Application of hugonions for efficient computation of shock and detonation waves

Developed as a numerical device for fast computation of shock hydrodynamics, hugonions have been successfully used for analysis of strong shock waves in non-reacting media [Lee et al., J. Acoust. Soc. Am. 140, 3435 (2016)]. Hugonions are particle-like hydrodynamic discontinuities that travel, interact with one another, and annihilate. In this paper, we demonstrate that the concept of hugonions can be extended to detonation waves in reacting media, in which the chemical reaction of positive thermicity leads to different equations of state ahead and behind the detonation shock. The Chapman-Jouguet (CJ) model of detonation is recast in such a way that the D-discussion remains the same as in the classical CJ theory while the piston problem is solved more efficiently using hugonions. Tested for both non-reacting (the Sod shock tube problem) and reacting (1-D detonation waves) media, the hugonion-based approach is shown to be superior in speed to the existing computational methods such as Godunov’s scheme.