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Properties of Detonation Waves
Author(s) -
Tegnér J. K.
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19961110)19:16<1279::aid-mma822>3.0.co;2-n
Subject(s) - detonation , dimensionless quantity , shock wave , mathematics , mechanics , viscosity , computation , shock (circulatory) , classical mechanics , mathematical analysis , physics , explosive material , thermodynamics , chemistry , medicine , organic chemistry , algorithm
The phenomenon of unphysical wave propagation speeds sometimes occurs in numerical computations of detonation waves on coarse grids. The strong detonation wave splits into two parts, a weak detonation which travels with the speed of one cell per time step and an ordinary shock wave. We analyse a simplified set of equations and look for travelling wave solutions. It is shown that the solution depends on the dimensionless number Kr = μ K / Q ρ 1 . Here μ is the viscosity, K is the rate of reaction, Q is the heat release available in the process and ρ 1 is the density at the unburnt state. It is shown that the density peak of the travelling wave depends on Kr and also, that if Kr is sufficiently large there is no travelling wave solution. The erroneous behaviour above is explained as an effect of the artificial viscosity necessarily inherent in the numerical methods when coarse grids are used. To prevent this unphysical behaviour we suggest the use of an ‘artificial rate of reaction’ such that the actual value of Kr used in the numerical method retains its correct physical value.