೑ὐ߇޽ࠆ‫ޕ‬዁᧪⊛ߦ⸘▚߇ᄢⷙᮨൻߔࠇ߫ߔࠆ߶ߤ‫⋥ޔ‬੤ᩰሶ CFD ߪߘߩ⸘▚᭴ㅧߩන⚐ߐߩὐߢ᦭೑ߦߥࠆߎߣ߇੍ᗐߐࠇࠆ‫ⷰߚߒ߁ߎޕ‬ὐ߆ࠄ‫⋥ޔ‬੤ᩰሶᴺߩ೑ὐࠍ↢߆ߒߟߟߐࠄߦ⸘▚ⓨ㑆ߩ⸃௝ᐲ೙ᓮߣ⚵ߺวࠊߖߚᚻᴺߣߒߡ Building-Cube Method(BCM) ߇ឭ᩺ߐࠇߚ [1]‫ᧄޕ‬ᚻᴺߢߪߎࠇ߹ߢߦⶄ㔀ᒻ⁁ߦኻߔࠆ㜞ㅦߢࡠࡃࠬ࠻ߥ⥄േᩰሶ↢ᚑ [2]‫ޔ‬ᄢⷙᮨࠪࡒࡘ࡟࡯࡚ࠪࡦߦ߅ߌࠆ㜞ല₸⸘▚ [3] ࠍ㆐ᚑߒߚ߶߆‫⥶ޔ‬ⓨᯏ⠢๟ࠅߩ㕖☼ᕈᵹ૕⸃ᨆ [4, 5]‫⥶ޔ‬ⓨᯏਥ⣉๟ࠅߩ㕖ቯᏱᵹ⸃ᨆ [6, 7]‫ߩ࠭ࠗࡁࡦࠔࡈࡦࠫࡦࠛޔ‬વ៝⸃ᨆ [8]߳ߩᔕ↪߇ㅴࠎߢ߅ࠅ‫ޔ‬ᣂߚߥ CFD ᛛⴚߣߒߡߩၮ⋚ࠍ⏕┙ߒߟߟ޽ࠆ‫ޕ‬ ৻ᣇ‫ޔ‬BCM ࠍ↪޿ߚᄢⷙᮨࠪࡒࡘ࡟࡯࡚ࠪࡦߩታ⃻ߦะߌߡㅴ߻ߥ߆ߢ‫ޔ‬ታ↪ᕈߩⷰὐ߆ࠄߪ಴ജ࠺࡯࠲ߩࠨࠗ࠭߇ήⷞߢ߈ߥ޿໧㗴ߣߒߡ㗼࿷ൻߒߟߟ޽ࠆ‫࡯࡜ࠗࠝޕ‬ᣇ⒟ᑼߦၮߠߊቯᏱ⸃ᨆߢ޽ࠇ߫߹ߛߒ߽‫ޔ‬㕖ቯᏱߥᵹࠇ႐ߩ⸃ᨆߦߪᤨ♽೉ߩ⤘ᄢߥ࠺࡯࠲߇ᔅⷐߢ޽ࠆ‫߃଀ޕ‬߫೨ㅀߩ⥶ⓨᯏਥ⣉๟ࠅߩ㕖ቯᏱᵹ⸃ᨆ [7] ߢߪ㖸㗀⸃ᨆߩߚ߼ߩᤨ♽೉࠺࡯࠲ߣߒߡ⚂ 1000ࠬ࠹࠶ࡊಽߩᤨ♽೉࠺࡯࠲ࠍขᓧߒߡ޿ࠆ‫⸃ᧄޕ‬ᨆߦ߅ߌࠆᩰሶὐᢙߪ⚂ 1 ంὐߢ޽ࠅ‫ޔ‬઒ߦߎߩࠬ࠹࠶ࡊಽߛߌㅦᐲߣ࿶ജߩ‛ℂ㊂ࠍ଻ᜬߒࠃ߁ߣߔࠆߣ‫ޔ‬න♖ᐲ឵▚ߢ߽⚂ 1.6 TB ߣ㕖Ᏹߦ⤘ᄢߥ߽ߩߣߥߞߡߒ߹߁‫⤘ࠄࠇߎޕ‬ᄢߥ࠺࡯࠲ߪන⚐ߦࠬ࠻࡟࡯ࠫࠍ࿶ㄼߔࠆߛߌߢߥߊ‫ޔ‬ࠪࡒࡘ࡟࡯࡚ࠪࡦਛߩ࠺࡯࠲౉಴ജߦ߆߆ࠆᤨ㑆߇ήⷞߢ߈ߥߊߥࠆߎߣ߆ࠄ‫▚⸘ޔ‬ല₸ࠍਅߍࠆⷐ࿃ߦ߽ߥࠅ߁ࠆ‫ޕ‬಴ജ࠺࡯࠲ࠨࠗ࠭ߩ໧㗴ߪ BCM ߦ㒢ࠄߕ޽߹ߨߊࠪࡒࡘ࡟࡯࡚ࠪࡦߦẜ࿷ߒ‫ߩࡦ࡚ࠪ࡯࡟ࡘࡒࠪޔ‬ᄢⷙᮨൻߦ޽ࠊߖߡ⋥㕙ࠍ૛௾ߥߊߐࠇࠆ⺖㗴ߢ޽ࠆߣ޿߃ࠆ‫ޕ‬ ߘߎߢᧄⓂߢߪ࠺࡯࠲ࠨࠗ࠭ߩ⺖㗴ߦኻߔࠆߎࠇ߹ߢߩขࠅ⚵ߺߣߒߡ‫ޔ‬BCM ߩ⋥੤ᩰሶ᭴ㅧߣ↹௝╓ภൻᚻᴺࠍ⚵ߺวࠊߖߚ࠺࡯࠲࿶❗ᴺࠍ⚫੺ߔࠆߣߣ߽ߦ‫ߩߘޔ‬࿶❗⚿ᨐߦߟ޿ߡㅀߴࠆ‫ޕ‬CFD ࠃࠅᓧࠄࠇߚᵹ૕⸃ᨆ࠺࡯࠲ߩ࿶❗ᴺߣߒߡ‫ߚߞ૶ࠍ࠻࠶࡟ࡉ࡯ࠚ࠙ߦߢ߹ࠇߎޔ‬ᚻ
ᴺ [9] ߿‫⇣․ޔ‬୯ಽ⸃ࠍ૶ߞߚᚻᴺ [10] ߇ឭ᩺ߐࠇߡ޿ࠆ‫ ߒ߆ߒޕ‬BCM ߩ․ᓽߩ 1 ߟߦ╬ᣇ╬㑆㓒⋥੤ᩰሶ㧔ࡏࠢ࠮࡞㧕ߩណ↪߇޽ࠅ‫ߩߘޔ‬ᩰሶߪ࠺ࠫ࠲࡞↹௝⴫⃻ߦ߅ߌࠆࡇࠢ࠮࡞ߩ 3ᰴర߳ߩ᜛ᒛߣᝒ߃ࠆߎߣ߇ߢ߈ࠆ‫↹ޔߦࠄߐޕ‬௝╓ภൻᚻᴺ߇↹௝ߩㅪ⛯ᕈࠍ઒ቯߒߡ࠺࡯࠲ࠍ࿶❗ߔࠆ৻ᣇ‫ޔ‬ᵹ૕߽߹ߚㅪ⛯ᕈࠍ߽ߞߡ߅ࠅ‫ޔ‬ㅪ⛯ᕈߦߟ޿ߡ↹௝ߣᵹ૕ߩࠕ࠽ࡠࠫ࡯߇ᚑ┙ߔࠆ‫ ߡߞ߇ߚߒޕ‬BCM ࠍ↪޿ߚᵹ૕ࠪࡒࡘ࡟࡯࡚ࠪࡦߦߣߞߡ↹௝╓ภൻᚻᴺߪኈᤃߦㆡ↪
߇น⢻ߢ޽ࠅ‫↹߽߆ߒޔ‬௝࿶❗ߦḰߓߚ࿶❗₸߽ᦼᓙߢ߈ࠆ᦭ലߥᚻᴺߣ޿߃ࠆ‫⎇ᧄߢߎߘޕ‬ⓥ ߢߪ↹௝╓ภൻᚻᴺߣߒߡ೑↪ߐࠇ‫ ߟ߆ޔ‬CFD ߳ߩᔕ↪੐଀ࠍ᏷ᐢߊᜬߟ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ࠍਛᔃߦ࠺࡯࠲࿶❗ᴺࠍ᭴ᚑߒߚ‫ ߩߢ߹ࠇߎߡߒߘޕ‬BCM ߩᔕ↪੐଀߆ࠄᓧࠄࠇߚ࿶❗ᕈ㕖☼ᕈᵹ૕⸃ᨆ࠺࡯࠲‫߮ࠃ߅ޔ‬㕖࿶❗ᕈ☼ᕈᵹ૕⸃ᨆ࠺࡯࠲ߦㆡ↪ߒ‫ߩߘޔ‬ലᨐࠍᬌ⸽ߒߚ‫ޕ‬

 %XLOGLQJ&XEH0HWKRG ᧄᚻᴺߢߪ⸘▚㗔ၞో૕ߢ╬ᣇ╬㑆㓒⋥੤ᩰሶࠍណ↪ߔࠆߎߣߢ‫ࠆߌ߅ߦࡦ࡚ࠪ࡯࡟ࡘࡒࠪޔ‬೨ಣℂ࡮ᢙ୯⸘▚࡮ᓟಣℂߩߔߴߡߩᲑ㓏ߢಣℂࠍන⚐ൻߔࠆߎߣࠍ⋡ᜰߒߡ޿ࠆ‫ߦࠄߐޕ‬ዪᚲ⚦ಽൻࠍᩰሶߢߪߥߊ⸘▚ዊ㗔ၞᲤߦㆡ↪ߒ‫ޔ‬ዊ㗔ၞߩṶ▚㊂ࠍߺߥ╬ଔߦߔࠆߎߣߢ‫ޔ‬ᄢⷙᮨਗ೉⸘▚߳ߩኻᔕߩኈᤃߐ߽⁓ߞߡ޿ࠆ‫ޕ‬ ࿑ 1 ߦ BCM ߢ↪޿ࠆ⸘▚ᩰሶࠍ␜ߔ‫ޕ‬ᵹࠇ႐ߪⶄᢙߩ┙ᣇ૕ዊ㗔ၞߦಽഀߐࠇ‫ ࠄࠇߎޔ‬1 ߟ‫ ߩࠇߙࠇߘޕ‬cube ߪฦゲᣇะߦᩰሶὐᢙߩ╬ߒ޿⋥੤ᩰሶ‫ޔ‬
1 ߟࠍ cube ߣ๭ࠎߢ޿ࠆ㧔࿑ 1 Ꮐ㧕ߔߥࠊߜ╬ᣇ╬㑆㓒⋥੤ᩰሶࠍౝ൮ߒߡ߅ࠅ‫ ࠍࠇߎޔ‬cell ߣ๭ࠎߢ޿ࠆ㧔࿑ 1 ฝ㧕‫ ޕ‬BCM ߪ⋥੤ᩰሶ߇ᜬߟ․㐳ࠍߘߩ߹߹ᒁ߈⛮޿ߢ߅ࠅ‫ޔ‬㜞ຠ⾰ᩰሶߩ⥄േ↢ᚑ࡮㜞ᰴ♖ᐲ⸃ᴺߩኈᤃߥዉ౉࡮න⚐ߥ⸘▚᭴ㅧߣ޿ߞߚ೑ὐࠍᜬߟ‫ ߦࠄߐ ޕ‬BCM ߢߪ cube ᭴ㅧߦࠃࠅዪᚲ⚦ಽൻ߽ኈᤃߦዉ౉ߢ߈‫ ߟ߆ޔ‬cube ᲤߩṶ▚⽶⩄߇╬ߒ޿ߎߣ߆ࠄ㜞޿ਗ೉ൻല₸߽ᦼᓙߢ߈ࠆ‫߅ߥޕ‬cube ߦࠃࠆዊ㗔ၞಽഀߪᢙ୯⸘▚㕙ߢߩࡔ࡝࠶࠻ߛߌߢߪߥߊ‫▚⸘ޔ‬㗔ၞࠍㆡಾߥ☸ᐲߢಽ⸃ߢ߈ࠆߣ޿߁ὐߢᓟಣℂߦ߅޿ߡ߽ᕲᕺࠍਈ߃ࠆ‫ᧄߌࠊࠅߣޕ‬Ⓜߩਥ㗴ߢ޽ࠆ࠺࡯࠲࿶❗ߦ߅޿ߡߪߎߩ㗔ၞಽഀᴺ߇㊀ⷐߥᓎഀࠍᨐߚߒߡ߅ࠅ‫ࠍ⚦⹦ޔ‬ᰴ┨ߢㅀߴࠆ‫ޕ‬࿑ 1 Building-Cube Method ߦࠃࠆ⃿๟ࠅߩᩰሶ↢ᚑ଀㧔Ꮐ㧦cube‫ޔ‬ฝ㧦cell㧕!
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  ࠺࡯࠲࿶❗ᚻᴺ 㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߣ (PEHGGHG=HURWUHH:DYHOHW ╓ภൻ 㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߪ᏷ᐢ޿Ꮏቇಽ㊁ߢ೑↪ߐࠇߡ޿ࠆାภಣℂᛛⴚߢ޽ࠅ‫ ߦ․ޔ‬CFD
ߩಽ㊁ߦ߅޿ߡߪᩰሶ⚦ಽൻ [11]‫᠄ⴣޔ‬ᵄᬌ಴ [12]‫ੂޔ‬ᵹߩ᷵᛽಴ [13] ߥߤߦ೑↪ߐࠇߡ޿ࠆ‫ޕ‬ᧄᄌ឵ߦࠃࠅ౉ജାภߪૐ๟ᵄᢙᚑಽߢ޽ࠆㄭૃᚑಽߣ‫ޔ‬㜞๟ᵄᢙᚑಽߢ޽ࠆ⹦⚦ᚑಽߦಽ⸃ߐࠇࠆ‫ޕ‬ᄌ឵ߦࠃߞߡᓧࠄࠇߚㄭૃᚑಽߦኻߒߡౣᏫ⊛ߦᄌ឵ࠍታⴕߔࠆߎߣߢ‫ޔ‬ାภࠍ๟ᵄᢙߦ
ᔕߓߡಽ⸃ߔࠆߎߣ߇ߢ߈ࠆ‫ޕ‬ ࿑ 2 ߦ 2 ᰴరᵹ૕⸃ᨆ࠺࡯࠲ߦኻߒߡ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ࠍታⴕߒߚ⚿ᨐࠍ␜ߔ‫ߢߎߎޕ‬ߪ╬ᣇ╬㑆㓒⋥੤ᩰሶࠍ೑↪ߒߚ౞ᩇ๟ࠅߩᵹ૕⸃ᨆ࠺࡯࠲㧔ᩰሶὐᢙ 256256㧕ߩ߁ߜਥᵹᣇะㅦᐲࠍ଀ߦߣࠅ㧔࿑ 2 Ꮐ㧕‫ޔ‬ᄌ឵ࠍታⴕߒߡ޿ࠆ‫ޕ‬ฦゲߩᄌ឵ߢᓧࠄࠇߚૐ๟ᵄᢙᚑಽࠍㄭૃᚑಽߣߺߥߔߎߣߢ‫ߪ࠲࡯࠺ޔ‬ᄌ឵೨ߩ 4 ಽߩ 1 ߩࠨࠗ࠭㧔ᩰሶὐᢙ 128128㧕ߩㄭૃᚑಽߣ‫ޔ‬4 ಽߩ 3 ߩࠨࠗ࠭㧔ᩰሶὐᢙ 128128 ߩ 3 㗔ၞ㧕ߩ⹦⚦ᚑಽߦಽ㔌ߐࠇࠆ㧔࿑ 2 ਛᄩ㧕‫ޕ‬ᄌ឵ᓟߩ࠺࡯࠲ߢߪㄭૃᚑಽߪᄌ឵೨࠺࡯࠲ߣ߶߷หߓಽᏓࠍᜬߟ৻ᣇ‫⚦⹦ޔ‬ᚑಽߩᜬߟ୯ߪዊߐߊߥߞߡ޿ࠆ‫੹ޔߪߣߎߩߎޕ‬࿁଀ߦߣߞߚᵹࠇ႐ߩࠛࡀ࡞ࠡ࡯ߩ߶ߣࠎߤ߇ૐ๟ᵄᢙᚑಽߦ㓸⚂ߐࠇߡ߅ࠅ‫ޔ‬ㅒߦ㜞๟ᵄᢙᚑಽߩࠛࡀ࡞ࠡ࡯߇ዊߐ޿ߎߣࠍ␜ߒߡ޿ࠆ‫ߦࠄߐޕ‬ㄭૃᚑಽߦኻߒߡౣᏫ⊛ߦ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ࠍታⴕߔࠆߎߣ߇ߢ߈‫ޔ‬ାภߪౣ߮ㄭૃᚑಽߣ⹦⚦ᚑಽߦಽ㔌ߐࠇࠆ㧔࿑ 2 ฝ㧕‫ޕ‬ౣᏫ⊛ߥᄌ឵ߦ߅޿ߡ߽߿ߪࠅ⹦⚦ᚑಽߩᜬߟ୯ߪዊߐ޿‫ࠄ߆଀ᧄޕ‬␜ߐࠇࠆࠃ߁ߦ‫ߦ⥸৻ޔ‬ㅪ⛯ᕈࠍᜬߟାภߦ߅޿ߡߪᄌ឵ᓟߩㄭૃᚑಽߪᄢ߈ߊ‫⚦⹦ޔ‬ᚑಽߪዊߐߊߥࠆ‫ޕ‬ ࿑ 2 ฝߢ␜ߒߚᄌ឵ᓟߩᚑಽߪ࿑ 3 ߦ␜ߔࠃ߁ߦ‫ޔ‬ㄭૃᚑಽߦㄭ޿஥ࠍⷫ‫ޔ‬㆙޿஥ࠍሶߣߔࠆᧁ᭴ㅧߣߺߥߔߎߣ߇ߢ߈ࠆ‫ᧁߩߎޕ‬᭴ㅧࠍᔕ↪ߒߚ↹௝╓ภൻᚻᴺ߇ Embedded Zerotree
Wavelet (EZW) ╓ภൻ [14] ߢ޽ࠆ‫ޕ‬వߩᄌ឵଀ࠍ߰߹߃ࠆߣ‫ߦ⥸৻ޔ‬ㅪ⛯ᕈࠍᜬߟାภߢߪᧁ᭴ㅧߩᩮߦㄭ޿ࡁ࡯࠼ߢߪ୯߇ᄢ߈ߊߥࠅ‫ޔ‬ㅒߦᩮ߆ࠄ㔌ࠇࠆ߶ߤ୯߇ዊߐߊߥࠆ‫߁޿ߣޔ‬௑ะ߇޽ࠆ‫ ߡߒߘޕ‬EZW ╓ภൻߢߪߎߩ஍ࠅࠍ೑↪ߔࠆߎߣߢ࠺࡯࠲ࠍ࿶❗ߔࠆ‫╓ᧄ߅ߥޕ‬ภൻᚻ
ᴺߪ߽ߣ߽ߣ↹௝ߦኻߒߡឭ᩺ߐࠇߚ߽ߩߢ޽ࠅ‫ޔ‬2 ᰴరࡇࠢ࠮࡞࠺࡯࠲ࠍኻ⽎ߣߒߡ޿ࠆ߇‫ޔ‬
ߎࠇࠍ BCM ߇ขࠅᛒ߁ 3 ᰴరࡏࠢ࠮࡞࠺࡯࠲߳ߣ᜛ᒛߔࠆߩߪኈᤃߢ޽ࠆ‫ߚ߹ޕ‬࿑ 3 ߆ࠄ␜ߐࠇࠆࠃ߁ߦ‫ޔ‬㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߢࡃ࡜ࡦࠬߩߣࠇߚᧁ᭴ㅧࠍ᭴▽ߔࠆߦߪฦゲᣇะߢหߓᢙߛߌ࠺࡯࠲߇ߥߌࠇ߫ߥࠄߥ޿ߣ޿߁೙⚂߇޽ࠆ‫ ߒ߆ߒޕ‬BCM ߦ߅޿ߡߪߔߴߡߩ cube ߇ฦゲߢหᢙߩ cell ࠍᜬߞߡ޿ࠆߚ߼‫ߩߎޔ‬೙⚂ߪ໧㗴ߦߥࠄߥ޿‫ޕ‬࿑ 4 ߦ BCM ࠍ↪޿ߡᓧߚ 2ᰴర౞ᩇ๟ࠅߩᵹ૕⸃ᨆ࠺࡯࠲㧔ਥᵹᣇะㅦᐲ㧕ߣ‫ߩߘޔ‬㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵⚿ᨐࠍ␜ߔ‫ޕ‬
BCM ߩ⋥੤ᩰሶ᭴ㅧߩ߅߆ߍߢ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵߇ cube න૏ߢታⴕߢ߈ࠆߛߌߢߥߊ‫ޔ‬Ᏹߦࡃ࡜ࡦࠬߩߣࠇߚᧁ᭴ㅧࠍ᭴▽ߒല₸⊛ߦ╓ภൻߔࠆߎߣ߇น⢻ߣߥࠆ‫ޕ‬ ߥ߅ EZW ╓ภൻߢߪ౉ജߣߒߡᢛᢙࠍߣࠆ৻ᣇ‫ޔ‬࿶❗ኻ⽎ߩᵹ૕⸃ᨆ࠺࡯࠲ߪ৻⥸ߦታᢙߢ޽ࠆߚ߼‫ޔ‬೨ಣℂߣߒߡ㊂ሶൻࠍታⴕߒߡ޿ࠆ‫ޕ‬㊂ሶൻ߽฽߼ߚ࿶❗ታⴕᚻ㗅ߦߟ޿ߡߪᰴ▵ߢ⹦ㅀߔࠆ‫ޕ‬ 

࿑ 2 2 ᰴరᵹ૕⸃ᨆ࠺࡯࠲㧔ਥᵹᣇะㅦᐲ㧕ߦኻߔࠆ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߩㆡ↪
㧔Ꮐ㧦ᄌ឵೨‫ޔ‬ਛᄩ㧦1 ࿁ᄌ឵ᓟ‫ޔ‬ฝ㧦2 ࿁ᄌ឵ᓟ㧕࿑ 3 ㄭૃᚑಽߦኻߔࠆౣᏫ⊛ߥ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ࠃࠅ᭴▽ߐࠇࠆᧁ᭴ㅧ

࿑ 4 2 ᰴర BCM ᵹ૕⸃ᨆ࠺࡯࠲㧔ਥᵹᣇะㅦᐲ㧕ߦኻߔࠆ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߩㆡ↪
㧔Ꮐ㧦ᄌ឵೨‫ޔ‬ฝ㧦1 ࿁ᄌ឵ᓟ㧕










!
"#$%&'()*+,-./012/34

  ࠺࡯࠲࿶❗ᚻ㗅 ࠺࡯࠲࿶❗ߩࡔࠗࡦࡊࡠ࠮ࠬߪ೨▵ߢ⚫੺ߒߚ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߣ⛯ߊ EZW ╓ภൻߢ޽ࠅ‫ޔ‬೨ಣℂߣߒߡ㊂ሶൻ‫ޔ‬ᓟಣℂߣߒߡ࠺࡯࠲ࠨࠗ࠭ࠍߐࠄߦ೥ᷫߔࠆߚ߼ߩࠛࡦ࠻ࡠࡇ࡯╓ภൻࠍ⸳ߌߡ޿ࠆ‫⎇ᧄޕ‬ⓥߢߪ㔌ᢔ࠙ࠚ࡯ࡉ࡟࠶࠻ᄌ឵ߦ Cohen-Daubechies-Feauveau 9/7 ࠙ࠚ࡯ࡉ࡟࠶࠻ [15]‫╓࡯ࡇࡠ࠻ࡦࠛޔ‬ภൻߦ࡟ࡦࠫࠦ࡯࠳࡯ [16] ࠍ↪޿ߡ޿ࠆ‫ߚ߹ޕ‬㊂ሶൻߪએਅߩᑼߢ⴫ߐࠇࠆ㧦qinteger§q ·round¨ real ¸¨ ' ¸© q ¹(1)਄ᑼߦ߅޿ߡ qreal ߪ౉ജାภߣߒߡߩታᢙ‫ޔ‬qinteger ߪ಴ജߣߒߡߩᢛᢙ‫ޔ‬round ߪ྾ᝥ੖౉ᢛ
ᢙൻߩ㑐ᢙߢ޽ࠆ‫ޕ‬㊂ሶൻࠍㅢߓߡ౉ജ࠺࡯࠲ߪ㕖นㅒߦ࿶❗ߐࠇ‫ޔ‬Ǎq ߇㊂ሶൻᓟߩ࠺࡯࠲ࠨ
ࠗ࠭ߣ࠺࡯࠲ຠ⾰ߩ࠻࡟࡯࠼ࠝࡈࠍ᳿ቯߔࠆ‫ޕ‬Ǎq ߇ዊߐ޿߶ߤ㊂ሶൻᓟߩ࠺࡯࠲ຠ⾰ߪ⛽ᜬߐࠇࠆ߇‫ޔ‬಴ജߐࠇࠆᢛᢙߩ᏷߇ᄢ߈ߊߥࠆߎߣ߆ࠄ࠺࡯࠲ࠨࠗ࠭ߪᄢ߈ߊߥࠆ‫ޕ‬ㅒߦǍq ߇ᄢ߈޿႐วߦߪ㊂ሶൻᓟߩ࠺࡯࠲ࠨࠗ࠭ߪዊߐߊߥࠆ߽ߩߩ‫࠲࡯࠺ߩߘޔ‬ຠ⾰ߪૐߊߥߞߡߒ߹߁‫ޕ‬
ᧄⓂߢ␜ߔ࿶❗੐଀ߦ߅޿ߡߪ㊂ሶൻࠬ࠹࠶ࡊࠨࠗ࠭ࠍ৻᭽ᵹ㖸ㅦ߽ߒߊߪ৻᭽ᵹㅦᐲࠍၮḰߣߒߡ Ǎq = 1.210-4 ߣߒ‫ ߦࠄߐޔ‬Capizzano [17] ߩዪᚲ⚦ಽൻߩᜰᮡࠍෳ⠨ߦߒߡᵹࠇ႐ߩ᭽
⋧ߦᔕߓߡ㊂ሶൻࠬ࠹࠶ࡊࠨࠗ࠭ߦ㊀ߺઃߌࠍⴕߥߞߡ޿ࠆ‫ޕ‬ ࠺࡯࠲࿶❗⚿ᨐ 21(5$0 ⠢๟ࠅߩᵹࠇ⸘▚⚿ᨐ࠺࡯࠲ߩ࿶❗ BCM 㕖☼ᕈ࿶❗ᕈᵹ૕⸃ᨆࠦ࡯࠼ [4] ࠍ↪޿ߡ ONERA M6 ⠢๟ࠅߩᵹࠇ႐ࠍ⸘▚ߒ‫ޔ‬ᓧࠄࠇߚᵹ૕⸃ᨆ࠺࡯࠲ࠍ࿶❗ߒߚ‫ ✚ߚ޿↪ߦ▚⸘ޕ‬cell ᢙߪ⚂ 2100 ਁὐߢ‫⋧ޔ‬ᒰߔࠆ࠺࡯࠲ࠨࠗ
࠭ߪ 1 ‛ℂ㊂޽ߚࠅ⚂ 85 MB㧔න♖ᐲ឵▚㧕ߢ޽ࠆ‫଻ޕ‬ሽ㊂ߢ޽ࠆኒᐲ‫ޔ‬ㆇേ㊂㧔3 ᚑಽ㧕‫ࠛޔ‬ࡀ࡞ࠡ࡯ߩ⸘ 5 ‛ℂ㊂ࠍ଻ሽߔࠆ႐ว‫ޔ‬ว⸘ߩ࠺࡯࠲ࠨࠗ࠭ߪ 1 ࠬ࠹࠶ࡊ޽ߚࠅ⚂ 430 MB ߣߥࠆ‫ࡂ࠶ࡑࠆߌ߅ߦࡦ࡚ࠪ࡯࡟ࡘࡒࠪޕ‬ᢙߣㄫ߃ⷺߪታ㛎᧦ઙߦၮߠ߈‫ ࠇߙࠇߘޔ‬0.84 ߣ 3.06qߣ⸳ቯߒߚ‫ޕ‬ ࿶❗೨ᓟߢߩࡑ࠶ࡂᢙಽᏓ߅ࠃ߮⴫㕙࿶ജଥᢙಽᏓߩᲧセࠍߘࠇߙࠇ࿑ 5‫ޔ‬6 ߦ␜ߔ‫ޕ‬࿶❗ᓟߩ࠺࡯࠲߆ࠄߪ‫ޔ‬࿶❗೨ߩ࠺࡯࠲ߣ߶߷หߓಽᏓ߇ᓧࠄࠇߡ޿ࠆߎߣ߇⷗ߡขࠇࠆ‫ߚ߹ޕ‬࿑ 7 ߦ65%߅ࠃ߮ 90%ࠬࡄࡦᢿ㕙ߢߩ࿶ജଥᢙࡊࡠ࠶࠻ࠍ␜ߔ‫ߩࠇߙࠇߘޕ‬ᢿ㕙ߦ߅޿ߡ࿶❗ᓟߩ࠺࡯࠲߆ࠄᓧࠄࠇࠆࡊࡠ࠶࠻ߪ‫ޔ‬࿶❗೨ߩ࠺࡯࠲ߩࡊࡠ࠶࠻ࠍ⦟ߊౣ⃻ߒߡ޿ࠆ‫ޕ‬ߎࠇࠄߩ⚿ᨐ߆ࠄ‫ޔ‬ᧄ࿶❗ᚻᴺࠃࠅᓧࠄࠇࠆ࿶❗࠺࡯࠲߇ቯᕈ⊛࡮ቯ㊂⊛ߦᅷᒰߥຠ⾰ࠍᜬߟߎߣࠍ⏕⹺ߒߚ‫৻ޕ‬ᣇߢ࠺࡯࠲ࠨࠗ࠭ߦߟ޿ߡߪ‫ޔ‬࿶❗ᓟߩ࠺࡯࠲ࠨࠗ࠭ߪ 5 ‛ℂ㊂ߩ࿶❗ߢว⸘⚂ 15 MB ߣߥࠅ‫ޔ‬࿶❗೨࠺࡯࠲ࠨࠗ࠭㧔⚂ 430 MB㧕ߩ⚂ 3.5%߹ߢዊߐߊߔࠆߎߣ߇ߢ߈ߚ‫ޕ‬  

࿑ 5 ONERA M6 ⠢ᢿ㕙ࡑ࠶ࡂᢙಽᏓᲧセ㧔Ꮐ㧦࿶❗೨‫ޔ‬ฝ㧦࿶❗ᓟ㧕࿑ 6 ONERA M6 ⠢⴫㕙࿶ജଥᢙಽᏓᲧセ㧔Ꮐ㧦࿶❗೨‫ޔ‬ฝ㧦࿶❗ᓟ㧕࿑ 7 ONERA M6 ⠢⴫㕙࿶ജଥᢙࡊࡠ࠶࠻Ყセ㧔Ꮐ㧦65%ࠬࡄࡦᢿ㕙‫ޔ‬ฝ㧦90%ࠬࡄࡦᢿ㕙㧕!
"#$%&'()*+,-./012/34

  ) ࡟࡯ࠪࡦࠣࠞ࡯๟ࠅߩᵹࠇ⸘▚⚿ᨐ࠺࡯࠲ߩ࿶❗ BCM ☼ᕈ㕖࿶❗ᕈᵹ૕⸃ᨆࠦ࡯࠼ [7] ࠍ↪޿ߡ F1 ࡟࡯ࠪࡦࠣࠞ࡯๟ࠅߩᵹࠇ႐ࠍ⸘▚ߒ‫ޔ‬ᓧࠄࠇߚᵹ૕⸃ᨆ࠺࡯࠲ࠍ࿶❗ߒߚ‫✚ߚ޿↪ߦ▚⸘ޕ‬ᩰሶὐᢙߪ⚂ 2.4 ంὐߢ‫⋧ޔ‬ᒰߔࠆ࠺࡯࠲
ࠨࠗ࠭ߪ 1 ‛ℂ㊂޽ߚࠅ⚂ 970 MB㧔න♖ᐲ឵▚㧕ߢ޽ࠆ‫ޕ‬ᵹ૕ߩ㕖࿶❗ᕈߩ઒ቯ߆ࠄኒᐲߪᏱ
ߦ৻ቯߣߒ‫ޔ‬ㅦᐲ㧔3 ᚑಽ㧕ߣ࿶ജߩ⸘ 4 ‛ℂ㊂ࠍ଻ሽߔࠆ႐ว‫ޔ‬ว⸘ߩ࠺࡯࠲ࠨࠗ࠭ߪ 1 ࠬ࠹࠶ࡊ޽ߚࠅ⚂ 3.8 GB ߦ㆐ߔࠆ‫࠭࡞ࡁࠗ࡟ࠆߌ߅ߦࡦ࡚ࠪ࡯࡟ࡘࡒࠪޕ‬ᢙߪゞ૕㐳ࠍၮḰߣߒߡ
1.5107 ߣ⸳ቯߒߚ‫࠭࡞ࡁࠗ࡟ᧄޕ‬ᢙߦ߅޿ߡߪ‛૕⴫㕙ߩႺ⇇ጀߪහᐳߦੂᵹߦㆫ⒖ߒ‫ޔ‬ゞ૕ᒻ⁁ߣ߽޽޿߹ߞߡ㕖Ᏹߦⶄ㔀ߥᵹࠇ႐ࠍᒻᚑߔࠆ‫ޕ‬ ࿶❗೨ᓟߢߩਥᵹᣇะㅦᐲಽᏓߩᲧセࠍ࿑ 8 ߦ␜ߔ‫ⶄޕ‬㔀ߥᵹࠇ႐ߥ߇ࠄ߽࿶❗ᓟߩ࠺࡯࠲߆
ࠄ࿶❗೨ߩ࠺࡯࠲ߣ㆖⦡ߩߥ޿⚿ᨐ߇ᓧࠄࠇߡ޿ࠆߎߣ߇⷗ߡขࠇࠆ‫ߚ߹ޕ‬࿑ 9 ߦߪ‫ޔ‬ਥᵹᣇะㅦᐲಽᏓߦ᷵ᐲ╬୯㕙ࠍ㊀⇥ߒߚ⚿ᨐࠍ␜ߒߡ޿ࠆ‫ޕ‬ᵹࠇ႐ߣห᭽ߦ╬୯㕙ߪ㕖Ᏹߦⶄ㔀ߥ᭴ㅧߢߪ޽ࠆ߽ߩߩ‫ޔ‬࿶❗ᓟߩ࠺࡯࠲߆ࠄ߽⦟ߊౣ⃻ߐࠇߡ޿ࠆߎߣ߇ࠊ߆ࠆ‫৻ޕ‬ᣇߢ࠺࡯࠲ࠨࠗ࠭ߦߟ޿ߡ‫ޔ‬࿶❗ᓟߩ࠺࡯࠲ࠨࠗ࠭ߪ 4 ‛ℂ㊂ߩ࿶❗ߢว⸘⚂ 140 MB ߣߥࠅ‫ޔ‬࿶❗೨࠺࡯࠲ࠨࠗ࠭㧔⚂ 3.8 GB㧕ߩ⚂ 3.7%߹ߢዊߐߊߔࠆߎߣ߇ߢ߈ߚ‫ޕ‬೨▵ߩ࿶❗੐଀ߢߪ㕖☼ᕈᵹ૕ࠍขࠅ
ᛒߞߡ޿ߚߚ߼ߦ‛ℂ㊂ߩᄌൻߪ‛૕ㄭறߦ㒢ࠄࠇߡ޿ߚ߇‫ߩ▵ᧄޔ‬࿶❗੐଀߆ࠄߪᓟᵹ߽฽߼ߚ㜞࡟ࠗࡁ࡞࠭ᢙ㕖ቯᏱᵹࠇߦߟ޿ߡ߽⦟ᅢߥ࿶❗₸ߣ࿶❗ᓟ࠺࡯࠲ຠ⾰ࠍ␜ߔߎߣ߇ߢ߈ߚ‫ޕ‬ ᧄ⸘▚੐଀ߦ߅޿ߡ‫ߢ⸒✜ޔ‬ㅀߴߚਥ⣉ߩ㕖ቯᏱ⸃ᨆ੐଀ߦߥࠄߞߡ઒ߦ 1000 ࠬ࠹࠶ࡊಽߩ࠺࡯࠲ࠍ಴ജߔࠆ႐ว‫ߪ࠭ࠗࠨ࠲࡯࠺ߩߘޔ‬ว⸘ߢ⚂ 3.8 TB ߦ߹ߢ㆐ߔࠆ‫ߦࠇߎޕ‬ኻߒߡᧄ▵ߢ␜ߒߚ࿶❗₸߇ᵹ૕⸘▚ࠍㅢߓߡ଻ߚࠇࠆߣ઒ቯߔࠆߥࠄ߫‫ޔ‬࿶❗ߦࠃࠅ࠺࡯࠲ࠨࠗ࠭ࠍ⚂140 GB ߹ߢᛥ߃ࠆߎߣ߇ߢ߈ࠆ‫ޔࠅࠃߦࠇߎޕ‬ᵹ૕⸃ᨆ࠺࡯࠲ߩขࠅ࿁ߒߦߟ޿ߡ഍⊛ߥᡷༀ߇ᦼᓙߢ߈ࠆ‫ޕ‬ ⚿⺰ BCM ߩ⋥੤ᩰሶ᭴ㅧࠍᵴ↪ߒߡ↹௝╓ภൻᚻᴺࠍᔕ↪ߒߚ࠺࡯࠲࿶❗ᚻᴺࠍ᭴ᚑߒ‫ޔ‬㕖☼ᕈᵹ૕ߥࠄ߮ߦ☼ᕈᵹ૕ߩ⸃ᨆ࠺࡯࠲ߦㆡ↪ߒߚ‫⚿ߩߘޕ‬ᨐ‫ߪ࠭ࠗࠨ࠲࡯࠺ޔ‬࿶❗೨ߩ 4%એਅ߹
ߢ࿶❗ߢ߈ࠆߎߣࠍ␜ߔߣߣ߽ߦ‫ޔ‬࿶❗ᓟߩ࠺࡯࠲߆ࠄߪ࿶❗೨ߩ࠺࡯࠲ߣ㆖⦡ߩߥ޿ࡑ࠶ࡂᢙಽᏓ‫ޔ‬࿶ജଥᢙಽᏓ‫ޔ‬ㅦᐲಽᏓ߇ᓧࠄࠇࠆߎߣࠍ⏕⹺ߒߚ‫੹ޕ‬ᓟߪ࿶❗ಣℂߩᤨ㑆⍴❗ࠍ࿑ࠆߣߣ߽ߦ‫ޔ‬㗔ၞᲤߩ㊀ߺઃߌࠍᦨㆡൻߔࠆߎߣߢߐࠄߦല₸⊛ߥ࿶❗ࠍ࿑ࠅ‫ޔ‬ታ↪⊛ߥ࠷࡯࡞ߣߒߡ⊒ዷߐߖߡ޿ߊ੍ቯߢ޽ࠆ‫ޕ‬⻢ㄉ ᧄ⎇ⓥߪ᧲ർᄢቇࠨࠗࡃ࡯ࠨࠗࠛࡦࠬ࠮ࡦ࠲࡯ߩࠬ࡯ࡄ࡯ࠦࡦࡇࡘ࡯࠲ࠍ೑↪ߔࠆߎߣߢታ⃻ߔࠆߎߣ߇ߢ߈ߚ‫⎇ߚ߹ޕ‬ⓥߦ޽ߚߞߡߪห࠮ࡦ࠲࡯㑐ଥฦ૏ߦߏᜰዉߣߏදജࠍ޿ߚߛ޿ߚ‫ޕ‬ᧄ⎇ⓥߪ⑼⎇⾌ (21226018) ߩഥᚑࠍฃߌߚ߽ߩߢ޽ࠆ‫⻢ߡߒ⸥ޕ‬ᗧࠍ⴫ߔ‫ޕ‬  

࿑ 8 F1 ࡟࡯ࠪࡦࠣࠞ࡯๟ࠅߩਥᵹᣇะㅦᐲಽᏓ㧔Ꮐ㧦࿶❗೨‫ޔ‬ฝ㧦࿶❗ᓟ㧕࿑ 9 F1 ࡟࡯ࠪࡦࠣࠞ࡯๟ࠅߩਥᵹᣇะㅦᐲಽᏓߣ᷵ᐲ╬୯㕙ߩ㊀⇥㧔Ꮐ㧦࿶❗೨‫ޔ‬ฝ㧦࿶❗ᓟ㧕!"#$%&'()*+,-./01.23ෳ⠨ᢥ₂[1] Nakahashi, K., “High-Density Mesh Flow Computations with Pre-/Post- DataCompressions,” AIAA Paper 2005-4876, 2005.
[2] Ishida, T., Takahashi, S., Nakahashi, K., “Efficient and Robust Cartesian Mesh
Generation for Building-Cube Method,” Journal of Computational Science andTechnology, Vol. 2, No. 4, pp. 435-446, 2008.
[3] 㜞ᯅବ, ⍹↰ፏ, ਛᯅ๺ඳ, ዊᨋᐢ᣿, ጟㇱ౏⿠, ਅ᧛㓁৻, ᦥᚒ㓉, ᠜૒ᤘ⵨, “ᄢⷙᮨ㕖࿶❗ᕈᵹ૕ࠪࡒࡘ࡟࡯࡚ࠪࡦߩᎿቇ໧㗴߳ߩᔕ↪,” SENAC Vol. 42, No. 1, pp. 107-114, 2009.
[4] Nakahashi, K., “Immersed Boundary Method for Compressible Euler Equations in the
Building-Cube Method,” AIAA Paper 2011-3386, 2011.
[5] ⷏᧛ᐽቁ, ૒‫ᧁޘ‬ᄢテ, ਛᯅ๺ඳ, “࿶❗ᕈ Building-Cube Method ࠍ↪޿ߚ⠢๟ࠅߩ㕖ቯᏱ㕖☼ᕈᵹࠇ⸃ᨆ,” ╙ 25 ࿁ᢙ୯ᵹ૕ജቇࠪࡦࡐࠫ࠙ࡓ⻠Ṷ㓸, 2011.
[6] ૒‫ᧁޘ‬ᄢテ, ᕲ↰ඳ, ਛᯅ๺ඳ, “Building-Cube ᴺߦࠃࠆ㕖ቯᏱᵹ૕⸃ᨆߣⓨജ㖸ផቯ,”
SENAC Vol. 44, No. 1, pp. 33-45, 2011.
[7] Deguchi, A., Sasaki, D., Nakahashi, K., Murayama, M., Yamamoto, K., Yokokawa, Y.,“Aeroacoustic Simulation of JAXA Landing Gear by Building-Cube Method andNon-compact Curle’s Equation,” AIAA Paper 2012-0388, 2012.
[8] Fukushima, Y., Sasaki, D., Nakahashi, K., “Code Development of Linearized Euler
Equation on Block-Structured Cartesian Mesh for Complicated Geometries,” AIAA Paper
2012-0832, 2012.
[9] Kang, H., Lee, D., Lee, D., “A Study on CFD Data Compression Using Hybrid
Supercompact Wavelets,” KSME International Journal, Vol. 17, No. 11, pp. 1784-1792,2003.
[10] Lorente, L.S., Vega, J.M., Velazquez, A., “Compression of aerodynamic databases using
high-order singular value decomposition,” Aerospace Science and Technology, Vol. 14, pp.
168-177, 2010.
[11] Vasilyev, O., Paolucci, S., “A dynamically adaptive multilevel wavelet collocation method
for solving partial differential equations in a finite domain,” Journal of Computational
Physics, Vol. 125, pp. 498-512, 1996.
[12] Gerritsen, M., “Designing an efficient solution strategy for fluid flows,” Ph.D. Thesis,
Stanford University, 1996.
[13] Farge, M., Schneider, K., Pellegrino, G., Wray, A.A., Rogallo, R.S., “Coherent vortex
extraction in three-dimensional homogeneous turbulence: Comparison between
CVS-wavelet and POD-Fourier decompositions,” Physics of Fluids, Vol. 15, No. 10, pp.
2886-2896, 2003.
[14] Shapiro, J.M., “Embedded Image Coding Using Zerotrees of Wavelet Coefficients,” IEEE
transactions on signal processing, Vol. 41, No. 12, pp. 3445-3462, 1993.
[15] Cohen, A., Daubechies, I., Feauveau, J.C., “Biorthogonal Bases of Compactly SupportedWavelets,” Communication on Pure and Applied Mathematics, Vol. 45, pp. 485-560, 1992.
[16] Martin, G.N.N., “Range encoding: an algorithm for removing redundancy from a
digitized message,” Video and Data Recording Conference, 1979.
[17] Capizzano, F., “Turbulent Wall Model for Immersed Boundary Methods,” AIAA Journal
Vol. 49, No. 11, pp. 2367-2381, 2011.

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