Geodesic
Two approaches to the mathematical modeling of detonation wave
Matematičeskoe modelirovanie, Tome 28 (2016) no. 2, pp. 133-145.

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The work is dedicated to the numerical investigation of different modes of gaseous pulsating detonation wave propagation using two approaches. In the first one the problem is solved in the laboratory frame and the detonation is initiated near the closed end of the channel. In the second approach the modeling is carried out in the shock-attached frame. For this purpose the second approximation order algorithm for the integration of shock evolution equation using gridcharacteristic method is proposed. The stable, weakly unstable and irregular modes of detonation wave propagation are investigation using both approaches. The qualitative and quantitative differences between two approaches are marked out.
Keywords: numerical modeling, detonation wave, grid-characteristic method, shock-attached frame. 
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A. I. Lopato; P. S. Utkin. Two approaches to the mathematical modeling of detonation wave. Matematičeskoe modelirovanie, Tome 28 (2016) no. 2, pp. 133-145. http://geodesic.mathdoc.fr/item/MM_2016_28_2_a11/

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