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.. Structured-grid, 31 II.2 Reconstruction of g in cells i ? 1, i, and i + 1 at first and second order accuracy 32 II.3 Illustration of an AP scheme [71, 33 II.4 Right part of the Riemann problem . . . . . . . . . . . . . . . . . . . . . . . . . 37

.. , T. .. , .. Bgk, E. Bgk, and E. , 49 III.3 Characteristics for the reflection of a rarefaction wave and a shock wave 51 III.4 Velocity error for the reflection of a rarefaction wave and a shock wave 51 III.5 Density solution for the oblique shock with bilinear interpolation (21×21) . . . . 52 III.6 Density solution for the oblique shock with bilinear interpolation (81×81) 53 III.7 Density solution for the oblique shock with bicubic interpolation (21×21) 53 III.8 Density for the oblique shock with the present method (21×21) 54 III.10 Zoom on post-shock values for the 55 III.11 Oblique shock solution for the 55 III.12 Comparison of the specular and Euler-AP conditions for 56 III.13 Zoom on post-shock values for the 56 III.14 Temperature error in L 1 norm for two different velocity grids 57 III.15 Density solution with the Euler-AP method and map of the error 58 III.17 Computational time with respect to the number of velocity grid points . . . . . 59 III.18 Pressure solution and error map for the density, III.1 Immersed interface on a Cartesian mesh 47 III.2 Graphic 54 III.9 Comparison of the specular and Euler-AP conditions for the p 60 III.20 L 1 and L ? norm of the pressure error for the ringleb flow . . . . . . . . . . . . 62 III.21 Steady state solution and error for the Couette flow. . . . . . . . . . . . . . . . . 62 III.22 Horizontal velocity and streamlines for, p.64

T. Bgk and E. , 65 III.25 Mach number and velocity vectors at t=1.2 for P c /P atm = 66 III.26 Mach number and velocity vectors at t=5 for P c /P atm = 66 III.27 Mach number and velocity vectors at t=11 for P c /P atm =, III.24 Computational domain at 66 III.28 Mach number and velocity vectors at steady state for P c, p.67, 2000.

.. Strong-scalability, 73 IV.5 Representation of velocity-space cells in phase space in 1D 75 IV.6 Test case 1: Normalized Maxwellian distribution functions 77 IV.7 Test case 1, Kn ? = 10 ?5 : Density and temperature solution 78 IV.8 Test case 1, Kn ? = 10 ?5 : local grids for ? = 6 (first criteria) 79 IV.9 Test case 1, Kn ? = 10 ?5 : local grids for ? = 6 (both criteria) error on density, velocity and energy, 80 IV.11 Test case 1, Kn ? = 10 ?5 : L ? error on density, velocity and energy . . . . . . . 80 IV.12 Test case 1, Kn ? = 10 ?5 : Conservation error . . . . . . . . . . . . . . . . . . . 81 IV.13 Test case 1, Kn ? = 10 ?5 : Normalized number of velocity grid points used and computational time with respect to the global grid calculation, p.81

I. Of-kn and ?. , 16 Test case 1: Computational time and total number of velocity grid points used for different values, p.82

1. Apollo-capsule, 95 V.3 Steady state solution for different capsule forms and positions of the center of mass, p.98

.. La-discrétisation-en-temps, 157 III Condition au bord préservant la limite asymptotique sur grilles cartésiennes, p.158

I. Optimisation-du-temps-de-calcul and .. , 159 IV.1 Parallélisation, 161 V.1 L'´ equation de transport de particules . . . . . . . . . . . . . . . . . . . . 162 V

V. Figure, Nombre de Mach et vecteurs vitesse pour P c /P atm =, 200000.

E. Il-modello, 170 II Schemi numerici per i modelli cinetici

I. Una-particolarità-dei-flussi-complessì-e-la-presenza-di-due-tipi-di-regimi, il regime idrodinamico e il regime rarefatto. Troviamo questo tipo di coesistenza nelle pompe a vuoto oppure nel caso di rientro ipersonico di un veicolo in atmosfera, Il regime rarefattò e caratterizzato da una importante distanza tra le molecole di gas rispetto alla dimensione caratteristica del problema

. Nel-caso-di-dispositivi-microscopici, anche se la densità di molecole nonènonè bassa (e quindi la distanza media tra le molecolè e piccola), il regimepù o essere definito rarefatto a causa della ridotta lunghezza caratteristica del problema In questi casi, il comportamento microscopico delle molecole di gaspù o essere diverso dal comportamento medio del flusso (macroscopico) Se la distanza tra le molecole diventa molto piccola, il regimè e chiamato idrodinamico

. In-un-contesto-industriale, la realizzazione di esperimenti in condizione reali, come il rientro di capsule in atmosfera, diventa difficile a causa delle basse pressioni e delle alte velocità che devono