Incorrect propagation speed of discontinuities may occur by straightforward application of standard dissipative schemes for problems that contain stiff source terms for underresolved grids even for time steps within the CFL condition. By examining the dissipative discretized counterpart of the Euler equations for a detonation problem that consists of a single reaction, detailed analysis on the spurious wave pattern is presented employing the fractional step method, which utilizes the Strang splitting. With the help of physical arguments, a threshold values method (TVM), which can be extended to more complicated stiff problems, is developed to eliminate the wrong shock speed phenomena. Several single reaction detonations as well as multispecies and multi-reaction detonation test cases with strong stiffness are examined to illustrate the performance of the TVM approach.

Development of a detonation wave due to α heating following short pulse laser irradiation in pre-compressed deuterium–tritium (DT) plasma is considered. The laser parameters required for development of a detonation wave are calculated. We find that a laser irradiance and energy of IL = 1.75 × 1023 W/cm2 and 12.8 kJ accordingly during 1.0 ps in a pre-compressed target at 900 g/cm3 creates an α heating fusion detonation wave. In this case, the nuclear fusion ignition conditions for the pre-compressed DT plasma are achieved along the detonation wave orbit.

The high order inverse Lax-Wendroff (ILW) procedure is extended to boundary treatment involving complex geometries on a Cartesian mesh. Our method ensures that the numerical resolution at the vicinity of the boundary and the inner domain keeps the fifth order accuracy for the system of the reactive Euler equations with the two-step reaction model. Shock wave propagation in a tube with an array of rectangular grooves is first numerically simulated by combining a fifth order weighted essentially non-oscillatory (WENO) scheme and the ILW boundary treatment. Compared with the experimental results, the ILW treatment accurately captures the evolution of shock wave during the interactions of the shock waves with the complex obstacles. Excellent agreement between our numerical results and the experimental ones further demonstrates the reliability and accuracy of the ILW treatment. Compared with the immersed boundary method (IBM), it is clear that the influence on pressure peaks in the reflected zone is obviously bigger than that in the diffracted zone. Furthermore, we also simulate the propagation process of detonation wave in a tube with three different widths of wall-mounted rectangular obstacles located on the lower wall. It is shown that the shock pressure along a horizontal line near the rectangular obstacles gradually decreases, and the detonation cellular size become large and irregular with the decrease of the obstacle width.

In this paper, we extend the high order finite-difference method with subcell resolution (SR) in [34] for two-species stiff one-reaction models to multispecies and multireaction inviscid chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.

Numerical simulation based on the Euler equation and one-step reaction model is carried out to investigate the process of deflagration to detonation transition (DDT) occurring in a straight duct. The numerical method used includes a high resolution fifth-order weighted essentially non-oscillatory (WENO) scheme for spatial discretization, coupled with a third order total variation diminishing Runge-Kutta time stepping method. In particular, effect of energy release on the DDT process is studied. The model parameters used are the heat release at q = 50,30,25,20,15,10 and 5, the specific heat ratio at 1.2, and the activation temperature at Ti = 15, respectively. For all the cases, the initial energy in the spark is about the same compared to the detonation energy at the Chapman-Jouguet (CJ) state. It is found from the simulation that the DDT occurrence strongly depends on the magnitude of the energy release. The run-up distance of DDT occurrence decreases with the increase of the energy release for q = 50 ~ 20, and increases with the increase of the energy release for q = 20 ~ 5. This phenomenon is found to be in agreement with the analysis of mathematical stability theory. It is suggested that the factors to strengthen the DDT would make the detonation more stable, and vice versa. Finally, it is concluded from the simulations that the interaction of the shock wave and the flame front is the main reason for leading to DDT.

An improved method of space-time conservation element and solution element (CE/SE) is developed to solve the equations of conservation laws in fluid dynamics. The present method substantially differs in both concept and methodology from the traditional CE/SE method. In this paper the improved second-order CE/SE method is presented in a hexahedral grid. Furthermore, the present CE/SE method was successfully applied to solve the interaction problem of shock waves and detonation. Several numerical examples were also given. Numerical results have compared with the results of experiments and other computational methods. The compared results have shown a good agreement. The improved CE/SE method has higher accuracy and becomes a more prospective scheme.

Ce travail fait suite à l'étude théorique de la réponse d'un système plaque-liquide infini, soumis à un champ de pression uniforme se déplaçant avec une vitesse constante [J. Renard, A. Langlet, O. Pennetier, Response of a large plate-liquid system to a moving pressure step. Transient and stationary aspects, J. Sound and Vibration 265 (2003) 699–724].Dans la première partie de cet article, après avoir rappelé les équations du problème, on applique la méthode numérique établie dans la référence précédente pour calculer la réponse dynamique couplée au champ de pression créé par une détonation.Dans la deuxième partie, on présente le montage expérimental grâce auquel la mesure des déformations sur une plaque reposant sur de l'eau permet de caractériser la réponse dynamique du système à une détonation.L'objectif principal de cet article est de montrer que la modélisation du couplage fluide-structure qui a été effectuée, décrit convenablement la réponse observée, en particulier les ondes accompagnant le front de chargement.

Notre travail est consacré à l'étude de la diffraction de la détonation dans des mélanges acétylène/oxygène stoechiométriques dilués par l'argon (50 %; 66,7 % et 81 % en fraction molaire), d'un tube dans un cône. Les expériences ont été menées dans un tube de diamètre intérieur de 52 mm connecté à une chambre via des divergents coniques de demi angle variant de 15° à 90°. L'histoire de la transition a été enregistrée sur des plaques recouvertes de noir de carbone, ce qui nous a permis de déterminer les conditions critiques de transmission de la détonation et de décrire les phénomènes impliqués en fonction de l'angle de divergence et de la dilution en argon. Des résultats de simulations numériques bidimensionnelles axisymétriques sont présentés et discutés. Si les tendances expérimentales ont été reproduites, il est apparu qu'un accord quantitatif ne peut être obtenu en utilisant une réaction globale exothermique. Des calculs préliminaires ont été menés avec une loi de libération de l'énergie chimique en deux étapes exothermiques successives. Nos premiers résultats sont en accord qualitatif avec les observations expérimentales relatives à la double structure cellulaire de la détonation des systèmes réactifs où l'énergie est libérée conformément au modèle utilisé dans ces simulations, modèle qui pourrait s'avérer utile dans le cas des mélanges étudiés ici.