Geodesic
A scheme for detonation wave computation on moving meshes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2260-2282 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method for computing detonation waves on moving meshes is described. The detonation process is simulated by solving two-dimensional gas dynamics equations and a chemical reaction equation written in integral form. The numerical method is based on a Godunov-type scheme of second-order accuracy in time and space. The burning zone is resolved by applying adaptive mesh refinement. At every instant of time, the mesh is constructed by minimizing a Dirichlet functional. Numerical results are presented for the one-dimensional Chapman–Jouguet detonation and for unstable overdriven detonation in one and two space dimensions. 
@article{ZVMMF_2005_45_12_a13,
     author = {B. N. Azarenok},
     title = {A scheme for detonation wave computation on moving meshes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2260--2282},
     year = {2005},
     volume = {45},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a13/}
}
TY  - JOUR
AU  - B. N. Azarenok
TI  - A scheme for detonation wave computation on moving meshes
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 2260
EP  - 2282
VL  - 45
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a13/
LA  - ru
ID  - ZVMMF_2005_45_12_a13
ER  - 
%0 Journal Article
%A B. N. Azarenok
%T A scheme for detonation wave computation on moving meshes
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 2260-2282
%V 45
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a13/
%G ru
%F ZVMMF_2005_45_12_a13
B. N. Azarenok. A scheme for detonation wave computation on moving meshes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2260-2282. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a13/

[1] Cherkashin V. A., Chislennoe modelirovanie detonatsionnykh voln, IPMatem. RAN, M., 1974

[2] Godunov S. K., Zabrodin A. V., Ivanov M. Ya. i dr., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[3] Chorin A. J., “Random choice solution of hyperbolic systems”, J. Comput. Phys., 22 (1976), 517–531 | DOI | MR

[4] Deryugin Yu. N., Kopyshev V. P., Proshin M. M., Tikhomirov B. P., “K raschetu detonatsii po modeli Forest Fire metodom Godunova”, Vopr. at. nauki i tekhn., 1, M., 1990, 48–52

[5] Bourlioux A., Majda A. J., Roytburd V., “Theoretical and numerical structure for unstable one-dimensional detonations”, SIAM J. Appl. Math., 51:2 (1991), 303–343 | DOI | MR | Zbl

[6] Colella P., Majda A. J., Roytburd V., “Theoretical and numerical structure for reacting shock waves”, SIAM J. Sci. Statist. Comput., 7 (1986), 1059–1080 | DOI | MR | Zbl

[7] Hwang P., Fedkiw R., Merriman B. et al., “Numerical resolution of pulsating detonation waves”, Combustion Theory and Modeling, 4:3 (2000), 217–240 | DOI | Zbl

[8] Pember R. B., “Numerical methods for hyperbolic conservation laws with stiff relaxation. I: Spurious solutions”, SIAM J. Appl. Math., 53 (1993), 1293–1330 | DOI | MR | Zbl

[9] Quirk J. J., “Godunov-type schemes applied to detonation flows”, Combustion in High-Speed Flows, Kluwer, Dordrecht, 1994, 575–596

[10] Ton V. T., “Improved shock-capturing methods for multicomponent and reacting flows”, J. Comput. Phys., 128 (1996), 237–253 | DOI | MR | Zbl

[11] Oran E., Boris J. P., Numerical simulation of reactive flow, Elsevier, New York, 1987 | Zbl

[12] Azarenok B. H., Ob odnoi realizatsii skhemy S. K. Godunova vysokogo poryadka approksimatsii, VTs RAN, M., 1997

[13] Azarenok B. N., Ivanenko S. A., “O primenenii adaptivnykh setok dlya chislennogo resheniya nestatsionarnykh zadach gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 40:9 (2000), 1386–1407 | MR | Zbl

[14] Liseikin V. D., “Postroenie strukturirovannykh setok na $n$-mernykh poverkhnostyakh”, Zh. vychisl. matem. i matem. fiz., 31:11 (1991), 1670–1683 | MR

[15] Ivanenko S. A., Adaptivno-garmonicheskie steki, VTs RAN, M., 1997

[16] Ivanenko S. A., Charakhchyan A. A., “Krivolineinye setki iz vypuklykh chetyrekhugolnikov”, Zh. vychisl. matem. i matem. fiz., 28:4 (1988), 503–514 | MR

[17] Ivanenko S. A., “Upravlenie formoi yacheek v protsesse postroeniya setki”, Zh. vychisl. matem. i matem. fiz., 40:11 (2000), 1662–1684 | MR | Zbl

[18] Azarenok B. N., “O primenenii variatsionnogo barernogo metoda v giperbolicheskikh zadachakh gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 43:7 (2003), 1072–1095 | MR | Zbl

[19] Zeldovich Ya. B., Kompaneets A. S., Teoriya detonatsii, Gostekhizdat, M., 1955

[20] van Leer B., “Towards the ultimate conservative difference scheme. V: A second order sequel to Godunov's methods”, J. Comput. Phys., 32 (1979), 101–136 | DOI

[21] Godunov C. K., Vospominaniya o raznostnykh skhemakh, Nauchn. kniga, Novosibirsk, 1997

[22] Ben-Artzi M., “The generalized Riemann problem for reactive flows”, J. Comput. Phys., 81 (1989), 70–101 | DOI | MR | Zbl

[23] Erpenbeck J. J., “Stability of idealized one-reaction detonations”, Phys. Fluids, 7 (1964), 684–696 | DOI | Zbl

[24] Lee H. I., Stewart D. S., “Calculation of linear detonation instability: one-dimensional instability of plane detonation”, J. Fluid Mech., 216 (1990), 103–132 | DOI | Zbl

[25] Fickett W., Wood W. W., “Flow calculations for pulsating one-dimensional detonations”, Phys. Fluids, 9 (1966), 903–916 | DOI

[26] Papalexandris M. V., Leonard A., Dimotakis P. E., “Unsplit schemes for hyperbolic conservation laws with source terms in one space dimension”, J. Comput. Phys., 134 (1997), 31–61 | DOI | MR | Zbl

[27] Fickett W., Davis W. C., Detonation, Univ. of California Press, Berkeley, CA, 1979

[28] Bourlioux A., Majda A. J., “Theoretical and numerical structure for unstable two-dimensional detonations”, Combustion and Flame, 90 (1992), 211–229 | DOI

[29] Azarenok B. N., Tang T., Second-order Godunov-type scheme for reactive flow calculations on moving meshes, Report, http://www.math.ntnu.no/conservation/2003/043.html