Some mathematical models and numerical methods used by the authors to model two-dimensional flows with detonation waves using high performance computing are described. An efficiency analysis of numerical algorithm parallelization is performed. The results of numerical experiments on the initiation of detonation in complex geometry regions are discussed. The problems in question are important both from the standpoint of fundamental issues of the nature of detonation flows in gas mixtures and from the standpoint of a number of practical applications. The paper was prepared on the basis of the authors' report at the International Conference on Parallel Computing Technologies (PaVT-2008; http://agora.guru.ru/pavt2008).

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