Although the Discontinuous Galerkin (dg) method has seen widespread use for compressible flow problems in a single fluid with constant material properties, it has yet to be implemented in a consistent fashion for compressible multiphase flows with shocks and interfaces. Specifically, it is challenging to design a scheme that meets the following requirements: conservation, highorder accuracy in smooth regions and non-oscillatory behavior at discontinuities (in particular, material interfaces). Following the interface-capturing approach of Abgrall [1], we model flows of multiple fluid components or phases using a single equation of state with variable material properties; discontinuities in these properties correspond to interfaces. To represent compressible phenomena in solids, liquids, and gases, we present our analysis for equations of state belonging to the Mie-Grüneisen family. Within the dg framework, we propose a conservative, high-order accurate, and non-oscillatory limiting procedure, verified with simple multifluid and multiphase problems. We show analytically that two key elements are required to prevent spurious pressure oscillations at interfaces and maintain conservation: (i) the transport equation(s) describing the material properties must be solved in a non-conservative weak form, and (ii) the suitable variables must be limited (density, momentum, pressure, and appropriate properties entering the equation of state), coupled with a consistent reconstruction of the energy. Further, we introduce a physics-based discontinuity sensor to apply limiting in a solution-adaptive fashion. We verify this approach with one-and two-dimensional problems with shocks and interfaces, including high pressure and density ratios, for fluids obeying different equations of state to illustrate the robustness and versatility of the method. The algorithm is implemented on parallel graphics processing units (gpu) to achieve high speedup.

Conventional compression-ignition (CI) engines have long offered high thermal efficiencies and torque across a wide range of loads, but often require extensive exhaust gas treatment that decreases efficiency to meet ever-increasing emissions regulations. One strategy to decrease emissions is to split the fuel injection into a series of smaller injections. In this paper, we explore a new way of discovering optimal control strategies for the next generation of CI engines using deep reinforcement learning (DRL). We outline a DRL procedure to maximize the weighted reward of engine work while minimizing end-of-cycle NO x emissions. Through the procedure outlined in this paper, we show that the DRL agent is able to reduce NO x emissions threefold while only decreasing network by 2%. We demonstrate the use of transfer learning (TL) across hierarchies of physical models to accelerate the learning process, making this approach feasible for a range of control problems within this space. This paper presents a framework and demonstration for using DRL to design control systems in technology areas such as multi-pulse engine control where a hierarchy of models combined with multi-objective rewards are used for optimal operation.

In this work, we investigate the growth of interface perturbations following the interaction of a shock wave with successive layers of fluids. Using the Discontinuous Galerkin method, we solve the two-dimensional multifluid Euler equations. In our setup, a shock impacts up to four adjacent fluids with perturbed interfaces. At each interface, the incoming shock generates reflected and transmitted shocks and rarefactions, which further interact with the interfaces. By monitoring perturbation growth, we characterize the influence these instabilities have on each other and the fluid mixing as a function of time in different configurations. If the third gas is lighter than the second, the reflected rarefaction at the second interface amplifies the growth at the first interface. If the third gas is heavier, the reflected shock decreases the growth and tends to reverse the Richtmyer-Meshkov instability as the thickness of the second gas is increased. We further investigate the effect of the reflected waves on the dynamics of the small scales and show how a phase difference between the perturbations or an additional fluid layer can enhance growth. This study supports the idea that shocks and rarefactions can be used to control the instability growth.

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In this work, we examine the hydrodynamics of high-energy-density (HED) shear flows. Experiments, consisting of two materials of differing density, use the OMEGA-60 laser to drive a blast wave at a pressure of ∼50 Mbar into one of the media, creating a shear flow in the resulting shocked system. The interface between the two materials is Kelvin-Helmholtz unstable, and a mixing layer of growing width develops due to the shear. To theoretically analyze the instability's behavior, we rely on two sources of information. First, the interface spectrum is well-characterized, which allows us to identify how the shock front and the subsequent shear in the post-shock flow interact with the interface. These observations provide direct evidence that vortex merger dominates the evolution of the interface structure. Second, simulations calibrated to the experiment allow us to estimate the time-dependent evolution of the deposition of vorticity at the interface. The overall result is that we are able to choose a hydrodynamic model for the system, and consequently examine how well the flow in this HED system corresponds to a classical hydrodynamic description.

In this work, we use machine learning (ML) techniques to develop presumed probability density function (PDF) models for large eddy simulations of reacting flows. The joint sub-filter PDF of mixture fraction and progress variable is modeled using various ML algorithms and commonly used analytical models. The ML algorithms evaluated in the work are representative of three major classes of ML techniques: traditional ensemble methods (random forests), deep learning (deep neural networks), and generative learning (conditional variational autoencoder (CVAE)). The first two algorithms are supervised learning algorithms, and the third is an unsupervised learning algorithm. Data from direct numerical simulation of the low-swirl burner [1] are used to develop training data for sub-filter PDF models. Models are evaluated on predictions of the sub-filter PDFs as well as predictions of the filtered reaction rate of the progress variable, computed through an integral of the product of the sub-filter PDF and the conditional means of the reaction rate. This a-priori modeling study demonstrates that deep learning models for presumed PDF modeling are * Corresponding author Email addresses: marc.henrydefrahan@nrel.gov (M. T. Henry de Frahan), ray.grout@nrel.gov (R. W. Grout) three times more accurate than analytical β-β PDF models and linear regression models. These models are as accurate as random forest models while using five times fewer trainable parameters and being 25 times faster for inference. In this work, conditional unsupervised learning did not present additional advantages beyond supervised learning with a feed-forward neural network. We illustrate how models generalize to other regions of the flow and develop criteria based on the Jensen-Shannon divergence to quantify the performance of a model on new data.

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