Formation of Astrophysical Objects 2022

Transcript

1. Riemann solverΛ༻͍ͨDensity-Independent Smoothed Particle Hydrodynamics(DISPH)ͷ࠶ߏ੒ ᴷ ৽ SPH εΩʔϜ:Godunov DISPH ๏ʹ͍ͭͯ ᴷ ౬ઙ୓޺, ৿ਖ਼෉ ஜ೾େֶ December 2, 2022 ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 1 / 22
2. ໨࣍ 1 ֤छεΩʔϜʹ͍ͭͯ SPH ๏ Density-Independent SPH ๏, GSPH ๏ Godunov DISPH ๏ Integral Approach 2 ςετܭࢉ ࣮ݧͷ໨త Riemann ໰୊ 2D ੩ਫѹฏߧ 2D Kelvin-Helmholtz ෆ҆ఆੑ ·ͱΊ 3 sheer switch ͷվྑʹ޲͚ͯ ໰୊఺ ݪҼͷ༧૝ վળࡦ 4 ࠓޙͷํ਑ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 2 / 22
3. ֤छεΩʔϜʹ͍ͭͯ SPH ๏ SPH ๏ಋग़ʹ༻͍ΔѹॖੑྲྀମͷӡಈํఔࣜɺΤωϧΪʔํఔࣜ dv(r) dt = − 1 ρ(r) ∇P(r) + FAV (α) (1) du(r) dt = − P(r) ρ(r) ∇ · v(r) + GAV (α) (2) • σϝϦοτ ▶ ྲྀମͷ઀৮ෆ࿈ଓ໘Λ͏·͘ѻ͑ͣɺͦͷͨΊྲྀମͷෆ҆ఆੑͷ੒௕Λ๦͛Δ ▶ িܸ೾Λଊ͑ΔͨΊʹਓ޻తͳࢄҳ߲͕ӡಈํఔࣜɺΤωϧΪʔํఔࣜʹඞཁɻ ਓޱ೪ੑͷڧ͞Λௐઅ͢Δ೚ҙύϥϝʔλ α ΛਓؒͷखͰௐ੔͢Δඞཁ ▶ ཭ࢄԽͷࡍʹཻࢠ෼෍ͷඇ౳ํੑ͔Β͘Δۭؒθϩ࣍ͷޡ͕ࠩൃੜ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 3 / 22
4. ֤छεΩʔϜʹ͍ͭͯ Density-Independent SPH ๏, GSPH ๏ DISPH ๏ɺGSPH ๏ͱ͸ • [Saitoh and Makino, 2013] Ͱ DISPH ๏͕ɺ[Inutsuka, 2002] Ͱ GSPH ๏͕։ൃ͞Εͨɻ DISPH ๏ ઀৮ෆ࿈ଓ໘Ͱ࿈ଓͳѹྗΛΧʔωϧਪ ఆ͠ɺྲྀମͷඍ෼ํఔࣜΛղ͍͍ͯΔɻ ਓ޻೪ੑ͕ඞཁɻ GSPH ๏ ཻࢠಉ࢜ͷ૬ޓ࡞༻ͷܭࢉͷࡍʹ Riemannsolver Λ༻͍ΔɻࠓճͷൃදͰ͸ [Cha and Whitworth, 2003] ʹΑΔ Case3 ͷ GSPH Λ࢖༻ɹਓ޻೪ੑඞཁͳ͠ɻ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 4 / 22
5. ֤छεΩʔϜʹ͍ͭͯ Godunov DISPH ๏ զʑ͕։ൃͨ͠ GDISPH ๏ʹ͍ͭͯ • DISPH ๏ͱಉ͘͡ɺີ౓ͷ୅ΘΓʹ઀৮ෆ࿈ଓ໘Ͱ࿈ଓͳѹྗΛΧʔωϧਪఆ͠ɺ GSPH ๏ͷಋग़ʹ฿ͬͯີ౓ʹཅʹґଘ͠ͳ͍ SPH ํఔࣜΛ࡞੒͍ͯ͘͠ɻ ρ(r) = ΣjmjW(|rj − r|, h(r)) (3) GDISPH ๏ಋग़ʹ༻͍Δࣜ q(r) = ΣjmjujW(|rj − r|, h(r)) = P(r) γ − 1 (4) F(r) ∼ ∫ F(r′)W(|r − r′|, h(r′))d3r′ (5) ѹॖੑྲྀମͷӡಈํఔࣜɺΤωϧΪʔํఔࣜ dv(r) dt = − 1 ρ(r) ∇P(r) (6) du(r) dt = − P(r) ρ(r) ∇ · v(r) (7) ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 5 / 22
6. ֤छεΩʔϜʹ͍ͭͯ Godunov DISPH ๏ GDISPH ๏ʹ͓͚Δ Case3 ܕͷӡಈํఔࣜɺΤωϧΪʔํఔࣜ ˙ vi = −ΣjmjujP∗ ij u∗ ij [ 1 q2 i ∇iW(ri − rj, hi) + 1 q2 j ∇iW(ri − rj, hj) ] ˙ ui = −ΣjmjujP∗ ij u∗ ij [ v∗ ij − vi ] [ 1 q2 i ∇iW(ri − rj, hi) + 1 q2 j ∇iW(ri − rj, hj) ] (8) ఴ͑ࣈʹ*ͷ෇͍ͨ෺ཧྔͷܭࢉํ๏ʹ͸ࣗ༝౓Λ࣋ͨͤΔɻ GSPH ๏Ͱ͸ɺriemann solver ͷղɻ ྫͱͯ͠ɺu∗ ij = ui, v∗ ij = vi+vj 2 ͱ͠ɺP∗ ij ͸ riemann solver ͔ΒٻΊΔύλʔϯΛ GDISPH Case3 2 2 ͱ໊͚ͮΔɻ(ຊൃදͰ͸͜Ε͕ॏཁͳ GDISPH ͷεΩʔϜ) Χʔωϧͷۭؒඍ෼ʹ͸ɺ[Garc´ ıa-Senz et al., 2012] ͕ߟҊͨ͠ IA Λ࢖༻͢Δ͔൱͔ͷࣗ༝ ౓͕ଘࡏɻ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 6 / 22
7. ֤छεΩʔϜʹ͍ͭͯ Integral Approach Integral Approach(IA) ͱ͸ • [Garc´ ıa-Senz et al., 2012] ͕೤֦ࢄ߲౳ʹݱΕΔ 2 ֊ඍ෼߲ͷܭࢉʹ࢖༻͞Ε͍ͯͨํ๏ ([Brookshaw, 1985]) ΛҰ֊ඍ෼ʹԠ༻ • 1 ֊ඍ෼ͰݱΕΔΧʔωϧͷۭؒඍ෼Λผͷ΋ͷʹม͑Δ͚ͩͰΑ͍ɻ ∇iW(ri − rj, hi) ∼ τ−1 i (rj − ri)Wij(hi) ∇iW(ri − rj, hj) ∼ τ−1 j (rj − ri)Wij(hj) τ(r) = [∫ (r′ − r) ⊗ (r′ − r)W(|r − r′|, h(r)) ] d3r′ (9) • IA ʹΑΓ෺ཧྔͷ 1 ֊ඍ෼ͷਫ਼౓͕ྑ͘ͳΓɺۭؒ 0 ࣍ͷޡࠩ΋খ͘͞ͳΔ͜ͱ͕ใࠂ ͞Ε͍ͯΔɻ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 7 / 22
8. ςετܭࢉ ࣮ݧͷ໨త ࣮ݧͷ໨త • SPH ๏ɺDISPH ๏ ▶ Χʔωϧͷۭؒඍ෼Λ IA ʹ͢Δ͔൱͔ • Case3 ͷ GSPH ๏ ▶ Χʔωϧͷۭؒඍ෼Λ IA ʹ͢Δ͔൱͔ ▶ riemann solver ͷߴਫ਼౓Խ͢Δ͔൱͔ɺ͢ΔͳΒྲྀ଎੍ݶؔ਺ΛԿʹ͢Δ͔ • Case3 ͷ GDISPH ๏ ▶ Χʔωϧͷۭؒඍ෼Λ IA ʹ͢Δ͔൱͔ ▶ ఴ͑ࣈʹ*ͷ෇͍ͨ෺ཧྔΛ riemann solver Ͱղ͔͘൱͔ɺղ͔ͳ͍ͳΒԿʹ͢Δ͔ ▶ riemann solver ͷߴਫ਼౓Խ͢Δ͔൱͔ɺ͢ΔͳΒྲྀ଎੍ݶؔ਺ΛԿʹ͢Δ͔ riemann solver ͷߴਫ਼౓Խ͸ [Cha and Whitworth, 2003] ͷ΍ΓํͰߦͬͨɻ ֤εΩʔϜʹର༷ͯ͠ʑͳ૊Έ߹Θͤͷύλʔϯ͕ଘࡏɻ͜ͷதͰ࠷΋༏ΕͨεΩʔϜΛબ ఆ͢ΔͨΊɺ໿ 150 ݸͷύλʔϯʹؔͯ͠ riemann ໰୊,2D ੩ਫѹฏߧ,2D Kelvin-Helmholtz ෆ҆ఆੑͷܭࢉΛߦͬͨɻͦͷதͰ͍͔ͭ͘ͷεΩʔϜΛϐοΫΞοϓ͠ɺͦͷಛੑΛൺֱ ݕ౼͢Δɻ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 8 / 22
9. ςετܭࢉ Riemann ໰୊ Riemann ໰୊ ڧ͍িܸ೾͕ൃੜ͢Δ໰୊ { ρ = 1, P = 1000, v = 0 x < 0 ͷͱ͖ ρ = 1, P = 0.1, v = 0 x > 0 ͷͱ͖ (10) ີ౓ ѹྗ ଎౓ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 9 / 22
10. ςετܭࢉ Riemann ໰୊ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 10 / 22
11. ςετܭࢉ 2D ੩ਫѹฏߧ 2D ੩ਫѹฏߧ ॳظ৚݅ͷ··มಈ͠ͳ͍ͷ͕෺ཧతͳղ ѹྗ͸શྖҬͰҰఆɹ • Ի଎ Cs = 1.02 ͰܭࢉྖҬΛԣ੾Δ࣌ؒ໿ 1.0 ͷ 8 ഒͰ͋Δ t = 8.0 ·Ͱܭࢉ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 11 / 22
12. ςετܭࢉ 2D ੩ਫѹฏߧ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 12 / 22
13. ςετܭࢉ 2D Kelvin-Helmholtz ෆ҆ఆੑ 2D Kelvin-Helmholtz ෆ҆ఆੑ Ґஔ y = 0.25, y = 0.75 ͷͦΕͧΕʹɺy ࣠ํ޲ͷ଎౓ʹ 2 ೾௕෼ͷઁಈΛ༩͍͑ͯΔ ෆ҆ఆੑͷ੒௕ͷλΠϜεέʔϧ τKH = 1.06 ͷ໿ 2 ഒͷ t = 2.0 ·Ͱܭࢉ GSPH,GDISPH ͱ SPH,DISPH ͷൺֱͷͨΊɺbalsara switch ͸͋͑ͯ֎ͯ͠ܭࢉ ॳظ৚݅ ༩͑ͨઁಈ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 13 / 22
14. ςετܭࢉ 2D Kelvin-Helmholtz ෆ҆ఆੑ Balsara switch ͱ͸ • [Balsara, 1995] ʹΑͬͯఏҊ͞Εͨख๏ • ਓ޻೪ੑ߲͸ຊདྷিܸ೾ྖҬͰͷΈಇ͍ͯ΄͍͕͠ɺγΞྖҬͰ΋ಇ͍ͯ͠·͏ɻ • ͦΕΛ๷͙ͨΊɺBalsara switch ͕Α͘࢖ΘΕ͍ͯΔɻ Balsara switch ਓ޻೪ੑ߲ʹ 0.5(Fi + Fj) Λ͔͚ΔɻγΞྖҬͰ͸ Fi, Fj Λ 1 ΑΓখ͘͞ɺিܸ೾ྖҬͰ͸ Fi, Fj ͕ 1 ʹͳΔΑ͏ʹઃఆɻ Fi = |∇i · vi| |∇i · vi| + |∇i × vi| + 0.0001ci/hi (11) ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 14 / 22
15. ςετܭࢉ 2D Kelvin-Helmholtz ෆ҆ఆੑ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 15 / 22
16. ςετܭࢉ 2D Kelvin-Helmholtz ෆ҆ఆੑ • ࠨ͸ਓ޻೪ੑͷύϥϝʔλ α = 0.5ɺ ӈ͸ α = 3ɻӈͷ΄͏͕ਓ޻೪ੑ͕ ڧ͍ɻ • ਓ޻೪ੑ͕ڧ͍ → γΞྖҬͰͷਓ޻ ೪ੑ͕݁Ռతʹେ͖͘ͳΔ → ෆ҆ఆ ੑͷ੒௕͕཈੍ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 16 / 22
17. ςετܭࢉ ·ͱΊ ·ͱΊ • GDISPH Case3 2 2 ▶ Riemann ໰୊ɺ੩ਫѹฏߧ໰୊ʹ͓͍ͯ DISPH ͱಉ༷ͳ݁Ռ,Kelvin-Helmholtz ෆ҆ఆੑʹ ؔͯ͠͸ GSPH ͱಉ༷ͳ݁ՌɻSPH ͷεΩʔϜͱͯ͠ɺѹॖੑྲྀମͷ໰୊Λ͖ͪΜͱղ͚ ͍ͯΔɻ ▶ ߴਫ਼౓Խͨ͠৔߹ɺ೪ੑ͕খ͘͞ͳΔ͜ͱ͕ݪҼͰڧ͍িܸ೾ԼͰͷৼಈ͕ൃੜͯ͠͠ ·͏ɻ ▶ ߴਫ਼౓ԽʹΑͬͯ Kelvin-Helmholtz ෆ҆ఆੑͷ੒௕͕ଅਐ͞ΕΔɻओͳཁҼ͸೪ੑ͕খ͞ ͘ͳͬͨ͜ͱͰγΞྖҬͷ೪ੑ͕খ͘͞ͳ͔ͬͨΒ • IA ▶ Kelvin-Helmholtz ෆ҆ఆੑͰ͸ɺIA ԽʹΑΓ੒௕͕ଟগଅਐ͞ΕΔɻ͔͠͠ɺ੩ਫѹฏߧ໰ ୊͔Β DISPH ܥͷεΩʔϜͰ͸ IA ԽʹΑΓϊΠζΛर͍΍͘͢ͳ͍ͬͯΔɻ • SSPH,DISPH ▶ Kelvin-Helmholtz ෆ҆ఆੑʹ͓͍ͯɺಉ༷ͳ݁ՌɻGSPH,GDISPH ΑΓ΋ෆ҆ఆੑͷ੒௕͕ ଅਐ͞Ε͍ͯΔ͕ɺ͔͔͍ͬͯΔ೪ੑ͕ GSPH,GDISPH ΑΓ΋খ͍͔͞Βɻ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 17 / 22
18. sheer switch ͷվྑʹ޲͚ͯ ໰୊఺ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 18 / 22
19. sheer switch ͷվྑʹ޲͚ͯ ݪҼͷ༧૝ ݪҼͷ༧૝ ϊΠζͷਖ਼ମ ཻ֤ࢠʹ͓͚Δɺۭؒ 0 ࣍ͷޡࠩ΍ O(h2) ͷޡࠩͷ͔͔Γํͷҧ͍ʹΑΔ΋ ͷɻཻ֤ࢠؒͷඍົͳ਺஋ͷͣΕ͕ɺ ඇৗʹ೾௕ͷখ͍͞ઁಈͱͳΔɻ ϊΠζ͕େ͖͘੒௕͢Δཧ༝ • balsara switch ͷಋೖʹΑͬͯγΞྖ ҬͰͷ೪ੑ͕΄΅ 0 ʹͳΔɻ • ڪΒ͘෺ཧతʹ͸ɺྲྀମͷ೪ੑ͕େ ͖͘ͳΔͱɺKH ෆ҆ఆੑ͕ى͜Δ ࠷খͷ೾௕΋େ͖͘ͳΔɻ ೪ੑ͕ 0 ͳΒ͹ɺ ͲͷΑ͏ͳ೾௕ʹରͯ͠΋ෆ҆ఆੑ੒௕ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 19 / 22
20. sheer switch ͷվྑʹ޲͚ͯ վળࡦ վળࡦ • ෺ཧతͳઁಈʹΑΔෆ҆ఆੑͷ੒௕͸ڐ͠ɺ਺஋తͳϊΠζʹΑΔઁಈͷ੒௕͸཈͑Δɻ → balsara switch ͷڧ͞Λௐઅ͢Δ͜ͱͰ࣮ݱΛ໨ࢦ͢ɻ Balsara switch • ਓ޻೪ੑ߲ʹ 0.5(Fi + Fj) Λ͔͚Δɻ Fi = |∇i · vi| |∇i · vi| + |∇i × vi| + 0.0001ci/hi (12) զʑͷఏҊख๏ • Fi, Fj ͷ୅ΘΓʹ F′ i , F′ j Λ༻͍Δɻ • β ͸ [0, 1] ͷ࣮਺ΛऔΔ೚ҙύϥϝʔλɻβ = 1 Ͱ balsara switch Φϯɹ β = 0 Ͱ balsara switch Φϑ F′ i = 1 + β(Fi − 1) (13) ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 20 / 22
21. sheer switch ͷվྑʹ޲͚ͯ վળࡦ DISPH ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 21 / 22
22. ࠓޙͷํ਑ ࠓޙͷํ਑ • ೪ੑྲྀମͷ Kelvin-Helmholtz ෆ҆ఆੑͷ෼ࢄؔ܎͔ΒɺO(h) ఔ౓ͷ೾௕ͷઁಈͷ੒௕Λ ແࢹͰ͖ΔΑ͏ͳύϥϝʔλ β ͷઃఆํ๏Λݟ͚ͭΔɻ • GSPH,GDISPH ΁ͷ Balsara switch ͷద༻Λߦ͏ɻ • ఆྔతͳධՁΛ༻͍Δ • ͕Μ͹Δ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 22 / 22
23. ࠓޙͷํ਑ ग़య Figure: ”Fancy SPH convolution scheme (verbose, modified colors scheme)” created by Jlcercos is licenced under CC BY-SA 4.0(https://creativecommons.org/licenses/by-sa/4.0/) ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 22 / 22
24. ࠓޙͷํ਑ Reference I [Balsara, 1995] Balsara, D. S. (1995). Von neumann stability analysis of smoothed particle hydrodynamicsŠsuggestions for optimal algorithms. Journal of Computational Physics, 121(2):357–372. [Brookshaw, 1985] Brookshaw, L. (1985). A method of calculating radiative heat diffusion in particle simulations. Publications of the Astronomical Society of Australia, 6(2):207 r 210. [Cha and Whitworth, 2003] Cha, S.-H. and Whitworth, A. P. (2003). Implementations and tests of godunov-type particle hydrodynamics. Monthly Notices of the Royal Astronomical Society, 340(1):73–90. [Garc´ ıa-Senz et al., 2012] Garc´ ıa-Senz, D., Cabez´ on, R. M., and Escart´ ın, J. A. (2012). Improving smoothed particle hydrodynamics with an integral approach to calculating gradients. Astronomy & astrophysics, 538:A9. [Inutsuka, 2002] Inutsuka, S.-i. (2002). Reformulation of smoothed particle hydrodynamics with riemann solver. Journal of Computational Physics, 179. ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 22 / 22
25. ࠓޙͷํ਑ Reference II [Saitoh and Makino, 2013] Saitoh, T. R. and Makino, J. (2013). A DENSITY-INDEPENDENT FORMULATION OF SMOOTHED PARTICLE HYDRODYNAMICS. The Astrophysical Journal, 768(1):44. ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 22 / 22
26. ࠓޙͷํ਑ ಋग़ͷࡍʹ༻͍ΔԾఆɾۙࣅ • ҎԼͷࣜΛຬͨ͢ Fij ͕ଘࡏ͢Δ ∫ F(r) q2(r) W(|r − ri|, h(r))W(|r − rj|, h(r))d3r = F∗ ij ∫ 1 q2(r) W(|r − ri|, h(r))W(|r − rj|, h(r))d3r (14) • Case3 ͷܗʹ͢ΔͨΊʹҎԼͷۙࣅ͕੒Γཱͭͱ͢Δ [∇i − ∇j]W(|ri − r|, h(r))W(|rj − r|, h(r)) ∼ ∇iW(|ri − r|, h(r))δ(|r − rj|) − δ(|r − ri|)∇jW(|rj − r|, h(r)) (15) • Godunov SPH ๏Ͱ͸ɺࣜ (14) ʹ͓͍ͯ q(r) ͕ ρ(r) ʹஔ͖׵Θ͍ͬͯΔɻFij ͸ཻࢠ i ͱཻࢠ j ͷத৺෇ۙͰͷɺཻࢠ i ͱཻࢠ j ͷ෺ཧྔΛ༻͍ͨ Riemann solver ͷղ ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 22 / 22
27. ࠓޙͷํ਑ GDISPH ΁ͷ Balsara switch ͷద༻ • GSPHɺGDISPH ʹ Balsara switch ͷద༻Λߦͬͨྫ͸ͳ͍ɻ • DISPH ͸ (ඇਓ޻೪ੑ߲)+(ਓ޻೪ੑ߲) ʹཅʹ෼͔Ε͍ͯΔ͕ɺGDISPH ͸ 1 ͭͷ߲ʹ ·ͱ·͍ͬͯͯ෼཭͍ͯ͠ͳ͍ɻ զʑͷఏҊख๏ • (DISPH ͷඇਓ޻೪ੑ߲)+0.5(F′ i + F′ j)(GDISPH ͷ߲ - DISPH ͷඇਓ޻೪ੑ߲) Λɺ GDISPH ͷࣜͱͯ͠༻͍Δɻ • F′ i = F′ j = 1(Balsara switch Φϑ) Ͱͨͩͷ GDISPH ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 22 / 22
28. ࠓޙͷํ਑ GDISPH ౬ઙ ୓޺, ৿ ਖ਼෉ (ஜ೾େֶ) DISPH, Godunov SPH, Godunov DISPH, IA December 2, 2022 22 / 22