Geodesic
The $P_1$ and $P_2$ approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 9, pp. 1692-1703
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The spherical harmonics method in the $P_1$ and $P_2$ approximations is used to analyze radiative heat transfer for a space vehicle entering a planet's atmosphere. Strong blowing of ablated materials from the vehicle surface is taken into account by using a two-layer flow model without allowance for the viscosity and thermal conduction of the gas. The heating and ablation of a multilayered thermal protection system are determined simultaneously with the vehicle's flight trajectory, which is calculated taking into account the mass loss due to the ablation. The approach is illustrated by computing the flight of a space vehicle shaped as a spherical segment or a spherically blunted cone entering the Jovian atmosphere at a speed of 60 km/s and an entry angle of $-5^\circ$. 
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V. M. Borisov; A. A. Ivankov. The $P_1$ and $P_2$ approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 9, pp. 1692-1703. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_9_a11/

[1] Apshtein E. Z., Pilyugin H. H., Sevast'yanenko V. G., Tirskii G. A., “Radiatsionnyi teploobmen pri vkhode tel v atmosferu Zemli i planet so sverkhorbitalnymi skorostyami”, Itogi nauki i tekhn. VINITI. Ser. Mekhan. zhidkosti i gaza, 23, 1989, 116–236

[2] Anfimov H. A., Rumynskii A. N., “Luchisto-konvektivnyi teploobmen i teplozaschita kosmicheskikh apparatov, spuskaemykh na poverkhnost Zemli i drugikh planet Solnechnoi sistemy”, Probl. mekhan. i teploobmena v kosmich. tekhn., Mashinostr., M., 1982, 54–81

[3] Rumynskii A. N., Churkin V. P., “Obtekanie zatuplennykh tel giperzvukovym potokom vyazkogo izluchayuschego gaza”, Zh. vychisl. matem. i matem. fiz., 14:6 (1974), 1553–1570

[4] Stulov V. P., Mirskii V. N., Vislyi A. I., Aerodinamika bolidov, Fizmatlit, M., 1995

[5] Belotserkovskii O. M., Fomin V. N., “Obtekanie i radiatsionnyi nagrev zatuplennykh tel, dvizhuschikhsya pod uglami ataki $\alpha\ge0^\circ$”, Probl. mekhan. i teploobmena v kosmich. tekhn., Mashinostr., M, 1982, 26–36

[6] Belotserkovskii O. M., Golomazov M. M., Shabalin A. B., “Issledovanie vliyaniya silnogo vduva gaza s poverkhnosti na giperzvukovoe obtekanie zatuplennykh tel”, Zh. vychisl. matem. i matem. fiz., 21:4 (1981), 1018–1030

[7] Golomazov M. M., Shabalin A. B., “Giperzvukovoe obtekanie isparyayuschikhsya tel pod uglami ataki”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1984, no. 1, 132–137

[8] Gershbein E. A., Sukhodolskaya E. Ya., Sukhodolskii S. L., Tirskii G. A., “O dvizhenii tel v atmosfere Yupitera s uchetom izmeneniya ikh massy i formy pod deistviem aerodinamicheskogo nagreva”, Kosmich. issl., 16:3 (1978), 378–387

[9] Gilinskii S. M., Telenin G. F., Tinyakov G. P., “Metod rascheta sverkhzvukovogo obtekaniya zatuplennykh tel s otoshedshei udarnoi volnoi”, Izv. AN SSSR. Mekhan. i mashinostr., 1964, no. 4, 9–28

[10] Golomazov M. M., Zyuzin A. P., “Ob odnom chislennom metode rascheta prostranstvennogo obtekaniya zatuplennykh tel s otoshedshei udarnoi volnoi”, Zh. vychisl. matem. i matem. fiz., 15:5 (1975), 1349–1355 | Zbl

[11] Pilyugin H. H., Tirskii G. A., Dinamika ionizovannogo izluchayuschego gaza, Izd-vo MGU, M., 1989 | Zbl

[12] Borisov V. M., Ivankov A. A., “Raschet perenosa luchistoi energii pri giperzvukovom obtekanii zatuplennykh tel s ispolzovaniem $P_1$ i $P_2$-priblizhenii metoda sfericheskikh garmonik”, Zh. vychisl. matem. i matem. fiz., 32:6 (1992), 952–966 | MR | Zbl

[13] Borisov V. M., Ivankov A. A., “Raschet radiatsionnykh teplovykh potokov s uchetom silnogo vduva pri vkhode kosmicheskikh apparatov v atmosferu Venery”, Zh. vychisl. matem. i matem. fiz., 45:6 (2005), 1081–1091 | MR | Zbl

[14] Ivankov A. A., “Ob odnom metode rascheta silnogo vduva s poverkhnosti zatuplennykh tel pri giperbolicheskikh skorostyakh vkhoda v atmosfery planet”, Izv. RAN. Mekhan. zhidkosti i gaza, 2006, no. 1, 149–159

[15] Ivankov A. A., “O chislennom reshenii zadachi progreva mnogosloinoi teplozaschity spuskaemogo apparata s uchetom unosa massy vneshnikh i vnutrennikh sloev pokrytiya”, Zh. vychisl. matem. i matem. fiz., 45:7 (2005), 1279–1288 | MR | Zbl

[16] Chetverushkin B. N., Matematicheskoe modelirovanie zadach dinamiki izluchayuschego gaza, Nauka, M., 1985 | Zbl

[17] V. I. Moroz (red.), Rabochaya model atmosfery i okoloplanetnogo prostranstva Yupitera, Preprint, IKI AN SSSR, M., 1976

[18] Baula G. G., Markelova T. V., Nikolaev V. N. i dr., Model izlucheniya vysokotemperaturnykh gazovykh ob'emov dlya rascheta teploobmena letatelnykh apparatov, RD 50-25645.114-84. Metod, ukazaniya, Izd-vo standartov, M., 1984

[19] Polezhaev Yu. V., Yurevich F. B., Teplovaya zaschita, Energiya, M., 1976

[20] Borisov V. M., “K postanovke zadach gazodinamiki s uchetom teplovogo izlucheniya”, Matem. modelirovanie aerotermokhim. yavlenii, VTs AN SSSR, M., 1974, 40–60

[21] Sivukhin D. V., Optika, Nauka, M., 1985