1D Lagrangian Gas Dynamics. g t
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1 Te KT Dfferece Sceme for Te KT Dfferece Sceme for D Laraa Gas Damcs t 0 t t 0
2 Dfferece Sceme for D Dfferece Sceme for D Laraa Gas Damcs 0 t m 0 / / F F t t 0 / / F F t 0 / F F t
3 Dfferece Sceme for D Dfferece Sceme for D Laraa Gas Damcs / / / / / c F / / / / / / / c F c F
4 Dfferece Sceme for D Dfferece Sceme for D Laraa Gas Damcs / D D / / D D / D / / / / D D / /
5 Dfferece Sceme for D Laraa Gas Damcs V D D D m mod, m mod, 3/ / / / / m mod,
6 A test roblem for te laraa dfferece sceme te et fve sldes te reslts of a test roblem mercal model are reseted Te tal codtos are: te frst reo dest 4, secfc teral eer 0.5, veloct ; te secod reo dest, secfc teral eer e-6, veloct 0. Bodar codtos: te left bodar sto wt veloct, te rt oe rd wall. Te lots reset dest ad veloct for 0 sccessve tmes.
7 dest veloct
8 dest veloct
9 dest veloct
10 dest veloct
11 dest veloct
12 Nmercal Reslts Dscsso Te mercal reslts sow, tat te sceme as erted ts ood qalt from te ler aret KT sceme Te smootess s mmal eve after more, ta 0 soc reflectos te mber of ot at te soc s ot more te fve Some etro traces are reseted d at tte bodares ad at te lace, were tall te soc as bee located
13 Te teral terface treatmet KT sceme allows to cosder teral matter terfaces O te et slde oe ca see te reslts of D soc roblem treatmet Te soc moves tro artfcal terface, all matter arameters at te rt sde of terface are eqal to te left matter oes. Te dfferece s ol te left- ad rt- cells volmes
14 Soc wave roblem. Blac dest, ree veloct.
15 Te teral terface treatmet Te reslts of calclato, reseted at te revos slde, sow tat etro traces cold aear te resece of te matter terface O te ators ot of vew a secal at- etro vscost sold be costrcted to dam ts o-mootoct
16 Dfferece Sceme for Mltdmesoal rrelar Grd Te mltdmesoal Voroo rd s sed To obta sceme for mlt-dmesoal case oe sold reformlate oral D KT sceme to mae eeralzato more obvos see te et sldes
17 Varato for eeralzato for mltdmesoal rrelar rd. V V F F / / / / V V F F / / / / V
18 Flow Calclatos.5 0 / F.5 0 / F V T C l l a Vscos Term Calclatos D D a V D D a V / / / / / D a V D D V / / / / D V
19 MMod Calclatos 3, MMod D 3, MMod D 3,, MMod MMod D
20 laato of Some Detals of te Mltdmesoal Sceme, Preseted o te Net Slde. s a set of mbers of cells, wc are ebor cells to te -t oe D, D are te reslts of mmod rocedre aled to te radets commo case s oes, calclated l d te Delae trales, cld -t ot Dr s a reslt of mmod oerato aled dto te corresod lalacas, calclated te ebor ots
21 Laraa KT Sceme for l G d rrelar Grd t 0 c t D D l D D l c t Dr r r t l r r c r
22 Laraa KT Sceme for l G d rrelar Grd Gradet of fctos: e crc crc S R S R 3, 3,, 3 e crc S R, , S 3 3 l bd f d R 3, 3,4 crc R crcmscrbed crcle rads of R crc 4,
23 Laraa KT Sceme for MMod calclatos: rrelar Grd D m mod D, D D Dr m mod r r, D 0, f, : s m mod{ } m{ } s m mod{ } m mod, m mod s
24 Laraa KT Sceme for l G d V rrelar Grd V Coordates: D D l c l c
25 Laraa KT Sceme for l G d V rrelar Grd V Veloctes: D D D D l c v D D D D v l c
26 er: Laraa KT Sceme for v rrelar Grd V c D D D D l were ;, Dr D D ; v, D ; D D, D D D, D, D ;
27 A test roblem for te mltdmesoal rrelar rd D case te et slde reslts of a test roblem mercal model are reseted. Te tal codtos are: te frst reo dest 4, secfc teral eer 0.5, veloct ; te secod reo dest, secfc teral eer e-6, veloct 0. Bodar codtos: te left bodar sto t wt veloct, te rt oe rd wall.
28 D Soc Wave for D rrelar Grd. Dest. Ro=4, U= Ro=, U=0 t=0.000 t=0.4 t=0.855 t=.609 t=.43 t=3.09 t=3.887
29 RT stablt. Ro=4 ={0, -00} Ro= Materal Dest
30 RT stablt. t=0.440 t=0.90 t=.00
31 RT stablt. Ro=4 ={0, -00} Ro= Materal Dest
32 RT stablt V. t=0.436 t=0.89 t=.645
33 RT stablt V. rrelar Grd
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