Existing process-based models for simulating coastal foredune evolution largely use the same analytical approach for estimating wind-induced surface shear stress distributions over spatially variable topography. Originally developed for smooth, low-sloping hills, these analytical models face significant limitations when the topography of interest exhibits large height-to-length ratios and/or steep, localized features. In this work, we utilize computational fluid dynamics (CFD) to examine the error trends of a commonly used analytical shear stress model for a series of idealized two-dimensional dune profiles. It is observed that the prediction error of the analytical model increases compared to the CFD simulations for increasing height-to-length ratio and localized slope values. Furthermore, we explore two data-driven methodologies for generating alternative shear stress prediction models, namely, symbolic regression and linear, projection-based, non-intrusive reduced-order modeling. These alternative modeling strategies demonstrate reduced overall error but still suffer in their generalizability to broader sets of dune profiles outside of the training data. Finally, the impact of these improvements on aeolian sediment transport fluxes is examined to demonstrate that even modest improvements to the shear stress prediction can have significant impacts on dune evolution simulations over engineering-relevant timescales.

Training object detection algorithms to operate in complex geo-environments remains a significant challenge, necessitating large and diverse datasets (i.e., unique backgrounds and conditions) that are not always readily available. Physically generating requisite data can also be both cost and time prohibitive depending on the object(s) and area(s) of interest -- especially in the case of multi-spectral and hyper-spectral imagery. Thus, there is increasing interest in the use of synthetic data to supplement existing physical datasets. To this end, the US Army Engineer Research and Development Center (ERDC) continues to develop a computational test-bed with a tool suite called the VESPA or, the Virtual Environmental Simulation for Physics-based Analysis, to support synthetic multi-spectral and hyper-spectral EO/IR imagery generation. The VESPA consists of integrated (1) scene generation tools, (2) multi-fidelity models for simulating heat and mass transfer and atmospheric energy propagation in geo-environments and climates worldwide that are optimized for high performance computing (3) data interrogation utilities, and (4) component-level sensor models capable of producing AI/ML ready near- and far-field imagery that is comparable to that produced by real sensors. This study presents an overview of the VESPA, new advances/capabilities, and results from a recent detailed validation and verification study.

The increasing deployment of AI in critical sectors necessitates advancements in explainable AI (XAI) to ensure transparency and trustworthiness of AI decisions. This paper introduces a novel methodology that leverages the Virtual Environmental Simulation for Physics-based Analysis (VESPA) framework in conjunction with Randomized Input Sampling for Explanation (RISE) to provide enhanced explainability for AI models, particularly in complex simulated environments. VESPA, known for its high-fidelity, physics-based simulations across diverse conditions, generates a vast dataset encompassing various sensor configurations, environmental factors, and material responses. This dataset serves as the foundation for applying RISE, a model-agnostic approach that generates pixel-level importance maps by probing the AI model with masked versions of the input images. Through this integration, we offer a systematic way to visualize and understand the influence of different environmental elements on AI decisions. Our approach not only sheds light on the "black box" of AI decision-making processes but also provides a scalable framework for evaluating AI models' robustness and reliability under a wide array of simulated scenarios.

Autonomous vehicles (AVs) employ a wide range of sensing modalities including LiDAR, radar, RGB cameras, and more recently infrared (IR) sensors. IR sensors are becoming an increasingly common component of AVs’ sensor packages to provide redundancy and enhanced capabilities in conditions that are adverse for other types of sensors. For example, while RGB cameras are sensitive to lighting conditions and LiDAR performance is degraded in inclement weather such as rain, IR sensors are unaffected by lighting conditions and can contribute additional meaningful information in inclement weather. The US Army Corps of Engineers, Engineer Research and Development Center (ERDC) has developed the ERDC Computational Test Bed (CTB) to provide a suite of tools that can be used to support virtual development and testing of AVs. The CTB includes physics-based vehicle-terrain interaction, sensor and environment modeling, geo-environmental thermal modeling, software-inthe- loop capabilities, and virtual environment generation. Thermal modeling capabilities within the CTB utilize decades of near-surface phenomenology and autonomy research. Recent additions have been made to support large-domains commonly required for autonomous vehicle operations. These additions provide high-fidelity, physics-based thermal transfer and IR sensor models for creating high-quality synthetic imagery simulating IR sensors mounted on AVs. Highly parallelized thermal and IR sensor models for large-domain AV operations will be presented in this paper.

The goal of this study is to leverage emerging machine learning (ML) techniques to develop a framework for the global reconstruction of system variables from potentially scarce and noisy observations and to explore the epistemic uncertainty of these models. This work demonstrates the utility of exploiting the stochasticity of dropout and batch normalization schemes to infer uncertainty estimates of super-resolved field reconstruction from sparse sensor measurements. A Voronoi tessellation strategy is used to obtain a structured-grid representation from sensor observations, thus enabling the use of fully convolutional neural networks (FCNN) for global field estimation. An ensemble-based approach is developed using Monte-Carlo batch normalization (MCBN) and Monte-Carlo dropout (MCD) methods in order to perform approximate Bayesian inference over the neural network parameters, which facilitates the estimation of the epistemic uncertainty of predicted field values. We demonstrate these capabilities through numerical experiments that include sea-surface temperature, soil moisture, and incompressible near-surface flows over a wide range of parameterized flow configurations.

This work considers a uniquely configured swirling motion that develops inside a porous tube due to sidewall injection. The bulk fluid motion is modeled as a steady inviscid Trkalian flow field with a swirl-velocity component that increases linearly along the axis of the chamber. The underlying procedure consists of solving the compressible Bragg–Hawthorne equation using a Rayleigh–Janzen expansion that produces a closed-form approximation for the stream function. Based on the latter, most remaining flow attributes may be readily inferred. Results are then compared to their counterparts obtained using a strictly incompressible Trkalian motion. They are also benchmarked against available compressible solutions in an effort to characterize the dilatational effects caused by flow acceleration in long chambers or chambers with sufficiently large sidewall injection. In addition to the stream function, the velocity, pressure, temperature, and density are evaluated over a range of physical parameters. Finally, the distortions affecting the velocity profiles are characterized and shown to result in a blunter motion near the center and a steeper curvature near the sidewall as a consequence of high-speed flow. In comparison with a non-swirling complex-lamellar solution, we find the Trkalian motion to be generally faster and therefore capable of reaching sonic conditions in a shorter distance from the headwall.

This work presents an exact solution of Euler's incompressible equations in the context of a bidirectional vortex evolving inside a conically shaped cyclonic chamber. The corresponding helical flowfield is modeled under inviscid conditions assuming constant angular momentum. By leveraging the axisymmetric nature of the problem, a steady-state solution of the generalized Beltramian type is obtained directly from first principles, namely, from the Bragg–Hawthorne equation in spherical coordinates. The resulting stream function representation enables us to fully describe the ensuing swirl-dominated motion including its fundamental flow characteristics. After identifying an isolated singularity that appears at a cone divergence half-angle of 63.43°, two piecewise formulations are provided that correspond to either fluid injection or extraction at the top section of the conical cyclone. In this process, analytical expressions are readily retrieved for the three velocity components, vorticity, and pressure. Other essential flow indicators, such as the theoretically preferred mantle orientation, the empirically favored locus of zero vertical velocity, the maximum polar and axial velocities, the crossflow velocity, and other such terms, are systematically deduced. Results are validated using limiting process verifications and comparisons to both numerical and experimental measurements. The subtle differences between the present model and a strictly Beltramian flowfield are also highlighted and discussed. The conically cyclonic configuration considered here is relevant to propulsive devices, such as vortex-fired liquid rocket engines with tapered walls; meteorological phenomena, such as tornadoes, dust devils, and fire whirls; and industrial contraptions, such as cyclonic flow separators, collectors, centrifuges, boilers, vacuum cleaners, cement grinders, and so on.

The United State Army Corp of Engineers (USACE) Engineering Research and Development Center (ERDC) has developed a suite of computational tools called the Computational Test Bed (CTB) for advanced high-fidelity physics-based autonomous vehicle sensor and environment simulations. These tools provide insights into onboard navigation, image processing, sensor fusion techniques, and rapid data generation for artificial intelligence and machine learning techniques across the full spectrum (visible, NIR, MWIR, and LWIR) and for various sensor modalities (LiDAR, EO, radar). This paper presents ERDC's CTB that allows the community to design, develop, test, and evaluate the entire autonomy space from machine learning algorithm development using augmented synthetic data to large-scale autonomous system testing.

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as a non-intrusive method for propagating the latent-space dynamics in reduced order models. Here, we investigate employing deep autoencoders for discovering the reduced basis representation, the dynamics of which are then approximated by NODE. The ability of deep autoencoders to represent the latent-space is compared to the traditional proper orthogonal decomposition (POD) approach, again in conjunction with NODE for capturing the dynamics. Additionally, we compare their behavior with two classical non-intrusive methods based on POD and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system. Our findings indicate that deep autoencoders can leverage nonlinear manifold learning to achieve a highly efficient compression of spatial information and define a latent-space that appears to be more suitable for capturing the temporal dynamics through the NODE framework.

Modern reduced order models (ROMs) have widespread applicability in computational science and engineering as they allow accurate simulation of complex, nonlinear problems with minimal computational cost. In this paper, we introduce a Python-based implementation of a suite of data-driven ROM techniques for dynamical systems governed by time-dependent, nonlinear partial differential equations (PDEs). The versatility and accuracy of the presented ROM frameworks have been demonstrated with various numerical experiments in multiple publications. Therefore, this module is suitable not only as a tool for users in the industry, but it also provides a framework for researchers in academia to pursue further development.

In this work, two mathematical procedures are used to derive the incompressible mean flow profile in a simulated solid rocket motor that is modeled as a spinning right-cylindrical porous tube. The first approach starts with the Navier-Stokes equations and leads to a large wall-injection Reynolds number approximation. The second begins with the inviscid Bragg-Hawthorne equation, where the variation of the stagnation head is taken to reproduce the classical Taylor-Culick flow approximation for nonspinning rockets. To permit swirl to develop, the injected fluid is introduced with a finite angular momentum that is prescribed by the spinning rate of the motor. The core singularity that naturally evolves in the inviscid formulation is overcome through the use of viscous matched-asymptotic expansions. The closed-form expressions emerging from both techniques are then compared and verified using finite volume simulations of the unabridged Navier-Stokes equations. Results from all three approaches are found to be in substantial agreement over a wide range of Reynolds numbers, thus helping to validate the asymptotic treatment of the core boundary-layer analysis pursued in this and similar studies. Additional flow features, such as the vorticity and pressure, are also described and compared to the nonspinning motor case.

In this study, the Bragg–Hawthorne equation (BHE) is extended in the context of a steady, inviscid and compressible fluid, thus leading to an assortment of partial differential equations that must be solved simultaneously. A solution is pursued by implementing a Rayleigh–Janzen expansion in the square of the reference Mach number. The corresponding formulation is subsequently used to derive a compressible approximation for the Trkalian model of the bidirectional vortex. The approximate solution is compared to a representative computational fluid dynamics simulation in order to validate the modelling assumptions under realistic conditions. The latter is found to exhibit an appreciable steepening of the axial velocity profile, which is accompanied by an axial dependence in the mantle location that is somewhat reminiscent of the radial shifting of mantles reported in some experimental trials and simulations. In this context, flows with a strong swirl intensity do not seem to be significantly affected by the introduction of compressibility. Rather, as the swirl intensity is reduced the effects of compressibility become more noticeable, especially in the axial and radial velocity components. It may also be realized that imparting a progressively larger swirl component stands to promote the axisymmetric distribution of flow field properties, and these include an implicit resistance to dilatational effects in the tangential direction. From a broader perspective, this study provides a viable approximation to the Trkalian motion associated with cyclonic flows, while serving as a limited proof of concept for the compressible Bragg–Hawthorne procedure applied to a steady, axisymmetric and inviscid fluid.

In this work, the bulk gaseous motion inside cylindrical chambers driven by wall normal injection with and without reactive headwalls is explored. The base model is of the Trkalian type and is here extended to include approximations for arbitrary headwall injection patterns as well as compressibility effects for an exact similarity conforming headwall injection profile. The inviscid, non-reacting, swirling flow model is first generalized to capture a variety of headwall injection patterns through the concept of orthogonality. This leads to an approximation with some error which is quantified in the analysis. The velocity and vorticity fields are characterized for four representative injection patterns including a similarity conforming injection profile in the form of a Bessel function. The exact similarity conforming injection profile is then used in the development of a compressible approximation. Dilational effects are captured through a compressible Brag–Hawthorne framework in conjunction with a Rayleigh-Janzen expansion. Here again, the velocity and vorticity fields are obtained, along with the pressure, density, and temperature. These field variables are then compared to the incompressible case as well as the compressible complex-lamellar solution without swirl. Furthermore, the sonic length which functions as a normalizing parameter is calculated for several specific heat ratios and injection coefficients.

In this work, an exact inviscid solution is introduced for the incompressible Euler equation in the context of a bidirectional, cyclonic vortex in a right-cylindrical chamber with a hollow core. The presence of a gaseous core restricts the flow domain to an annular vortex region that extends into a toroid in three dimensional space. The procedure that we follow is based on the Bragg-Hawthorne framework, which is used in conjunction with a unique assortment of boundary conditions that mirror in large part those entailed in the derivation of a comparably complex-lamellar mean flow profile by Vyas and Majdalani (Vyas, A. B., and Majdalani, J., ”Exact Solution of the Bidirectional Vortex,” AIAA Journal, Vol. 44, No. 10, 2006, pp. 2208-2216). At the outset, a self-similar solution is retrieved from the Bragg-Hawthorne equation under the premises of steady, axisymmetric, and inviscid conditions, as opposed to the vorticity-streamfunction approach used previously. The resulting formulation is then utilized to describe the bidirectional evolution of the inner and outer vortex motions, including their fundamental properties, such as the interfacial layer known as the mantle, as well as the velocity, pressure, and vorticity fields, with particular attention being devoted to their peak values and spatial excursions that accompany successive expansions of the core radius. By way of confirmation, it is shown that removal of the hollow core restores the well-established solution in a fully flowing cylindrical chamber. Immediate applications of cyclonic flows include liquid and hybrid rocket engines, swirl-driven combustion devices, as well as a multitude of heat exchangers, centrifuges, cyclone separators, and flow separation contraptions that offer distinct advantages over conventional, non-swirling systems.

This paper introduces an innovative quadrupole vortex flowfield in the context of a simulated, right-cylindrical, hybrid rocket engine. By analogy to diamond-impregnated tricone roller bits used in the oil-extraction industry, the counter-rotating set of vortices produces a highly efficient fluid drill that leads to substantial increases in grain erosion at the propellant surface. Other effects include increased mixing between the hot combustion products in the core region and the turbulent boundary layer at the flame surface, improved combustion efficiency, higher fuel regression rates, longer particle residence times, better control of equivalence ratios, and greater predictability of performance as compared to classic hybrids. The quadrupole vortex motion also gives rise to a more energetic burning behavior, more complete and efficient combustion, sliver reduction, and increased combustion stability. In this work, a non-reactive model is used as a first step to derive the bulk gaseous motion associated with a quadrupole vortex. The corresponding velocity field is decomposed into forced vortex segments in the core region followed outwardly by irrotational bathtub vortices. The Milne-Thomson Circle Theorem is subsequently employed to derive the polar motion of the quadrupole vortices for a bounded potential field. The resulting formulation is then extended to the case of a uniformly expanding boundary corresponding to an ideally regressing fuel grain within a hybrid rocket engine. In addition to the velocity flowfield, expressions for the pressure and temperature ratios at every point within the chamber are subsequently determined and characterized. In closing, strengths and shortcomings of the present approach are discussed while providing recommendations for future consideration.