Approximations décentrées à faible dissipation pour des problèmes hyperboliques
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Approximations de´centre´es a` faible dissipation pour des proble`mes hyperboliques Christophe Debiez. N˚ 2811 Fe´vrier 1996. PROGRAMME 6. ISSN 0249-6399. apport de recherche.
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(68) X ´uUS X 3 _&^ IS#" Iy IX Domaine de validite de la methode de RK6. 4. RK6 3 2. Im. 1 0 -1 -2 -3 -4 -5. -4. -3. -2 Re. -1. 0. 1. z IS´ Uyª" " ´uIy I &e z i& z&#u. `. °²± q°´³.
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(71) E F X E J Comportement du facteur d’amplification. 1.1. Domaine de stabilite de RK6. 4. Nu=1.332 Nu=1.0. 1. "RK6" Nu=1.332 Nu=1.0. 3. 0.9 2. 0.8. 1. 0.6 Im. |G(theta)|. 0.7. 0.5. 0 -1. 0.4 0.3. -2. 0.2 -3. 0.1 0. 0. 1. ©. 2. 3. theta. 4. 5. 6. -4 -5. 7. \. -4. -3. -2 Re. -1. 0. 1. ^ 3 I S(US7 IS#" Uy IXU ¥
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(94) & gXS7 x" Uy ^z (S( ¥ ^ S E F _X E J Solutions exactes et approchees:T=1.,CFL=1.,N=100 - err=0.36202640E-05 1 "uexact" "uapprox" 0.8. Solutions exactes et approchees:T=1.,CFL=1.,N=100 - err=0.94376605E-01 1.2 "uexact" "uapprox" 1. 0.6 0.8. 0.4. 0.6 u(x,t). u(x,t). 0.2 0 -0.2 -0.4. 0.4 0.2. -0.6 0 -0.8 -1. 0. 0.2. p~. . 0.4. x. 0.6. 0.8. -0.2. 1. 0. 0.2. a\. 0.4. x. 0.6. 0.8. 1. ^ X 3 O x" Iy IU S(( &^ i¥
(95) E F E J . Solutions exactes et approchees:T=1.,CFL=1.,N=100 - err=0.75814244E-07 1 "uexact" "uapprox" 0.8. Solutions exactes et approchees:T=1.,CFL=1.,N=100 - err=0.79206840E-01 1.2 "uexact" "uapprox" 1. 0.6 0.8. 0.4. 0.6 u(x,t). u(x,t). 0.2 0 -0.2 -0.4. 0.4 0.2. -0.6 0 -0.8 -1. 0. -0.2. ^ X 3 O IS#" Uy IU S(( &^ ¥ ^\
(96) X W KDPRwuNDIyNQa\_yKDbSpbGcyIySR _yKQZl]^cyaeKGbu_S&uNQ[ cLSp_S c}NQwowuILK^[{z^k0S0_ju]¨wuIyKD¥^Z\£0P5S2j^SRZ: NDj^QSp[&cLa\KDbBj©E ]uF b^S2!NmMG]^S2_LEalbhJ ]u_yK ÂjuNmZ\S*S0c j© ]ub^S¾KDbo[&cLa\KDbj^al_y[ KDbGcLalbh]^SxwoKG]uI j^ae« kpILSpbGcLS0_n!NQZeSp]uIy_ juS0_wuNDIyNDP5£ cyIyS0_Yju]%_O[{z^k0PRNR_yNDbu_ PRNmcOILal[&Sxj^SxPRNQ_O_LS 0.2. 0.4. x. 0.6. 0.8. 1. 0. 0.2. 0.4. x. 0.6. 0.8. . `a`cb*dBefghg. 1.
(97) ~;Distribution de l’erreur en fonction du pas de discretisation spatiale. 0.1. 1. Distribution de l’erreur en fonction du pas de discretisation spatiale. CFL=2.310 CFL=0.5. CFL=2.310 CFL=0.5. Erreur_L2. Erreur_L2. 0.01. 0.001. 0.1. 0.0001. 1e-05 10. . 0 . 100 Nombre de mailles, N. 0.01 10. 1000. 1000.
(98) & gXS7 x" Uy ^z (S( ¥ ^ S E F _X E J . Distribution de l’erreur en fonction du pas de discretisation spatiale. 0.1. \. 100 Nombre de mailles, N. 1. Distribution de l’erreur en fonction du pas de discretisation spatiale. CFL=1.332 CFL=0.5. CFL=1.332 CFL=0.5. 0.01. Erreur_L2. Erreur_L2. 0.001. 0.0001. 0.1. 1e-05. 1e-06. 1e-07 10. p. 100 Nombre de mailles, N. . 0.01 10. 1000. 1000. ^ X 3 O x" Iy IU S(( &^ i¥
(99) E F E J . Distribution de l’erreur en fonction du pas de discretisation spatiale. 0.01. a\. 100 Nombre de mailles, N. 1. Distribution de l’erreur en fonction du pas de discretisation spatiale. CFL=1.867 CFL=0.5. CFL=1.867 CFL=0.5. 0.001. Erreur_L2. Erreur_L2. 0.0001 1e-05 1e-06. 0.1. 1e-07 1e-08 1e-09 10. 0.01 10. 0T ^ X 3 O IS#" Uy IU S(( &^ ¥ ^\
(100) X ª¦W7al_yKcyIya\" ¥u-u]u ^cLa\i KDb(juS5+YZ:wg S0KDIO]uILISp]uZeSxI wuIyKD£ ¥^i`Z\[0£0NmP5Zl[ Sx]^j^Z\k SxSRZ: NDj^QSp [&cyaeFKGp*b S0j©b( ]u¾b^KDSbo[&¾cLKGa\buKD[&b cyaejuKG]Bb_yb^alKDbGP*]o_L¥uK IL¹S5juNQj^ZeSRSUP5S c NQj©aeZ\Z\]uS0_%b^E SFL ¾KGwgbuKD[&]ucyaeIKGb%j^Spj^]ha\E (_OJ [&KG!bGNmZ\cLS0albG]o]uIy_US ju] 100 Nombre de mailles, N. $&%. . . . 1000. 100 Nombre de mailles, N. . `. °²± q°´³. 1000.
(101)
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