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Standing detonation engines are a promising detonation-based propulsion technology. The most commonly studied standing detonation configuration involves a straight-sided wedge that induces an oblique detonation wave. A recently introduced standing-detonation-engine concept entails a curved ramp that leads to formation of a curved detonation wave. The continuous compression or expansion induced by the ramp curvature can have significant influence on the flow characteristics and wave patterns of the detonation wave, offering greater flexibility in engine design than conventional wedge geometries. This study aims to further explore this relatively new standing-detonation-engine concept by examining the effect of ignition promoters, namely ozone, on the flow characteristics and reflection patterns of curved detonation waves induced by convex or concave ramps inside a confined combustion chamber. Simulations are performed using a positivity-preserving and entropy-bounded discontinuous Galerkin method with curved elements to exactly represent the ramp geometries. In the context of wedge-induced oblique detonation waves, ozone addition has been found to decrease the initiation length and lead to a smoother shock-detonation transition. This can then attenuate the detonation and reduce stagnation-pressure losses, thus improving the potential propulsion performance. In the context of detonation waves induced by curved ramps, although ozone addition similarly shortens the initiation zone, the curvature of the ramp introduces additional effects that can amplify or counteract both the ozone-induced contraction of the initiation zone and the aforementioned detonation attenuation. Furthermore, specific examples are presented wherein ozone addition changes the type of reflection pattern (e.g., regular reflection, stationary Mach reflection, and non-stationary Mach reflection).

This paper presents a conservative discontinuous Galerkin method for the simulation of supercritical and transcritical real-fluid flows without phase separation. A well-known issue associated with the use of fully conservative schemes is the generation of spurious pressure oscillations at contact interfaces, which are exacerbated when a cubic equation of state and thermodynamic relations appropriate for this high-pressure flow regime are considered. To reduce these pressure oscillations, which can otherwise lead to solver divergence in the absence of additional dissipation, an L2-projection of primitive variables is performed in the evaluation of the flux. We apply the discontinuous Galerkin formulation to a variety of test cases. The first case is the advection of a sinusoidal density wave, which is used to verify the convergence of the scheme. The next two involve one- and two-dimensional advection of a nitrogen/n-dodecane thermal bubble, in which the ability of the methodology to reduce pressure oscillations and maintain solution stability is assessed. The final test cases consist of two- and three-dimensional injection of an n-dodecane jet into a nitrogen chamber.

A well-known issue associated with the use of fully conservative schemes in multicomponent-flow simulations is the generation of spurious pressure oscillations at contact interfaces. These oscillations can rapidly lead to solver divergence even in the presence of smooth interfaces that are not fully resolved. In this note, we compare various strategies for reducing such oscillations that do not (a) introduce conservation error, (b) rely on artificial viscosity or limiting, or (c) degrade order of accuracy in smooth regions of the flow. The considered test case is one-dimensional advection of a high-pressure nitrogen/n-dodecane thermal bubble using the thermally perfect gas model. Several results are presented that contradict those corresponding to the more conventional hydrogen/oxygen thermal-bubble case.

This article concerns the development of a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for the multicomponent, chemically reacting, compressible Navier-Stokes equations with complex thermodynamics. In particular, we extend to viscous flows the fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin method for the chemically reacting Euler equations that we previously introduced. An important component of the formulation is the positivity-preserving Lax-Friedrichs-type viscous flux function devised by Zhang [J. Comput. Phys., 328 (2017), pp. 301-343], which was adapted to multicomponent flows by Du and Yang [J. Comput. Phys., 469 (2022), pp. 111548] in a manner that treats the inviscid and viscous fluxes as a single flux. Here, we similarly extend the aforementioned flux function to multicomponent flows but separate the inviscid and viscous fluxes, resulting in a different dissipation coefficient. This separation of the fluxes allows for use of other inviscid flux functions, as well as enforcement of entropy boundedness on only the convective contribution to the evolved state, as motivated by physical and mathematical principles. We also detail how to account for boundary conditions and incorporate previously developed techniques to reduce spurious pressure oscillations into the positivity-preserving framework. Furthermore, potential issues associated with the Lax-Friedrichs-type viscous flux function in the case of zero species concentrations are discussed and addressed. The resulting formulation is compatible with curved, multidimensional elements and general quadrature rules with positive weights. A variety of multicomponent, viscous flows is computed, ranging from a one-dimensional shock tube problem to multidimensional detonation waves and shock/mixing-layer interaction.

We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems -- that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid systems framework, we propose a hybrid estimation algorithm that can operate during both flows and jumps that, under a notion of hybrid persistence of excitation, guarantees convergence of the parameter estimate to the true value. Furthermore, we show that the parameter estimate is input-to-state stable with respect to a class of hybrid disturbances. Simulation results including a spacecraft application show the merits of our proposed approach.

In this second part of our two-part paper, we extend to multiple spatial dimensions the one-dimensional, fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme developed in the first part for the chemically reacting Euler equations. Our primary objective is to enable robust and accurate solutions to complex reacting-flow problems using the high-order discontinuous Galerkin method without requiring extremely high resolution. Variable thermodynamics and detailed chemistry are considered. Our multidimensional framework can be regarded as a further generalization of similar positivity-preserving and/or entropy-bounded discontinuous Galerkin schemes in the literature. In particular, the proposed formulation is compatible with curved elements of arbitrary shape, a variety of numerical flux functions, general quadrature rules with positive weights, and mixtures of thermally perfect gases. Preservation of pressure equilibrium between adjacent elements, especially crucial in simulations of multicomponent flows, is discussed. Complex detonation waves in two and three dimensions are accurately computed using high-order polynomials. Enforcement of an entropy bound, as opposed to solely the positivity property, is found to significantly improve stability. Mass, total energy, and atomic elements are shown to be discretely conserved.

In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for simulating the chemically reacting, compressible Euler equations with complex thermodynamics. The proposed formulation is an extension of the conservative, high-order numerical method previously developed by Johnson and Kercher [J. Comput. Phys., 423 (2020), 109826] that maintains pressure equilibrium between adjacent elements. In this first part of our two-part paper, we focus on the one-dimensional case. Our methodology is rooted in the minimum entropy principle satisfied by entropy solutions to the multicomponent, compressible Euler equations, which was proved by Gouasmi et al. [ESAIM: Math. Model. Numer. Anal., 54 (2020), 373--389] for nonreacting flows. We first show that the minimum entropy principle holds in the reacting case as well. Next, we introduce the ingredients required for the solution to have nonnegative species concentrations, positive density, positive pressure, and bounded entropy. We also discuss how to retain the aforementioned ability to preserve pressure equilibrium between elements. Operator splitting is employed to handle stiff chemical reactions. To guarantee satisfaction of the minimum entropy principle in the reaction step, we develop an entropy-stable discontinuous Galerkin method based on diagonal-norm summation-by-parts operators for solving ordinary differential equations. The developed formulation is used to compute canonical one-dimensional test cases, namely thermal-bubble advection, multicomponent shock-tube flow, and a moving hydrogen-oxygen detonation wave with detailed chemistry. We find that the enforcement of an entropy bound can considerably reduce the large-scale nonlinear instabilities that emerge when only the positivity property is enforced, to an even greater extent than in the monocomponent, calorically perfect case.

We present deep Chandra observations of the pre-merger galaxy cluster Abell 98. Abell 98 is a complex merging system. While the northern (A98N) and central subclusters (A98S) are merging along the north-south direction, A98S is undergoing a separate late-stage merger, with two distinct X-ray cores. We report detection of gas sloshing spirals in A98N and in the eastern core of A98S. We detect two cold front edges in A98N. We find two more surface brightness edges along the east direction of the eastern core and west direction of the western core of A98S. We measure the temperatures and gas densities across those edges, and find that the eastern edge appears to be a cold front while the western edge is a shock front with a Mach number of $\cal{M}$ $\approx$ 1.5. We detect a "tail" of X-ray emission associated with the eastern core of A98S. Our measurement indicates that the tail is cooler than the surrounding gas at a 4.2-$\sigma$ level, suggesting the tail is part of a cool core remnant that has been ram-pressure stripped., Comment: Submitted to The Astrophysical Journal

We report the first unambiguous detection of an axial merger shock in the early-stage merging cluster Abell 98 using deep (227 ks) Chandra observations. The shock is about 420 kpc south from the northern subcluster of Abell 98, in between the northern and central subclusters, with a Mach number of M $\approx$ 2.3 $\pm$ 0.3. Our discovery of the axial merger shock front unveils a critical epoch in the formation of a massive galaxy cluster, when two subclusters are caught in the early phase of the merging process. We find that the electron temperature in the post-shock region favors the instant collisionless model, where electrons are strongly heated at the shock front, by interactions with the magnetic field. We also report on the detection of an intercluster gas filament, with a temperature of kT = 1.07 $\pm$ 0.29 keV, along the merger axis of Abell 98. The measured properties of the gas in the filament are consistent with previous observations and numerical simulations of the hottest, densest parts of the warm-hot intergalactic medium (WHIM), where WHIM filaments interface with the virialization regions of galaxy clusters., Comment: Accepted for publication in The Astrophysical Journal Letters

We present a detailed description and verification of a discontinuous Galerkin finite element method (DG) for the multi-component chemically reacting compressible Navier-Stokes equations that retains the desirable properties of DG, namely discrete conservation and high-order accuracy in smooth regions of the flow. Pressure equilibrium between adjacent elements is maintained through the consistent evaluation of the thermodynamics model and the resulting weak form, as well as the proper choice of nodal basis. As such, the discretization does not generate unphysical pressure oscillations in smooth regions of the flow or at material interfaces where the temperature is continuous. Additionally, we present an hp-adaptive DG method for solving systems of ordinary differential equations, DGODE, which is used to resolve the temporal evolution of the species concentrations due to stiff chemical reactions. The coupled solver is applied to several challenging test problems including multi-component shocked flows as well as chemically reacting detonations, deflagrations, and shear flows with detailed kinetics. We demonstrate that the discretization does not produce unphysical pressure oscillations and, when applicable, we verify that it maintains discrete conservation. The solver is also shown to reproduce the expected temperature and species profiles throughout a detonation as well as the expected two-dimensional cellular detonation structure. We also demonstrate that the solver can produce accurate, high-order, approximations of temperature and species profiles without artificial stabilization for the case of a one-dimensional pre-mixed flame. Finally, high-order solutions of two- and three-dimensional multi-component chemically reacting shear flows, computed without any additional stabilization, are presented., Comment: Direct expansion of arXiv:1910.10544 Replacement: fixes bad figure reference