Numerical study of the economical earth-Mars and earth-Venus transfers.
Earth-Mars and earth-Venus economical transfers derived for optimal conditions with respect to characteristic velocity, obtaining exact numerical solution
Culp, R.↗
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Statistical Mechanics and Dynamics of the Outer Solar System.I. The Jupiter/Saturn Zone
We report on numerical simulations designed to understand how the solar system evolved through a winnowing of planetesimals accreeted from the early solar nebula. This sorting process is driven by the energy and angular momentum and continues to the present day. We reconsider the existence and importance of stable niches in the Jupiter/Saturn Zone using greatly improved numerical techniques based on high-order optimized multi-step integration schemes coupled to roundoff error minimizing methods.
numerical simulations planetesimals planet formati↗
High-Lift Optimization Design Using Neural Networks on a Multi-Element Airfoil
The high-lift performance of a multi-element airfoil was optimized by using neural-net predictions that were trained using a computational data set. The numerical data was generated using a two-dimensional, incompressible, Navier-Stokes algorithm with the Spalart-Allmaras turbulence model. Because it is difficult to predict maximum lift for high-lift systems, an empirically-based maximum lift criteria was used in this study to determine both the maximum lift and the angle at which it occurs. Multiple input, single output networks were trained using the NASA Ames variation of the Levenberg-Marquardt algorithm for each of the aerodynamic coefficients (lift, drag, and moment). The artificial neural networks were integrated with a gradient-based optimizer. Using independent numerical simulations and experimental data for this high-lift configuration, it was shown that this design process successfully optimized flap deflection, gap, overlap, and angle of attack to maximize lift. Once the neural networks were trained and integrated with the optimizer, minimal additional computer resources were required to perform optimization runs with different initial conditions and parameters. Applying the neural networks within the high-lift rigging optimization process reduced the amount of computational time and resources by 83% compared with traditional gradient-based optimization procedures for multiple optimization runs.
Greenman, Roxana M.↗
Optimization of direct air capture processes using reactive transport models of adsorption-desorption cycles
In this study, we develop and implement a reactive transport model in COMSOL Multiphysics® to address the challenges of direct air carbon capture. The model is validated against experimental data and used to simulate the cyclic steady state of the adsorption-desorption process. The optimization of this model is achieved through advanced trust-region methods integrated with Gaussian Processes. Key decision variables, including adsorption and desorption times, desorption temperature and pressure, input velocity, bed porosity, column length, and radius were optimized to minimize the capture cost. After optimization, a sensitivity analysis revealed the complex interplay between the decision variables and their effect on the specific energy and cost of removing the CO 2 . We optimized the capture cost while taking into account the trade-off between energy consumption and productivity. The resulting minimum capture cost was determined to be 265.2 $/t-CO 2 , which aligns with expected values reported in the literature. Numerical results suggest the effectiveness of the optimization strategies applied, and underscore the importance of simultaneous decision variable selection in improving the performance in direct air capture processes. We also extend the modeling approach to a 2D axisymmetric model to better visualize CO₂ uptake and temperature profiles, revealing significant radial gradients during the regeneration step. As a main drawback, this enhanced model comes with a computational cost approximately 40 times higher than that of the 1D model.
Adsorption-desorption process↗
Image Correlation Pattern Optimization for Micro-Scale In-Situ Strain Measurements
The accuracy and precision of digital image correlation (DIC) is a function of three primary ingredients: image acquisition, image analysis, and the subject of the image. Development of the first two (i.e. image acquisition techniques and image correlation algorithms) has led to widespread use of DIC; however, fewer developments have been focused on the third ingredient. Typically, subjects of DIC images are mechanical specimens with either a natural surface pattern or a pattern applied to the surface. Research in the area of DIC patterns has primarily been aimed at identifying which surface patterns are best suited for DIC, by comparing patterns to each other. Because the easiest and most widespread methods of applying patterns have a high degree of randomness associated with them (e.g., airbrush, spray paint, particle decoration, etc.), less effort has been spent on exact construction of ideal patterns. With the development of patterning techniques such as microstamping and lithography, patterns can be applied to a specimen pixel by pixel from a patterned image. In these cases, especially because the patterns are reused many times, an optimal pattern is sought such that error introduced into DIC from the pattern is minimized. DIC consists of tracking the motion of an array of nodes from a reference image to a deformed image. Every pixel in the images has an associated intensity (grayscale) value, with discretization depending on the bit depth of the image. Because individual pixel matching by intensity value yields a non-unique scale-dependent problem, subsets around each node are used for identification. A correlation criteria is used to find the best match of a particular subset of a reference image within a deformed image. The reader is referred to references for enumerations of typical correlation criteria. As illustrated by Schreier and Sutton and Lu and Cary systematic errors can be introduced by representing the underlying deformation with under-matched shape functions. An important implication, as discussed by Sutton et al., is that in the presence of highly localized deformations (e.g., crack fronts), error can be reduced by minimizing the subset size. In other words, smaller subsets allow the more accurate resolution of localized deformations. Contrarily, the choice of optimal subset size has been widely studied and a general consensus is that larger subsets with more information content are less prone to random error. Thus, an optimal subset size balances the systematic error from under matched deformations with random error from measurement noise. The alternative approach pursued in the current work is to choose a small subset size and optimize the information content within (i.e., optimizing an applied DIC pattern), rather than finding an optimal subset size. In the literature, many pattern quality metrics have been proposed, e.g., sum of square intensity gradient (SSSIG), mean subset fluctuation, gray level co-occurrence, autocorrelation-based metrics, and speckle-based metrics. The majority of these metrics were developed to quantify the quality of common pseudo-random patterns after they have been applied, and were not created with the intent of pattern generation. As such, it is found that none of the metrics examined in this study are fit to be the objective function of a pattern generation optimization. In some cases, such as with speckle-based metrics, application to pixel by pixel patterns is ill-conditioned and requires somewhat arbitrary extensions. In other cases, such as with the SSSIG, it is shown that trivial solutions exist for the optimum of the metric which are ill-suited for DIC (such as a checkerboard pattern). In the current work, a multi-metric optimization method is proposed whereby quality is viewed as a combination of individual quality metrics. Specifically, SSSIG and two auto-correlation metrics are used which have generally competitive objectives. Thus, each metric could be viewed as a constraint imposed upon the others, thereby precluding the achievement of their trivial solutions. In this way, optimization produces a pattern which balances the benefits of multiple quality metrics. The resulting pattern, along with randomly generated patterns, is subjected to numerical deformations and analyzed with DIC software. The optimal pattern is shown to outperform randomly generated patterns.
Bomarito, G. F.↗
Optimization of actuator arrays for aircraft interior noise control
A numerical procedure for grouping actuators in order to reduce the number of degrees of freedom in an active noise control system is evaluated using experimental data. Piezoceramic actuators for reducing aircraft interior noise are arranged into groups using a nonlinear optimization routine and clustering algorithm. An actuator group is created when two or more actuators are driven with the same control input. This procedure is suitable for active control applications where actuators are already mounted on a structure. The feasibility of this technique is demonstrated using measured data from the aft cabin of a Douglas DC-9 fuselage. The measured data include transfer functions between 34 piezoceramic actuators and 29 interior microphones and microphone responses due to the primary noise produced by external speakers. Control inputs for the grouped actuators were calculated so that a cost function, defined as a quadratic pressure term and a penalty term, was a minimum. The measured transfer functions and microphone responses are checked by comparing calculated noise reductions with measured noise reductions for four frequencies. The grouping procedure is then used to determine actuator groups that improve overall interior noise reductions by 5.3 to 15 dB, compared to the baseline experimental configuration.
Cabell, R. H.↗
Optimization of spray breakup model parameters for predicting fuel spray and film characteristics in gasoline direct injection engines
This study investigated the behavior of gasoline direct injection (GDI) sprays using computational fluid dynamics (CFD). The authors developed an approach to identify optimal spray breakup model parameters by evaluating an error function across numerous simulations, with the goal of minimizing discrepancies from experimental data. Using the optimal setup, the simulated spray matched well with projected liquid volume distributions, liquid penetration, and spray width measured in a constant-pressure continuous-flow chamber. To further validate the approach, the same setup was tested across various fuels, injectors, and operating conditions. Subsequently, the optimal setup, along with a recently developed spray-wall interaction model, were applied to a direct-injection spark-ignited engine under late-injection conditions to predict and evaluate fuel film formation and evolution at varying engine coolant temperatures. Here, with the centrally mounted injector directing the spray toward the piston, simulations indicated that the spray tends to impinge on the piston surface. The proposed simulation framework also accurately captured the aggregate film area on the piston surface, aligning with previously published experimental results. Moreover, simulations showed that increasing the coolant temperature from cold start conditions (333 K) to warm conditions (363 K) reduced the fuel mass deposited on the piston by roughly 50%. Furthermore, for the spray-guided engine configuration studied in this work, the CFD model predicted minimal film deposition on the spark plug electrodes regardless of the coolant temperatures due to a relatively weak in-cylinder flow during the compression phase.
Computational fluid dynamics (CFD)↗
Overview of optimal trajectories for flight in a windshear
Optimal flight trajectories for the B-727, B-737, and B-747 aircraft in the presence of wind shear are studied. The takeoff problem and the abort landing problem are considered with reference to flight in a vertical plane. In the former, optimal trajectories are computed by minimizing the peak deviation of the absolute path inclination from a reference value; in the latter, optimal trajectories are computed by minimizing the peak value of the altitude drop. Numerical computations show that, for both the problems under consideration, the optimal trajectories of the three aircraft show the same qualitative behavior. Hence, it appears that the near-optimal guidance schemes developed for the B-727 can be extended to the other two aircraft, albeit with some quantitative modification.
Miele, A.↗
Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model
This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.
15 GEOTHERMAL ENERGY↗
Computational modeling of microalgal biofilm growth in heterogeneous rotating algal biofilm reactors (RABRs) for wastewater treatment
Rotating algal biofilm reactors (RABRs) are innovative systems designed to cultivate microalgae biofilms efficiently. In this paper, we have developed a novel mathematical model to accurately capture the growth dynamics of algae biofilms within RABR. By considering the spatial heterogeneity of the RABR, we introduce a PDE-based model that addresses the spatial variations across the substratum, enabling a more accurate simulation of biofilm growth in RABRs. The photosynthesis process is modeled through reactive kinetics, driving the growth of the algae biofilm. To analyze the system's behavior, we employ finite difference numerical methods to solve the complex PDE model. We then conduct extensive numerical simulations to understand algae biofilm growth in the RABR environment under various operational factors and environmental conditions. One primary focus in these simulations is to investigate the impact of various harvesting strategies, harvesting frequencies, light intensity, and light exposure on the overall biomass productivity of the algae biofilm. The numerical results provide valuable insights into optimizing algae biofilm growth and designing harvesting techniques in RABR systems. Our proposed novel mathematical model provides an effective platform for the theoretical investigation and design of RABRs for wastewater treatment.
09 BIOMASS FUELS↗
Applying a Compact Porous Media Model to Numerically Derive Resistance Coefficients for Lattice Structures
Additive Manufacturing allows for exploring various geometries to achieve specific engineering criteria. Lattices are one geometry with unique properties, including being periodically repeating structures which allow flow through them to be represented as a porous media according to Darcy-Forchheimer equations. These equation’s coefficients are generally experimentally derived, but this work demonstrates the ability to numerically derive them with CFD. Simulations were performed using three-dimensional stead state Reynolds-averaged Navier-Stokes with a k-ω Shear Stress Transport turbulence model using Ansys Fluent. Three lattice geometries were investigated and drag coefficients were derived. The method was validated against externally published data for similar geometries demonstrating strong agreement, and grid convergence for all simulations was calculated with a Grid Convergence Index method. Wall roughness is demonstrated to have a non-negligible impact on results and roughness values are considered for the primary focus Octahedral geometry where both smooth wall and rough wall coefficients were derived. The porosity coefficients for the Octahedral geometry at 1.0 [m/s] were found to be 2.89×10 6 and 2.90×10 6 [1/(Pa*m*s)] for the permeability coefficients, 6.37×10 1 and 5.44×10 1 [m 2 /kg] for the inertial resistance coefficients, and with a max pressure drop of 5116.7 [Pa] and 4429.5 [Pa] for the smooth walls and rough walls, respectively. The derived numerical method enables rapid exploration and optimization of new lattice designs for diverse engineering applications.
42 ENGINEERING↗
A flexible and differentiable coil proxy for stellarator equilibrium optimization
Balancing plasma performance and coil cost is a significant challenge when designing a stellarator power plant. Most current stellarator designs are produced through two-stage optimization: stage-1 for the equilibrium and stage-2 for a coil design that reproduces its magnetic configuration. Because few proxies connect both stages, two-stage optimization can produce plasmas that have high-quality physical properties but overly complex coils. In recent years, single-stage optimization has increasingly been used to optimize the plasma and coils simultaneously in order to improve the plasma–coil balance. However, all existing single-stage tools are specialized for filament coils, cannot model coil systems containing permanent magnets or dipole arrays, and continue to be challenged by numerical problems. The quasi-single-stage optimization finds a middle ground by integrating a coil optimization subproblem into stage-1 optimization. We present a flexible, differentiable coil complexity proxy based on the newly developed QUADCOIL coil optimization code. QUADCOIL is fast and can target realistic coil metrics and constraints that are unavailable to codes with comparable speed. We demonstrate the effectiveness and flexibility of the QUADCOIL proxy by presenting two QSS optimization studies. The first study produces a permanent magnet solution for the MUSE stellarator with 34% fewer magnets than previous solutions. The second study produces a coil solution for the ARIES-CS stellarator with 30% reductions in both peak and root-mean-square force.
Fu, Lanke [Princeton Plasma Physics Laboratory (PP↗
Numerical analysis of gas exhaust in Wendelstein 7-X using the direct simulation Monte Carlo method
The present work is focused on a 3D numerical assessment of the Wendelstein 7-X (W7-X) particle exhaust. For all the numerical simulations the direct simulation Monte Carlo solver of the DIVGAS workflow, has been employed. The complex 3D geometry of the sub-divertor region includes the pumping gap panel, supporting structures, cooling pipes as well as the cryo-vacuum pump. All the considered flow simulations correspond to the Standard magnetic configuration of W7-X. The main conclusions, which can be extracted from the present numerical analysis could be summarized as follows; The coupling between EMC3-EIRENE and DIVGAS, which considers the fact that the incoming neutral particle flux at the sub-divertor is based on realistic plasma background, has been demonstrated. Three plasma scenarios have been considered, for which is clearly seen that by increasing the heating power, the neutral pressure as well as the resulting pumping efficiency is increased. The obtained numerical results of the neutral pressure in the sub-divertor lie within a more general scan matrix, which assumes a wider range of incoming particle flux, namely 10 19 –10 24 (s −1 ). It has been observed that, the sub-divertor neutral pressure is proportional to the incoming neutral particle flux, with the effective pumping speed to be a constant of proportionality. The influence of switching off the cryo-vacuum pump on the sub-divertor pressure is rather modest and a weak increase of the neutral pressure in the sub-divertor is expected. Correlations of the sub-divertor pressure with the total incoming particle flux as well as the individual pumped flux at each of the AEH and AEP sections have been deduced. Moreover, it has been demonstrated that the influence of the incoming neutral particle flux on the albedo coefficient at the AEH and AEP pumping gaps is rather weak. All the above numerical findings will actively support the optimization of the W7-X particle exhaust, in view of future experimental campaigns.
DSMC method↗
Robust COTS objective for diffraction-limited, high-NA, long front working distance imaging
We present a robust objective lens optimized for applications requiring both high numerical aperture (NA) and long front working distance imaging, comprised of all commercial-off-the-shelf (COTS) spherical singlet lenses. Unlike traditional designs that require separate collimation and refocusing stages, our approach directly converges imaged light to the back focal plane using a single lens group. Our configuration corrects spherical aberrations and efficiently collects light to achieve diffraction-limited performance across a wide range of wavelengths while simplifying alignment and assembly. Using this approach, we design and construct an example objective lens that features a long front working distance of 61 mm and a clipped NA of 0.30 (limited by an aperture in our experimental setup). We experimentally verify that it achieves monochromatic diffraction-limited resolution at wavelengths from 375 nm to 866 nm without requiring replacement of the lenses or changing the inter-lens spacings, and its performance remains robust across a 46 mm range variation in total length (by adjusting mainly the back working distance). Additionally, we develop a quantitative method to measure the field of view (FOV) using an experimentally calibrated pinhole target. Under 397 nm illumination (i.e., from 40 Ca + ion fluorescence), the objective achieves a resolution of 0.87 μm with a 540 μm FOV. This robust, all-COTS, and versatile design is well-suited for a broad range of experiments, supporting high-precision measurements and exploring quantum phenomena.
Cui, Jiafeng [Oak Ridge National Laboratory (ORNL)↗
Material Discovery and Design Principles of Perovskite Oxides for Reversible Solid Oxide Cells (R-SOC)
Reversible solid oxide cells (R-SOCs) are highly efficient devices for energy conversion and storage, capable of operating for both hydrogen utilization and production. In fuel cell mode, an R-SOC consumes hydrogen or natural gas to generate electricity, while in electrolysis mode, it produces hydrogen from steam. The discover of new materials with rapid oxygen surface exchange kinetics and enduring stability is crucial for the economically viable commercialization of R-SOCs. To facilitate this pursuit, we conducted extensive Density Functional Theory (DFT) calculations and developed Machine Learning (ML) models to predict critical catalytic properties essential for R-SOCs, such as oxygen surface exchange/diffusivity, and area-specific resistance (ASR). BaCoxFeyZrzO3-d(BFCZ)(x+y+z=1) emerged as a promising family of electrode materials with high activity and stability, validated through systematic experimental study. Moreover, a robust numerical multiphysics model was developed to optimize materials and microstructure parameters, providing the ability to predict the performance of functional R-SOCs.
Liu, Jian↗
CO 2 Transport Infrastructure Outlook in the United States
Carbon capture and storage (CCS) represents one of the most important methods to mitigate anthropogenic carbon emissions at a large scale, playing a key role in meeting climate change targets (Bui et al., 2018) and for net-zero CO 2 by 2050 scenarios in the United States (Browning et al., 2023). This technology involves capturing CO 2 emissions from industrial processes, transporting them via pipelines, trucks, rails, or ships, and ultimately storing them in underground geological sites, such as saline aquifers or depleted oil reservoirs. Thus, to encourage carbon reduction initiatives, the U.S. Congress enacted the Bipartisan Budget Act in 2018, reforming the 45Q tax credit to benefit operators storing CO 2 in geologic formations (Jones and Sherlock, 2021). Additionally, the 2022 Inflation Reduction Act further expanded these incentives, providing additional support for CCS initiatives (Hackett and Kuehn, 2023). Although numerous studies describe the importance of optimal CO 2 transportation to support the decision-making of CCS projects aligned with the objective of net-zero emissions by 2050 (Abramson and Christensen, 2021; Chen and Pawar, 2023; Greig and Pascale, 2021), further efforts are required to optimize the transport infrastructure for national-scale CCS deployment. Therefore, in this study, we examine three nationwide scenarios with the SimCCS 3.0 tool (Ma et al., 2022, 2023, 2024) along with a novel geospatial splitting approach developed by Velasco-Lozano et al. (Velasco- Lozano et al., 2024a, 2024b). We present optimized pipeline networks that meet the dynamic evolution of annual capture amounts, describing the required total pipeline lengths at each stage as a function of the pipeline diameters. Thus, the cases presented demonstrate the feasibility of CO 2 pipeline infrastructure for large-scale CCS projects.
54 ENVIRONMENTAL SCIENCES↗
Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators
The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.
93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗
When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling
Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.
58 GEOSCIENCES↗