HAL Id: hal-00951401
https://hal.archives-ouvertes.fr/hal-00951401
Submitted on 24 Feb 2014
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Algorithm to refine a finite volume mesh admissible for
parabolic problems
Florence Hubert, Marie-Claude Viallon
To cite this version:
❭❚❪◗❫ ❴ ❵ ❛ ❜❝ ❪ ❞❃❪ ❡ ❢✑❣ ❤ ❜❴ ❵❥✐❦ ❧❇♠✬❜❤♥✶♥ ❴ ♦❇❴ ♣ ❪ ❵ ❪ ❴ ❢ ❛❃q✯❜❞ ❜❫ ♥ r❪ ❤❃s✑❴ ❢ ❵ ❝✑❣ ❞ t✺❫ ❴ ❵ ❝ ❜❤ ❜❴ ❵ ❛❃❴ ❵✶❤ ♥ ❪✠❝ ❴ ♦❆❣ ❜❵✈✉①✇✯②✴③ ❦ ④ ❦ ⑤⑥✴②✑③✓❦ ④ ❦ ⑤⑦ ⑧✬♥ ❪❇❛ ❴ ❢ ❞ ❫ ❪★❤ ❪ ❞ ♦①⑨❚❜❛✯❫ ♥ ❴ ❛ ❪ ❵◗❜❵◗❛ ❢ ❫ ♥❚❣❃♠✬❣ t❆❤♥✑❣ ❤✯⑩✣❶ ✐❷✣④ ❸ ❧✳✇❹✐❦❉③❚❷✣❺ ❧ ✐ ❦❉③✺❸ ❺ ❧✬❜❛✯❛ ❴ r❢ ❤❜❴ ❵✠❴ ❻ ❤ ♥ ❜❛✯❼ ❞ ❴ s r❪ ♦✠❽ ❭❚❪★❫ ❴ ♦❇❼✑❣ ❞ ❪❉❜❵◗❤ ♥ ❪★❛ ❪ ❡ ❢ ❪ r✜❤ ♥ ❪★⑧✬❾✳❿ ➀➁❣ ❼ ❼ ❞ ❴ ➂ ❜♦❃❣ ❤ ❜❴ ❵❆❴ ❵✠➃✯➄✴⑧❉➅✣➆✴❴ ❞ ❴ ❵ ❴ ❜✜❣ ❵ ❝✠❵ ❴ ❵◗❣ ❝ ♦❃❜❛ ❛❜s r❪ ♦❇❪ ❛ ♥ ❪ ❛ ❽ ➇ ❽❦ ❽❃➈✜➉ ➊❉➋❆➊ ➌ ➉ ➊ ➌ ➍✜❪ ❤✬➎➐➏✠➑✯➒ ⑦ ❭❚❪❉♠✬❣ ❵ ❤✳❤ ❴❃❫ ❴ ❵ ❵ ❪ ❫ ❤✬❣❇❫ ❴ ❣ ❞ ❛ ❪❉❛❡ ❢✑❣ ❞ ❪✯♣ ❞ ❜❝✺✐♦❇❪ ❛ ♥✠❛ ❜➓ ❪➁➔ → ❧✳❴ ❵✠✉❚➣◗↔ ❷◗↕✓➙ ➛ ④ ❤ ❴❆❣★➜ ❵ ❪❉♣ ❞ ❜❝✠❴ ❵ ✉❚➣◗↔ ❷◗➝❥③➐➔ ❺ → ➛❃✐✴♦❃❪ ❛ ♥✠❛ ❜➓ ❪★➞❆✇✚➔ ❺➟ → ❧ ❽ ➠ ❵❆❤♥ ❪❉➡ s ❢ ➢✑❪ ❞➡❇❝ ❴ ♦❃❣ ❜❵✠✉✠➣✠↔✴➤ ➔ ❺ →❹➥ ❷ ➥ ➙ ➛ ➅ ♠✳❪✯❞❪ ❼✑❪ ❣ ❤✬➦ ➎①❤ ❜♦❇❪ ❛✬❤ ♥ ❪✯➃✯➄✴⑧❥❫ ❴ ❵ ❛ ❤ ❞ ❢ ❫ ❤ ❜❴ ❵✠❣ ❫ ❫ ❴ ❞ ❝ ❜❵ ♣★❤ ❴❇❤ ♥ ❪ ➧ ❣ r❢ ❪✬❴ ❻✑❤♥ ❪✯❼✑❣ ❞ ❣ ♦❃❪ ❤ ❪ ❞✴➨◗❣ ❛✌❻❣ ❞✌❤ ♥ ❪✯➃✯➄✴⑧✶♦❇❪ ❛ ♥ ❪ ❛✳❣ ❞ ❪✬❫ ❴ ❵ ❫ ❪ ❞ ❵ ❪ ❝✜❽ ❿✑❴ ❞✌❤ ♥ ❪✬❵ ❴ ❵ ➩ ❣ ❝ ♦❃❜❛ ❛ ❜s r❪✬♣ ❞ ❜❝ ❛ ➅ ❤ ♥ ❪✯➜ ❵ ❪✬♣ ❞ ❜❝ ❜❛❉❵✑❣ ❤❢ ❞ ❣ rrt✠❪ ➂ ❤ ❪ ❵ ❝ ❪ ❝◗❤❴✠✉✺➣❚↔ ❷✺➝❥➙ ➛ ❽ ❿ ❴ ❞❉❤♥ ❪❇➆✴❴ ❞ ❴ ❵ ❴ ❜✜♦❇❪ ❛♥ ❪ ❛ ➅✣❞ ❪ ❫ ❣ rr✜❤ ♥✑❣ ❤✯❤ ♥ ❪❇❫ ❴ ❵ ❛ ❤ ❞ ❢ ❫ ❤ ❜❴ ❵◗❴ ❻✴❤ ♥ ❪❇♦❃❪ ❛ ♥ ❫ ❴ ❵ ❛ ❜❛ ❤ ❛✌❤❴❇❝ ❪ ❤ ❪ ❞ ♦❃❜❵ ❪✯❼✑❴ rt ♣ ❴ ❵✑❣ r ❞❪ ♣ ❜❴ ❵ ❛✬❣ ❞ ❴ ❢ ❵ ❝❃❛ ❴ ♦❃❪✯➜ ❵ ❜❤❪✯❛ ❪ ❤✳❴ ❻✣♣ ❜ ➧ ❪ ❵❃❼✑❴ ❜❵ ❤➩❛ ❜❤❪ ❛ ❽ ❭❚❪✯❫ ❴ ❵ ❛ ❤ ❞ ❢ ❫ ❤✌♥ ❪ ❞ ❪✯❤ ♥ ❪ ❝ ❢✑❣ r✣♦❇❪ ❛♥✠♠✬♥ ❴ ❛ ❪❉❼✑❴ ❜❵ ❤➩ ❛ ❜❤ ❪ ❛✬❫ ❴ ❜❵ ❫ ❜❝ ❪❉♠✬❜❤ ♥◗❤♥ ❪ ➧ ❪ ❞❤ ❜❫ ❪ ❛✳❴ ❻✴❤♥ ❪❉➃✯➄✴⑧❥♦❃❪ ❛ ♥ ❪ ❛★✐❛ ❪ ❪❆⑤➫ ②❧ ❽ ⑧✬♥ ❪❉❤♥ ❞ ❪ ❪✯❝ ❜➢✑❪ ❞ ❪ ❵ ❤✬♦❇❪ ❛♥ ❪ ❛✳❫ ❴ ❞ ❞ ❪ ❛ ❼✑❴ ❵ ❝ ❜❵ ♣★♠✬❜❤ ♥❆➎①✇❥➦ ④ ➨✠✇➭❦ ④ ➨◗✇❥➦❇❣ ❵ ❝❆➨✠✇❥➯ ④ ❣ ❞ ❪✯❛ ♥ ❴ ♠✬❵❆❴ ❵❆❿✴❜♣ ❢ ❞ ❪ ➇ ❽ ➀✈➓ ❴ ❴ ♦❹❴ ❻✜❤ ♥ ❪❉s ❢ ➢✑❪ ❞✯➓ ❴ ❵ ❪❉❜❛✬❼ ❞ ❴ ❼✑❴ ❛ ❪ ❝❆❻❴ ❞✬❤ ♥ ❪❉❫ ❣ ❛ ❪❉➨✠✇❥➯❇❜❵✠❿✴❜♣ ❢ ❞ ❪❉➦✠✐❣ ❧✳❣ ❵ ❝✺✐s✑❧ ❽ ❿✑❴ ❞✬➨✠✇➭❦ ➅ ❤♥ ❪❉➆✴❴ ❞ ❴ ❵ ❴ ❜ ❣ ❵ ❝❚➃✯➄✴⑧➁♦❇❪ ❛ ♥ ❪ ❛❉❫ ❴ ❜❵ ❫ ❜❝ ❪ ❽✑❿✑❴ ❞❉➨✓✇✼➦ ➅✜❤ ♥ ❪❇❫ ❪ rr❛★❴ ❻✌❤ ♥ ❪❃❤♠✳❴❆♦❃❪ ❛ ♥ ❪ ❛❇❣ ❞ ❪❇❤ ♥ ❪❃❛ ❣ ♦❃❪ ➅✜s ❢ ❤❉❤♥ ❪❇❫ ❪ ❵ ❤ ❪ ❞❛★❴ ❻✌❤ ♥ ❪ ❫ ❪ rr❛✯❣ ❞ ❪❉❝ ❜➢✑❪ ❞ ❪ ❵ ❤ ❛ ❽
Voronoi mesh n=1
NRT mesh n=1
NRT mesh n=2
NRT mesh n=5
Non−adm mesh n=1
Non−adm mesh n=2
Non−adm mesh n=5
Voronoi mesh n=2
Voronoi mesh n=5
➲ ➳➵ ➸ ➺➻✴➼ ➽ ➾✜➚ ➻✌➪✳➻➶➚ ➻ ➶✜➹➘ ➺➺➻➶➴ ➘ ➷ ➬ ➳➷ ➵✌➮✴➳➱➚❉✃✴❐✌❒ ➽