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1. Accurate deterministic projection methods for stiff detonation waves

   https://doi.org/10.4310/CMS.2024.v22.n4.a1  

   Chertock, Alina; Chu, Shaoshuai; Kurganov, Alexander (January 2024, Communications in Mathematical Sciences)

   We study numerical approximations of the reactive Euler equations of gas dynamics. In addition to shock, contact and rarefaction waves, these equations admit detonation waves appearing at the interface between different fractions of the reacting species. It is well-known that in order to resolve the reaction zone numerically, one has to take both space and time stepsizes to be proportional to the reaction time, which may cause the numerical method to become very computationally expensive or even impractical when the reaction is fast. Therefore, it is necessary to develop underresolved numerical methods, which are capable of accurately predicting locations of the detonation waves without resolving their detailed structure. One can distinguish between two different degrees of stiffness. In the stiff case, the reaction time is very small, while in the extremely stiff case, the reaction is assumed to occur instantaneously. In [A. Kurganov, in Hyperbolic problems: theory, numerics, applications, Springer, Berlin, 2003], we proposed a simple underresolved method—an accurate deterministic projection (ADP) method—for one-dimensional hyperbolic systems with stiff source terms including the reactive Euler equations in the extremely stiff regime. In this paper, we extend the ADP method to the (non-extremely) stiff case, multispecies detonation models, and the two-dimensional reactive Euler equations in all of the aforementioned regimes. We also investigate ways to distinguish between different regimes in practice as well as study the limitations of the proposed ADP methods with respect to the ignition temperature. We demonstrate the accuracy and robustness of the ADP methods in a number of numerical experiments with both relatively low and large ignition temperature, and illustrate the difficulties one may face when the ignition temperature is low. 

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2. Signatures of bimodality in nebular phase Type Ia supernova spectra

   https://doi.org/10.1093/mnras/staa003  

   Vallely, P J; Tucker, M A; Shappee, B J; Brown, J S; Stanek, K Z; Kochanek, C S (March 2020, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT One observational prediction for Type Ia supernovae (SNe Ia) explosions produced through white dwarf–white dwarf collisions is the presence of bimodal velocity distributions for the 56Ni decay products, although this signature can also be produced by an off-centre ignition in a delayed detonation explosion. These bimodal velocity distributions can manifest as double-peaked or flat-topped spectral features in late-time spectroscopic observations for favourable viewing angles. We present nebular-phase spectroscopic observations of 17 SNe Ia obtained with the Large Binocular Telescope. Combining these observations with an extensive search of publicly available archival data, we collect a total sample of 48 SNe Ia and classify them based on whether they show compelling evidence for bimodal velocity profiles in three features associated with 56Ni decay products: the [Fe ii] and [Fe iii] feature at ∼5300 Å, the [Co iii] λ5891 feature, and the [Co iii] and [Fe ii] feature at ∼6600 Å. We identify nine bimodal SNe in our sample, and we find that these SNe have average peak MV about 0.3 mag fainter than those that do not. This is consistent with theoretical predictions for explosions created by nearly head-on collisions of white dwarfs due to viewing angle effects and 56Ni yields. 

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3. Local 2D Simulations of the Ignition of a Helium Shell Detonation on a White Dwarf by an Impacting Stream

   https://doi.org/10.3847/1538-4357/ada034  

   Rajavel, Nethra; Townsley, Dean_M; Shen, Ken_J (January 2025, The Astrophysical Journal)

   Abstract The double detonation model is one of the prevalent explosion mechanisms of Type Ia supernovae (SNe Ia) wherein an outer helium shell detonation triggers a core detonation in the white dwarf (WD). The dynamically driven double degenerate double detonation (D⁶) is the double detonation of the more massive WD in a binary WD system where the localized impact of the mass transfer stream from the companion sets off the initial helium shell detonation. To have high numerical resolution and control over the stream parameters, we have implemented a study of the local interaction of the stream with the WD surface in 2D. In cases with lower base density of the shell, the stream's impact can cause surface detonation soon after first impact. With higher base densities, after the stream hits the surface, hot material flows around the star and interacts with the incoming stream to produce a denser and narrower impact. Our results therefore show that (1) a directly impacting stream for both a relatively high resolution and for a range of stream parameters can produce a surface detonation, (2) thinner helium shells ignite more promptly via impact, doing so sooner, and (3) there are lower limits on ignition in both shell density and incoming stream speed with lower limits on density being well below those shown by other work to be required for normal appearing SN Ia. This supports stream ignition and therefore the D⁶scenario, as a viable mechanism for normal SNe Ia. 

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4. Recent results on stability of planar detonations.

   Zumbrun, K (January 2017, Shocks, singularities and oscillations in nonlinear optics and fluid mechanics)

   We describe recent analytical and numerical results on stability and behavior of viscous and inviscid detonation waves obtained by dynamical systems/Evans function techniques like those used to study shock and reaction diffusion waves. In the first part, we give a broad description of viscous and inviscid results for 1D perturbations; in the second, we focus on inviscid high-frequency stability in multi-D and associated questions in turning point theory/WKB expansion. 

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5. Multi-scale modeling of shock initiation of a pressed energetic material III: Effect of Arrhenius chemical kinetic rates on macro-scale shock sensitivity

   https://doi.org/10.1063/5.0187735  

   Parepalli, P; Nguyen, Yen T; Sen, O; Hardin, D B; Molek, C D; Welle, E J; Udaykumar, H S (February 2024, Journal of Applied Physics)

   Multi-scale predictive models for the shock sensitivity of energetic materials connect energy localization (“hotspots”) in the microstructure to macro-scale detonation phenomena. Calculations of hotspot ignition and growth rely on models for chemical reaction rates expressed in Arrhenius forms; these chemical kinetic models, therefore, are foundational to the construction of physics-based, simulation-derived meso-informed closure (reactive burn) models. However, even for commonly used energetic materials (e.g., HMX in this paper) there are a wide variety of reaction rate models available. These available reaction rate models produce reaction time scales that vary by several orders of magnitude. From a multi-scale modeling standpoint, it is important to determine which model best represents the reactive response of the material. In this paper, we examine three global Arrhenius-form rate models that span the range of reaction time scales, namely, the Tarver 3-equation, the Henson 1-equation, and the Menikoff 1-equation models. They are employed in a meso-informed ignition and growth model which allows for connecting meso-scale hotspot dynamics to macro-scale shock-to-detonation transition. The ability of the three reaction models to reproduce experimentally observed sensitivity is assessed by comparing the predicted criticality envelope (Walker–Wasley curve) with experimental data for pressed HMX Class V microstructures. The results provide a guideline for model developers on the plausible range of time-to-ignition that are produced by physically correct Arrhenius rate models for HMX. 

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