NXO a Spatially High Order Finite Volume Numerical Method for Compressible Flows

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1 NXO Spty Hgh Ode Fnte Voume Nume Method fo Compebe Fow Jen-Me e Gouez One CFD Deptment Fouth HO CFD Wohop Heon June 4th

2 B of the NXO heme Eue o Nve-Stoe fo pefet g w of tte dof pe e nd pe equton Voume vege wde ten Coe pttonng of the gd : one ptton pe node hed memoy hybd pogmmng MPI / OpenMP o Cud Poynom eontuton gothm fo the onevtve vbe o fux denty fed Pepoeo phe : Weghted et-sque poynom degee dpt to the quty of the ten Gve the ntepoton oeffent of onevtve vbe fed fom voume vege to ufe vege Fo the Eue fuxe : e-enteed ten n ed ep. geen fo the ded eontuton poeton on one of the fe of th e ufe nteg of the poynom Fo the dffuve fuxe : Tget ntefe Intefe-enteed ten unon ed-geen Poeton of the gdent of the poynom Sme poynom eontuton ued fo the oveet gd poeton method NextFow : Spty Hgh-Ode Fnte Voume method fo ANS / ES Fouth HO CFD Wohop Heon June 4th

3 Addeng the gothm effeny be : uy veu numbe of dof Hghft Peue NextFow : Spty Hgh-Ode Fnte Voume method fo ANS / ES oe pttonng wde ho Fouth HO CFD Wohop Heon June 4th

4 Ptpton to the HO Wohop - Chengng the DG? Wohop Wohop 2 Wohop 3 mn / DNS Tyo-Geen Votex omputed on egu gd of teted Untedy mn : du o tme teppng Hevng N2 n the untedy we of ynde omputton of the fequeny o-n of the votex heddng Gd nd ode onvegene fo the oveet gd e Eue Ientop votex tnpot ght fgue eut mpoved eenty by ung the fux eontuton method Compon n the ondton of the HO wohop : 50 t Untey mn Hevng nd pthng n2 t eynod numbe 000 nd 5000 demontton of the gd onvegene fo both e modete omputton ot Eue Hgh ode geomety ngeb Fow wth nove fomuton of the method on Fnte Voume of H.O. geomety. Convegene dffute on the fnet gd but good eut n the oe one even wth ow ount of dof ute C-BC on uved w Wohop 3 Untey mn B3 Hevng nd pthng N2 3 dffeent moton of the wng Gd / tme tep / poynom ode onvegene to be onfmed modete omputton ot Fouth HO CFD Wohop Heon June 4th

5 HO Wohop 4 : Ce B3 Enegy exttng Gd nd ode onvegene fo the oveet gd e Compon n the ondton of the Nme HO / wohop dt ode : 50 Cot t Ndof/ Y- Wo extent TBu eqn Mometum Gd / 60 2./ Gd2 / 60 2./ Gd3 / 60 2./ Gd4 / 60 2./ Gd / 60 2./ Gd / 60 2./ Gd / 60 2./ Fouth HO CFD Wohop Heon June 4th

6 Hgh Ode CFD Wohop Ce 3.5 Tyo-Geen Votex Compon of tme devtve of entophy nd ed Dpton of net enegy Ouene of n out phenomenon Hgh Ode CFD Wohop Nhve Jn. 202

7 GPU mpementton of the NextFow ove Pefomne on eh K20Xm GPU : n 3 8e-8 pe HS 0.36 fo e n 4 25e-8 pe HS 0.50 fo e Tyo-Geen Votex ey 600 Computton on wedge Tyo Geen votex 256**3 - w-o 2 hou on 6 IVY-Bdge poeo tot 28 oe : 600 hou CPU Inte oe 25 mnute on 6 Te K20M GPU By ompon t the t HO CFD wohop th e equeted between 00 nd Inte oe Cpu hou dependng on the nume method. Tyo Geen votex 52**3 - w-o : 4 hou on 6 Te K20M GPU 7 GTC 206 Ap 7th Sn Joé Cfon

8 H.O. Fu 3D Voume to fe ntepoton : eontuton nd poeton XY C { } Y X Y X 2 Ω Ω n dv Y X ϖ ψ { } { } { } { } { } Ω n ϖ ψ Ω dv Y X : Voume moment of ode eontuton eo funton n Sten ze : nb of monom + 50% n λ ˆ n µ ˆ { } { } { } { } { } { } ' ' ' 0 P κ > + Μ / eontuton n eft ten ented on

9 FV NXO method : eontuton nd poeton ˆ ˆ Μ + Α 0 { } { } { ' ' '} { } S S Ω κ X Y ds Ω X Y ds ˆ ˆ { } { } 2/ Poeton on the ntefe ν { } { } { } { } η Ω X Y S ν ds η κ { } { } { } ν { } e X + ν { } e Y + ν { } e { } η { } { } g κ { } { } { } { } g ν C XY λ µ n ˆ λ n ˆ µ

10 FV NXO method : Invd fuxe opton : Voume vege ˆ : ufe vege ˆ : NXO heme n Ω W + S Fˆ Fˆ 0 t n n v n 2 opton fo the nvd fuxe Chtet Upwnd o ented Fˆ F W W W W Upwnd heme : one vege fux evuton fom the eft nd ght extpoted vege onevtve vbe htet pttng tte upwnd Fˆ F F τθ mx W W W W Cented heme : ntepoton of the e-vege fux denty teno n e of the ten to the ntefe + tbzton tem Mn nuy oue : F ˆ F Wˆ Upwnd heme F F W Cented heme

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