3D numerical simulation of MHD flows in semidetached binary systems

A. G. Zhilkin

Matematičeskoe modelirovanie, Tome 22 (2010) no. 1, pp. 110-124.

Résumé

3D numerical code for simulation of MHD flows in semidetached binary systems is developed. The code is based on finite-difference Godunov-type scheme for equations of magnetohydrodynamics in non-stationary curvilinear coordinates. The scheme has high resolution in regions of smoothness. The own magnetic field of accretor is considered as a dipole. To minimize errors for operations with large float numbers the only magnetic field induced by currents in accretion disk and circumbinary envelope is calculated in the scheme. Any demonstrative results of numerical simulation of mass transfer process in semidetached binary systems with tacking into account the magnetic field of accretor are presented.

Bibliographie

[1] Warner B., Cataclysmic variable stars, Cambridge Univ. Press, Cambridge, 1995

[2] Lipunov V. M., Astrofizika neitronnykh zvezd, Nauka, M., 1987, 296 pp.

[3] Bisikalo D. V., Boyarchuk A. A., Kuznetsov O. A., Chechetkin V. M., “Vliyanie vyazkosti na morfologiyu techeniya veschestva v polurazdelennykh dvoinykh sistemakh. Rezultaty trekhmernogo chislennogo modelirovaniya”, Astronomicheskii zhurnal, 77 (2000), 31–41

[4] Bisikalo D. V., Boyarchuk A. A., Kaigorodov P. V., Kuznetsov O. A., “Morfologiya vzaimodeistviya strui i kholodnogo akkretsionnogo diska v polurazdelennykh dvoinykh sistemakh”, Astronomicheskii zhurnal, 80 (2003), 879–890

[5] Bisikalo D. V., Boyarchuk A. A., Kaigorodov P. V., Kuznetsov O. A., “Struktura kholodnogo akkretsionnogo diska v polurazdelennykh dvoinykh sistemakh”, Astronomicheskii zhurnal, 81 (2004), 494–502

[6] Bisikalo D. V., Kaigorodov P. V., Boyarchuk A. A., Kuznetsov O. A., “O vozmozhenoi prirode provalov na krivoi bleska polurazdelennykh dvoinykh sistem so statsionarnymi diskami”, Astronomicheskii zhurnal, 82 (2005), 701–708

[7] Koldoba A. V., Romanova M. M., Ustyugova G. V., Lovelace R. V. E., “Three-dimensional magnetohydrodynamic simulations of accretion to an inclined rotator: the “cubed-sphere” method”, Astrophys. J., 576 (2002), L53–L56 | DOI

[8] Romanova M. M., Ustyugova G. V., Koldoba A. V., Wick J. V., Lovelace R. V. E., “Three-dimensional magnetohydrodynamic simulations of accretion to an inclined dipole. I. Magnetospheric flows at different $\Theta$”, Astrophys. J., 595 (2003), 1009–1031 | DOI

[9] Cox D. P., Daltabuit E., “Radiative cooling of a low-density plasma”, Astrophys. J., 167 (1971), 113 | DOI

[10] Dalgarno A., McCray R. A., “Heating and ionization of HI regions”, Annual Review of Astronomy and Astrophysics, 10 (1972), 375–426 | DOI

[11] Raymond J. C., Cox D. P., Smith B. W., “Radiative cooling of a low-density plasma”, Astrophys. J., 204 (1976), 290–292 | DOI

[12] Spittser L., Fizicheskie protsessy v mezhzvezdnoi srede, Mir, M., 1981

[13] Powell K. G., Roe P. L., Linde T. J., Gombosi T. I., De Zeeuw D. L., “A solution-adaptive upwind scheme for ideal magnetohydrodynamics”, J. Comp. Phys., 154 (1999), 284–309 | DOI | MR | Zbl

[14] Dellar P. J., “A note on magnetic monopoles and the one-dimensional MHD Riemann problem”, J. Comp. Phys., 172 (2001), 392–398 | DOI | MR | Zbl

[15] Tanaka T., “Finite volume TVD scheme on an unstructured grid system for three-dimensional MHD simulations of inhomogeneuos systems including strong background potential field”, J. Comp. Phys., 111 (1994), 381–389 | DOI | Zbl

[16] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001, 608 pp. | MR

[17] Hui W. H., Li P. Y., Li Z. W., “A unified coordinate system for solving the two-dimensional Euler equations”, J. Comput. Phys., 153 (1999), 596–637 | DOI | MR | Zbl

[18] Hui W. H., Kudriakov S., “A unified coordinate system for solving the three-dimensional Euler equations”, J. Comput. Phys., 172 (2001), 235–260 | DOI | MR | Zbl

[19] Zhilkin A. G., “Ob odnom sposobe dinamicheskoi adaptatsii raschetnykh setok k zadacham magnitnoi gidrodinamiki”, ZhVMiMF, 47 (2007), 1898–1912 | MR

[20] Chakravarthy S. R., Osher S., “A new class of high accuracy TVD schemes for hyperbolic conservation laws”, AIAA Papers, 1985, No 85-0363

[21] Dudorov A. E., Zhilkin A. G., Kuznetsov O. A., “Kvazimonotonnaya raznostnaya skhema povyshennogo poryadka tochnosti dlya uravnenii magnitnoi gidrodinamiki”, Matematicheskoe modelirovanie, 11:1 (1999), 101–116 | MR

[22] Lax P. D., “Weak solutions of nonlinear hyperbolic equations and their numerical computation”, Comm. Pure Appl. Math., 7:1 (1954), 159–193 | DOI | MR | Zbl

[23] Zhilkin A. G., “Ispolzovanie integrirovannykh adaptivnykh setok dlya chislennogo modelirovaniya mnogomernykh MGD techenii na kompyuterakh s parallelnoi arkhitekturoi”, Trudy Mezhdunarodnoi nauchnoi konferentsii Parallelnye vychislitelnye tekhnologii (PAVT-2007), t. 1, YuUrGU, Chelyabinsk, 2007, 256–268

[24] Giovannelli F., Gaudenzi S., Rossi C., Piccioni A., “Orbital parameters of SS Cygni”, Acta Astronomica, 33:2 (1983), 319–330 | MR

[25] Zhilkin A. G., Bisikalo D. V., “Gazodinamicheskaya struktura techeniya v sisteme SS Cyg”, Trudy Vserossiiskoi astronomicheskoi konferentsii VAK-2007, Kazan, 2007, 268–270

[26] Sytov A. Yu., Kaigorodov P. V., Bisikalo D. V., Kuznetsov O. A., Boyarchuk A. A., “Mekhanizm obrazovaniya obschei obolochki v tesnykh dvoinykh sistemakh”, Astronomicheskii zhurnal, 84 (2007), 926–936

[27] Bisikalo D. V., Kononov D. A., Kaigorodov P. V., Zhilkin A. G., Boyarchuk A. A., “Struktura techeniya veschestva v sisteme SS Cyg v spokoinom sostoyanii po rezultatam sravneniya nablyudaemykh i sinteticheskikh doplerovskikh tomogramm”, Astronomicheskii zhurnal, 85 (2008), 356–365

[28] Fabbiano G., Hartmann L., Raymond J., Steiner J., Branduardi-Raymont G., Matilsky T., “Coordinated $X$-ray, ultraviolet and optical observations of AM Herculis, U Geminorum and SS Cygni”, Astrophys. J., 243 (1981), 911 | DOI

[29] Kjurkchieva D., Marchev D., Ogloza W., “High-speed BVRI photometry of SS Cyg at quiscence and at outburst”, Astrophysics and Space Science, 262 (1999), 53–74 | DOI

[30] Sawada K., Matsuda T., Hachisu I., “Spiral shocks on a Roche lobe overflow in a semi-detached binary system”, Monthly Notices Roy. Astron. Soc., 219 (1986), 75–88