Geodesic
The asymptotical combustion modes in wide tubes
Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 15-28.

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The asymptotical combustion modes are considered in 2D tubes of various widths, including non-slip and slip wall boundary conditions. A new operator-splitting scheme was used as the solution method, high resolution minimal stencil explicit scheme for hyperbolic part and implicit scheme for diffusion one, as compared with known articles. An existence of symmetric concave multi-hump flame front was established for the problem with slip walls, which represents an intermediate asymptotics. This mode is unstable and transforms to the stable single-hump structure. A problem of “oscillating front” was computed in the tube with non-slip at the walls and open at both ends. It is shown that an accelerating maximum arises for tube widths of the critical order, which may be evidence of the formation of the detonation combustion mode. 
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D. Yu. Maksimov. The asymptotical combustion modes in wide tubes. Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 15-28. http://geodesic.mathdoc.fr/item/MM_2007_19_10_a1/

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