touyou
May 17, 2018
51

# 粒子法について その２

May 17, 2018

## Transcript

1. ཻࢠ๏ೖ໳
ͦͷ̎

2. ɾ̏ষʜ༷ʑͳԠ༻ྫ
ɾ̐ষʜฒྻԽʹؔͯ͠
ཻࢠ๏ೖ໳
ཻࢠ๏ೖ໳ͦͷ̎

3. φϏΤετʔΫεํఔࣜ
ɾྲྀମͷӡಈํఔࣜ
ɾV͕଎౓ɺH͕ॏྗՃ଎౓
ɾЛ͕ີ౓ɺӈลͷୈೋ߲͸೪ੑ߲
Du
Dt
=
1
⇢0
rP + ⌫r2u + g
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
AAACP3icbVBLSwMxGMz6rPVV9eglWAShWHaLoBehaBGPFewDum3Jptk2NMkuSVYoy/4j/4R/wZvoyYs38erNtLsHbR0IGWa+4UvGCxlV2rZfrKXlldW19dxGfnNre2e3sLffVEEkMWnggAWy7SFFGBWkoalmpB1KgrjHSMsbX0/91gORigbiXk9C0uVoKKhPMdJG6hduXF8iHNdcj8dRksQ1nVyeppqTxK4cBT07cQXyGIL1kiuilPcqME2Uptcw6ReKdtmeAS4SJyNFkKHeL7y7gwBHnAiNGVKq49ih7sZIaooZSfJupEiI8BgNScdQgThR3Xj23wQeG2UA/UCaIzScqb8TMeJKTbhnJjnSIzXvTcV/PY/Pbdb+RTemIow0EThd7EcM6gBOy4QDKgnWbGIIwpKat0M8QqY8bSrPm1Kc+QoWSbNSduyyc3dWrF5l9eTAITgCJ8AB56AKbkEdNAAGj+AZvII368n6sD6tr3R0ycoyB+APrO8fxL+wyg==

4. ɾද໘ுྗ
ɾߴ೪ੑྲྀମ
ɾඇχϡʔτϯྲྀମ
ɾཚྲྀ
ɾϙϦΰϯน
ൃలతػೳ
ཻࢠ๏ೖ໳ͦͷ̎

5. ɾѹྗͷܭࢉ΋ཅղ๏Ͱߦ͏
ˣ
ɾ୅ೖͷΈͰܭࢉՄೳ
ˣ
ɾฒྻԽ͕͠΍࣮͘͢ߦ͕࣌ؒ୹͍
ཅղ๏
ཻࢠ๏ೖ໳ͦͷ̎

6. ཅղ๏ͷ֓ཁ
ཻࢠ๏ೖ໳ͦͷ̎

7. ɾ৽͍͠ࢧ഑ํఔࣜ
ɾD͸Ի଎
ཅղ๏ͷ֓ཁ
ཻࢠ๏ೖ໳ͦͷ̎
@P
@⇢
= c2
AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu
AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu
AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu
AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu

8. มԽ͢Δͱ͜Ζ
ཻࢠ๏ೖ໳ͦͷ̎
1
⇢0
2d
0n0
X
j6=i
Pk+1
j
Pk+1
i
w(|r⇤
j
r⇤
i
|) =
1
t2
n⇤
i
n0
n0
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

9. มԽ͢Δͱ͜Ζ
ཻࢠ๏ೖ໳ͦͷ̎
1
⇢0
2d
0n0
X
j6=i
Pk+1
j
Pk+1
i
w(|r⇤
j
r⇤
i
|) =
1
t2
n⇤
i
n0
n0
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
P⇤ = c2⇢
n⇤ n0
n0
Pk+1 = c2⇢
nk+1 n0
n0

10. όέοτߏ଄
ཻࢠ๏ೖ໳ͦͷ̎
ɾҰఆͷେ͖͞ͷ
όέοτʹ෼͚Δ
ɾ֤όέοτʹ͸
௨͠൪߸Λ;Δ

11. ϦϯΫϦετߏ଄
ཻࢠ๏ೖ໳ͦͷ̎
ɾ࠷௿ݶͷ৘ใͰ
όέοτͷத਎Λ΋ͭ

͜ͷόέοτͷ'JSTUʜ
͜ͷόέοτͷ-BTUʜ
ͷOFYUʜ
ͷOFYUʜ
ͷOFYUʜ
ͷOFYUʜ

12. ৽͍࣮͠૷
ཻࢠ๏ೖ໳ͦͷ̎

13. ৽͍࣮͠૷
ཻࢠ๏ೖ໳ͦͷ̎
ཻࢠΛฒ΂Δ
Ծ଎౓Λܭࢉ͢Δ
Ծ଎౓Λ࢖ͬͯҠಈ͢Δ
ඇѹॖ৚݅Λຬͨ͢Α͏ʹ
ѹྗΛܭࢉ
Ґஔͱ଎౓Λ࠶ܭࢉ

14. ৽͍࣮͠૷
ཻࢠ๏ೖ໳ͦͷ̎
ཻࢠΛฒ΂Δ
όέοτ৘ใΛߋ৽
೪ੑ߲ॏྗ߲ͰԾ଎౓ͱԾҐஔ
࣮ࡍͷѹྗΛग़͢
ԾͷѹྗΛܭࢉ
࣮ࡍͷҐஔɾ଎౓Λग़͢

15. ݁Ռ
ཻࢠ๏ೖ໳ͦͷ̎

16. ݁Ռ
ཻࢠ๏ೖ໳ͦͷ̎
൒ӄղ๏ʜ࣮ߦ࣌ؒTFD
ཻࢠ਺εςοϓ਺໿
γϛϡϨʔγϣϯͨ࣌ؒ͠TFD
ཅղ๏ʜ࣮ߦ࣌ؒTFD
ཻࢠ਺εςοϓ਺໿
γϛϡϨʔγϣϯͨ࣌ؒ͠TFD
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