Abstract
We describe a mechanism which can cause crossflow instabilities in the approximation of multidimensional detonation waves. Crossflow instabilities can grow if a discontinuity is nearly aligned with the mesh and if the velocity transverse to the discontinuity is close to zero. When these conditions are met a continuous perturbation of the constant state transverse to the discontinuity can cause the crossflow instability to grow. In both the reactive and the nonreactive case such a continuous perturbation can be caused by oscillations which arise behind the discontinuity. In the nonreactive case these oscillations are a numerical artifact of the scheme, whereas in the reactive case the oscillations reflect a physical instability inherent in the problem. We suggest a fix which avoids the crossflow instability without limiting the oscillatory wave structure, which can arise behind detonation waves.
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Bale, D.S., Helzel, C. (2001). Crossflow Instabilities in the Approximation of Detonation Waves. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 140. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8370-2_13
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DOI: https://doi.org/10.1007/978-3-0348-8370-2_13
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-8370-2
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