Non-oscillatory shock-capturing finite element methods for the one-dimensional compressible Euler equations

1990 ◽  
Vol 11 (4) ◽  
pp. 405-426 ◽  
Author(s):  
J. Y. Yang ◽  
Fue-Sang Lien ◽  
Chang-An Hsu
Keyword(s):  
Finite Element ◽  
Euler Equations ◽  
Finite Element Methods ◽  
Shock Capturing ◽  
Compressible Euler Equations ◽  
One Dimensional ◽  
Compressible Euler ◽  
The One

scholarly journals The role of multidimensional instabilities in direct initiation of gaseous detonations in free space

2017 ◽  
Vol 813 ◽  
Author(s):  
Hua Shen ◽  
Matteo Parsani
Keyword(s):  
Euler Equations ◽  
Chemical Reaction ◽  
Critical Energy ◽  
Combustible Mixture ◽  
Compressible Euler Equations ◽  
Two Dimensional ◽  
One Dimensional ◽  
Direct Initiation ◽  
Compressible Euler ◽  
The One

We numerically investigate the direct initiation of detonations driven by the propagation of a blast wave into a unconfined gaseous combustible mixture to study the role played by multidimensional instabilities in direct initiation of stable and unstable detonations. To this end, we first model the dynamics of unsteady propagation of detonation using the one-dimensional compressible Euler equations with a one-step chemical reaction model and cylindrical geometrical source terms. Subsequently, we use two-dimensional compressible Euler equations with just the chemical reaction source term to directly model cylindrical detonations. The one-dimensional results suggest that there are three regimes in the direct initiation for stable detonations, that the critical energy for mildly unstable detonations is not unique, and that highly unstable detonations are not self-sustainable. These phenomena agree well with one-dimensional theories and computations available in the literature. However, our two-dimensional results indicate that one-dimensional approaches are valid only for stable detonations. In mildly and highly unstable detonations, one-dimensional approaches break down because they cannot take the effects and interactions of multidimensional instabilities into account. In fact, instabilities generated in multidimensional settings yield the formation of strong transverse waves that, on one hand, increase the risk of failure of the detonation and, on the other hand, lead to the initiation of local over-driven detonations that enhance the overall self-sustainability of the global process. The competition between these two possible outcomes plays an important role in the direct initiation of detonations.

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