第 46 回流体力学講演会 / 第 32 回航空宇宙数値シミュレーション技術シンポジウム論文集 99 HR-SLAU2 HR-AUSM + -up HR-SLAU2 and HR-AUSM + -up towards High Resolution Unsteady Aerodynamic Simu
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1 第 46 回流体力学講演会 / 第 3 回航空宇宙数値シミュレーション技術シンポジウム論文集 99 -SAU -AUS + - -SAU ad -AUS + - twards High eslti Usteady Aerdyami Simlatis by Keiihi Kitamra (Nagya Uiversity; rretly at Yhama Natial Uiversity) ad Atsshi Hashimt (JAXA) ABSTACT The reded dissiati arah has bee alied t AUS-family flx ftis f SAU ad AUS + - twards high reslti trasi bffet simlatis strtred grids. I this arah the dissiati term (f the ressre flx) i eah flx fti is lally trlled (0 < < : dissiati effiiet) where a ell-iterfae rietati agle is small (i.e. ell gemetry is early sqared) ad/r where flws are smth ad the rigial methds are revered therwise ( =). Nmerial tests demstrated that the rsed (High-eslti) -SAU ahieved better reslti (while maitaiig rbstess) fr a dble shear layer rblem (ah 0.0) ad deayig istri trblee (ah ) mared with the rigial terarts ( =) r a existig methd (-e) whereas -AUS + - shwed degraded reslti de t a large tff ah mber reqired fr a stability reas CFD () Bret () De (3) Zal DES 3 (4)-(8) (9)-(3) Wiler (4) e (5) e AUS AUS + - (6) SAU (7) SAU (8) AUS e (9)(0) () () e (4)(3) (High eslti) -e AUS -SAU - SAU -AUS + - (5) (5) -SAU -AUS + - Navier-Stes 3 l m 3 Q F t x Fv x Q l F l l E H 0 Fv l T m m x l l l x xl 3 x (a) (b) () i E H (H = E + (/)) =.4 Pr=0.7 =/Pr Eler =0
2 00 宇宙航空研究開発機構特別資料 JAXA-SP-4-00 F Fv S 0 Vi Q i i i i () t Vi i t Qi Fi i Si (+) (-) = ( v w ) i i r ri i (wiggle)w= w wiggle detetr e e < =0 (4)-(4d) 0 i i i i (4e) 0 (4f) i i i i Fig. Shemati f ell gemetri rerties. -e e (5) -e (4)(3) -e F- e F/ Q/ F e F F Aˆ Q Q 0 =0 = e =0 Wiler (4) max mi w (4a) mi=0. (5) f d s 3 fae fae 0 0 fae 0 3 fae i i 3 3 fd = =0 fae 0 e fd DDES (6) w 0 i i 0 (4) i i i 0 (4d) i (3) (4b) sig mi w (4g) = -SAU -SAU Shima AUS SAU (7) SAU FSAU F m SAU V V V V SAU V mi ( g) ( g) V V g ( ) g g maxmi 0 max 0 0 mi.0 V m m m m ~ N T v w H N 0 0 T x y z (5a) (5b) (5) (5d) (5e) (5f) (5g) (5h) (5i) (5)
3 第 46 回流体力学講演会 / 第 3 回航空宇宙数値シミュレーション技術シンポジウム論文集 0 ~ 0 0 P SAU P P sig 4 (5) 3 O( ) 3 O() - SAU 3 (5) -e (4a)(5a) -SAU -e SAU (8) 3 (5) -SAU -SAU P P ~ 0 0 SAU (7) P P 0 0 -SAU.4 (5) -SAU - SAU -SAU -SAU Vref -AUS + - i AUS + - (6) AUS + - SAU P 0 P 0 P P if therwise ~ 0 0 ~ SAU P P F SAU (5) (5l) (6) P P (7a) P P 0 0 (7b) AUS m m m m ~ N T v w H N 0 0 T x y z (8a) (8b) if 0 m AUS therwise (8) (8d) ~ ~ 4 8 K max 0 f K=0.5 =.0 K=0.75 = fa= (8m) ~ 5 AUS O 6 (8) O K 4 3 -AUS + - -SAU 3 a mi ~ * * max max ~ * H * V * V if therwise max mi w (4a) mi=0. =0 (8e) (8f) (8g) (8h) f a (8i) 6 f a (8) mi max (8) ~ V V AUS P P f V V (8l) (8m) K P P a (8) ~ AUS P P sig mi w (4g) (9)
4 0 宇宙航空研究開発機構特別資料 JAXA-SP-4-00 = = /3 USC (7) limiter 4 ge- Ktta Dble Shear ayer E-Sh (8) Ishi (9) (shear layer) [0 ] [0 ] 8 x=y=/8 v U tah x y U tah x y six U =.0 = /5 =0.05 Ishi (9) =.0 = /( ) = (/) 0.5 = / = U/ t=.e-3cf0.3t=.e-4 CF0.4 ge-ktta t= Very Fie e t=.e-3; CF0.93 -SAU SAU -AUS + - (=0.) AUS + - (=0.) -e e = =3 -AUS + - AUS + - =0=0. -SAU SAU -AUS + - (=0.) AUS + - (=0.) =0. =0. (8) 3 O() -e e O() 3 x = v 3 3d 5 Cmte- Bellte (30) t*=4 t*=98 rms (JAXA)0459 y 3 y y y (0a) (0b) (a) (b) 0.m/s =6 0-4 (3) 4 4a Kieti Eergy Preservig (KEP) e AUS + - SAU SAU AUS + - = e 4b -e -SAU -SAU KEP SAU -ee -SAU =0. -e =0. =0.5 AUS -SAU -AUS + - AUS e (-e) -SAU 0.0 -AUS e SAU JAXA JAXA JAXA ) avrilis D.J. et al.: Grid Qality ad eslti Isses frm the Drag Prediti Wrsh Series J. Airraft Vl. 46 N. 3 (009) ) Bret V. ad De S.: Zal-Detahed Eddy Simlati f Trasi Bffet a Civil Airraft Tye Cfigrati AIAA ) De S.: Zal-Detahed Eddy Simlati f the Flw ard a High-ift Cfigrati AIAA J. vl. 43 N ) Wag Z.J.: A Qadtree-based Adative Cartesia/Qad Grid Flw Slver fr Navier-Stes Eqatis Cmters ad Flids Vl ) H. Siegel S. ad her.: Hybrid Grid Geerati ethd fr Cmlex Gemetries AIAA J. Vl.48 (00) di:0.54/.j ) Kidr Y. r-yssef Y. ad evy Y.: bst Cartesia Grid Flw Slver fr High-eylds-Nmber Trblet Flw Simlatis AIAA J. Vl.48 (00) ) Hashimt A. raami K. Ayama T. Ishi K. Hishida. Saashita. ad ahr P.: Tward the Fastest Ustrtred CFD Cde 'FaSTA' AIAA ) Kitamra K. Fimt K. Shima E. Kz K. ad
5 第 46 回流体力学講演会 / 第 3 回航空宇宙数値シミュレーション技術シンポジウム論文集 03 Wag Z.J.: Validati f a Arbitrary Ustrtred CFD Cde fr Aerdyami Aalyses Tras. JSASS Vl.53 N ) avrilis D.J.: evisitig the east-sqares Predre fr Gradiet estrti Ustrtred eshes AIAA Paer ) Par J.S. Y S.H. ad Kim C.: lti-dimesial imitig Press fr Hyerbli Cservati aws Ustrtred Grids J. Cmt. Phys. Vl. 9 (00) ) Veatarisha V.: Cvergee t Steady State Sltis f the Eler Eqatis Ustrtred Grids with imiters J. Cmt. Phys. Vl ) ihala C. ad Ollivier-Gh C.: Aray Preservig imiter fr the High-rder Arate Slti f the Eler Eqatis J. Cmt. Phys. Vl. 8 (009) ) Kitamra K. ad Shima E.: Simle ad Parameter-Free Sed Sle imiter fr Ustrtred Grid Aerdyami Simlatis AIAA J. Vl. 50 N ) Wiler C.. Drgay A.J. ad ai.: A eded Dissiati Arah fr Usteady Flws Ustrtred Grids AIAA ) e P..: Arximate iema Slvers Parameter Vetrs ad Differee Shemes J. Cmt. Phys. Vl ) i.s.: A Seqel t AUS Part II: AUS + - fr All Seeds J. Cmt. Phys. Vl ) Shima E. ad Kitamra K.: Parameter-Free Simle w- Dissiati AUS-Family Sheme fr All Seeds AIAA J. Vl.49 N ) Kitamra K. ad Shima E.: Twards sh-stable ad arate hyersi heatig mtatis: A ew ressre flx fr AUS-family shemes J. Cmt. Phys. Vl ) Padlfi. ad D Ambrsi D.: Nmerial Istabilities i Uwid ethds: Aalysis ad Cres fr the Carble Pheme J. Cmt. Phys. Vl. 66 N ) Kitamra K. e P. ad Ismail F.: Evalati f Eler Flxes fr Hyersi Flw Cmtatis AIAA J. Vl. 47 N ) i.s. Chag C.H. Ngye. ad Thefas T.G.: Hw t Slve Cmressible ltiflid Eqatis - A Simle bst ad Arate ethd AIAA J. Vl. 46 N ) Kitamra K. Shima E. Fimt K. ad Wag Z.J.: Perfrmae f w-dissiati Eler Flxes ad Preditied U-SGS at w Seeds Cmmi. i Cmt. Phys. Vl.0 N ) Taallir N. Owlam B.B. ad Parashivi.: Selfadative widig fr large eddy simlati f trblet flws strtred elemets. J. Airraft 46(3): ) 7 C ) ) hamed K. Nadaraah S. ad Parashivi.: Detahed-eddy simlati f a wig ti vrtex at dyami stall ditis. J. Airraft 46(4): ) Va eer B.: Twards the Ultimate Cservative Differee Sheme. V. A Sed-Order Seqel t Gdv s ethd J. Cmt. Phys. Vl a) -SAU b) SAU ) -AUS + - (=0.) d) AUS + -(=0.) e) -e f) e Fig. Vrtiity trs at t=8 f =0.0 dble shear layer ases (a) SAU (b) SAU () -AUS + - (=0.) (d) AUS + - (=0.) (e) -e (f) e.
6 04 宇宙航空研究開発機構特別資料 JAXA-SP ) E W. ad Sh C.W.: A Nmerial eslti Stdy f High Order Essetially N-sillatry Shemes Alied t Imressible Flw J. Cmt. Phys. Vl. 0 (994) ) Ishi K. Ohishi N. ad Sawada K.: Imliit ES fr Tw-Dimesial Trblee Usig Sh Catrig te Sheme AIAA ) Cmte-Bellt G. ad Crrsi S.: Simle Eleria Time Crrelati f Fll- ad Narrw-bad Velity Sigal i a) b) Grid-Geerated Istri Trblee J. Flid eh ) / 46 3 A b) d) ) ) d) Fig. 3 Velity v rfiles alg x = at t=8 f =0.0 dble shear layer ases (a) shemes (b) shemes (lse-) () - SAU (d) -AUS + -. a) b) Fig. 4 Istri trblee reslts
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