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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Effect of artificial viscosity on shocked particle-laden flows for staggered grid Lagrangian methods

Abstract Shocked particle-laden flows are important to many natural and industrial processes. When simulating these systems, artificial viscosity is often required to prevent numerical artifacts, such as ringing, from arising in the pressure and density fields. The linear and quadratic coefficients of the artificial viscosity determine the amount of smoothing that occurs in these fields. For particle-laden flows, however, many of the fluid–particle interaction forces, for example, the pressure gradient force and unsteady forces, depend on gradients in the fluid fields. Furthermore, while the shock passes over a particle, these forces can be more dominant than drag. This means that the artificial viscosity coefficients affect how a particle and fluid interact when simulating shocked particle systems. Here this effect is investigated for isolated particles and for a particle curtain using a staggered grid Lagrangian approach. The artificial viscosity coefficients have a significant impact on the maximum force that a fluid imparts to a particle, which is important for determining whether a particle will break up in response to the shock. Furthermore, it is found that the density ratio between the particle and the fluid is important in determining whether the artificial viscosity coefficients have a significant impact on the particle’s motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Simulating Marine Stratocumulus Clouds using Lagrangian Superdroplet Method in ERF

This study investigates the simulation of marine stratocumulus (stratoCu) clouds – common in many offshore and coastal wind energy regions - using Lagrangian Superdroplet Method (SDM) implemented in Energy Research and Forecasting (ERF) model. Developed by the Wind Energy Technologies Office (WETO), ERF is a high-resolution atmospheric modeling tool that relies on traditional bulk microphysics schemes. Under an LLNL-led Laboratory Directed Research and Development (LDRD) project, SDM was integrated into ERF to improve cloud process fidelity by explicitly tracking individual “superdroplets”. This enables a realistic representation of the droplet size spectrum, cloud-atmosphere interactions, and potential feedbacks from wind plants on atmospheric flow and cloud structure.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.

Nonconvex optimization↗
DOE OSTI2024

An Empirical Quantile Estimation Approach for Chance-Constrained Nonlinear Optimization Problems

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.

Applied Probability↗
DOE OSTI2025

Extended FFT-based micromechanical formulation to consider general non-periodic boundary conditions

Here, this paper presents a new approach for applying non-periodic boundary conditions in the context of FFT-based methods to solve micromechanical problems in heterogeneous solids. The domain of the original problem is extended to satisfy the periodicity requirements at the boundary of the extended domain. The velocity constraint on the boundary of the original domain is replaced by a corresponding constraint on the velocity gradient in the extended volume, and a two-level augmented Lagrangian method is used to enforce the constraint. The proposed method is implemented as an extension of the large-strain elasto-viscoplastic FFT-based (LS-EVPFFT) model of Zecevic et al. (2022). The proposed method is verified in the cases of fully imposed velocity boundary conditions and mixed velocity/traction-free boundary conditions. The accuracy and convergence of the method are studied next, followed by applications to bending and indentation of polycrystals that illustrate the extended capabilities of the proposed formulation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Competition response of cloud supersaturation explains diminished Twomey effect for smoky aerosol in the tropical Atlantic

The Twomey effect brightens clouds by increasing aerosol concentrations, which activates more droplets and decreases cloud supersaturation in response to more competition for water vapor. To quantify this competition response, we used marine low cloud observations in clean and smoky conditions at Ascension Island in the tropical South Atlantic during the Layered Aerosol Smoke Interactions with Cloud (LASIC) campaign. These observations show similar increases in droplet number for increased accumulation-mode particles from surface-based and satellite cloud retrievals, demonstrating the importance of below-cloud aerosol measurements for retrieving aerosol–cloud interactions (ACI) in clean and smoky aerosol conditions. Four methods for estimating cloud supersaturation from aerosol–cloud measurements were compared, with cloud scene-based and parcel-based methods showing sufficient variability for a strong dependence on both aerosol accumulation number concentration and cloud-base updraft velocities. Decomposing aerosol-related changes in cloud albedo and optical depth shows the calculated competition response accounts for dampening the activation response by 12 to 35%, explaining the diminished Twomey effect at high aerosol concentrations observed for smoky conditions at LASIC and previously around the world. This result was consistent for independent supersaturation retrievals by cloud scene-based droplet number and cloud condensation nuclei and parcel-based multimode size-resolving Lagrangian methods. Translating aerosol effects to local radiative forcing with clean conditions as a proxy for preindustrial and smoky conditions for present-day showed that the competition response reduces cooling from the Twomey radiative forcing by 12 to 35%, providing an essential process-specific constraint for improving the representation of aerosol competition in climate model simulation of indirect aerosol forcing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Stability analysis of the Eulerian–Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension

In this paper, we construct a novel Eulerian–Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the initial conditions are smooth, and direct numerical methods may suffer from restricted time step sizes. To relieve the restriction, we propose an ELFV method, where the space-time domain was separated by the partition lines originated from the cell interfaces whose slopes are obtained following the Rakine–Hugoniot junmp condition. Unfortunately, to avoid the intersection of the partition lines, the time step sizes are still limited. To fix this gap, we detect effective troubled cells (ETCs) and carefully design the influence region of each ETC, within which the partitioned space-time regions are merged together to form a new one. Then with the new partition of the space-time domain, we theoretically prove that the proposed first-order scheme with Euler forward time discretization is total-variation-diminishing and maximum-principle-preserving with at least twice larger time step constraints than the classical first order Eulerian method for Burgers’ equation. Numerical experiments verify the optimality of the designed time step sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Pressure stability in explicitly coupled simulations of poromechanics with application to CO 2 sequestration

We study in detail the pressure stabilizing effects of the non-iterated fixed-stress splitting in poromechanical problems which are nearly undrained and incompressible. When applied in conjunction with a spatial discretization which does not satisfy the discrete inf–sup condition, namely a mixed piecewise linear–piecewise constant spatial discretization, the explicit fixed-stress scheme can have a pressure stabilizing effect in transient problems. This effect disappears, however, upon time step refinement or the attainment of steady state. The interpretation of the scheme as an Augmented Lagrangian method similar to Uzawa iteration for incompressible flow helps explain these results. Moreover, due to the slowly evolving solution within undrained seal regions, we show that the explicit fixed-stress scheme requires very large time steps to reveal its pressure stabilizing effect in examples of geologic CO 2 sequestration. We note that large time steps can result in large errors in drained regions, such as the aquifer or reservoir regions of these examples, and can prevent convergence of nonlinear solvers in the case of multiphase flows, which can make the explicit scheme an unreliable source of pressure stabilization. We conclude by demonstrating that pressure jump stabilization is as effective in the explicit fixed-stress setting as in the fully implicit setting for undrained problems, while maintaining the stability and convergence of the fixed-stress split for drained problems.

58 GEOSCIENCES↗
DOE OSTI2025

Near-ideal relaxed MHD in slab geometry

We investigate the solutions of the relaxed magnetohydrodynamic (MHD) model (RxMHD) of R. Dewar and Z. Qu. This model generalizes Taylor relaxation by including the ideal Ohm's law constraint using an augmented Lagrangian method, providing a pathway to extend the multi-region relaxed MHD (MRxMHD) model. We present the first numerical solution of the RxMHD model by Dewar and Qu, demonstrating that it is mathematically well-defined and computationally feasible for constructing MHD equilibria in slab geometry. We also show that a cross-field flow can exist without enforcing an arbitrary constraint on the angular momentum, as is done in the case of MRxMHD with flow. Our results also demonstrate the self-organization of fully relaxed regions during the optimization, which was an important motivation behind developing this model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

3D mesh regularization within an ALE code using a weighted line sweeping method

The Lagrangian formalism is widely used to simulate hydrodynamic responses in complex engineering applications, particularly those involving strong shock waves. However, as the mesh moves with the fluid, it can become highly distorted, requiring a regularization step. This involves constructing a new grid and remapping conservative quantities onto it to restore mesh quality. This work introduces a regularization method for block-structured meshes within a 3D ALE (Arbitrary Lagrangian-Eulerian) code. The proposed approach prevents mesh tangling while preserving the anisotropic features of the initial Lagrangian mesh. This regularization technique incorporates aspect ratio-based weights to control mesh smoothing. Unlike uniform rezoning techniques, this weighted approach maintains proximity to the Lagrangian mesh while improving mesh quality. Here, the method effectively handles concave geometries by mitigating the grid attraction phenomenon, which typically leads to mesh concentration along concave edges. Numerical experiments demonstrate its efficiency in regularizing severely deformed meshes, and its integration within the ALE framework is validated on challenging hydrodynamic test cases, including the triple point problem.

42 ENGINEERING↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints

Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.

augmented Lagrangian↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2024

A safe reinforcement learning algorithm for supervisory control of power plants

Traditional control theory-based methods require tailored engineering for each system and constant fine-tuning. In power plant control, one often needs to obtain a precise representation of the system dynamics and carefully design the control scheme accordingly. Model-free Reinforcement learning (RL) has emerged as a promising solution for control tasks due to its ability to learn from trial-and-error interactions with the environment. It eliminates the need for explicitly modeling the environment’s dynamics, which is potentially inaccurate. However, the direct imposition of state constraints in power plant control raises challenges for standard RL methods. To address this, we propose a chance-constrained RL algorithm based on Proximal Policy Optimization for supervisory control. Our method employs Lagrangian relaxation to convert the constrained optimization problem into an unconstrained objective, where trainable Lagrange multipliers enforce the state constraints. In conclusion, our approach achieves the smallest distance of violation and violation rate in a load-follow maneuver for an advanced Nuclear Power Plant design.

constrained optimization↗
DOE OSTI2024

A Survey of Multimaterial Treatments for Thermal Radiative Transfer

Arbitrary Lagrangian-Eulerian methods are a popular choice for hydrodynamic modeling in radiation (rad-hydro) simulations. Because these methods involve a relaxation step that moves the mesh relative to material boundaries, multimaterial spatial zones are generally present. Accurate treatments of these zones are needed to resolve various physical phenomena of interest for inertial confinement fusion applications. However, these codes are often paired with single-material, deterministic thermal radiative transfer (TRT) codes that are oblivious to the material compositions of each zone. These single-material TRT codes can only accept homogenized material properties (opacities, specific heats, etc.) from the hydrodynamic code and output homogenized solutions. After each TRT time step, the multimaterial hydrodynamic code must dehomogenize the quantities computed by the TRT package in order to update subzonal material temperatures. The process by which hydrodynamic codes perform this dehomogenization has not been well documented in previous literature, and the methods can vary significantly from code to code. The purpose of this paper is to document, study, and compare existing techniques used for rad-hydro simulations as well as present a new method with potentially promising results. We summarize several methods and give comparisons on infinite-medium problems as well a finite-medium problem for two of the methods.

42 ENGINEERING↗
DOE OSTI2024

TRACER Perspectives on Gulf-Breeze and Bay-Breeze Circulations and Coastal Convection

Abstract This study explores gulf-breeze circulations (GBCs) and bay-breeze circulations (BBCs) in Houston–Galveston, investigating their characteristics, large-scale weather influences, and impacts on surface properties, boundary layer updrafts, and convective clouds. The results are derived from a combination of datasets, including satellite observations, ground-based measurements, and reanalysis datasets, using machine learning, changepoint detection method, and Lagrangian cell tracking. We find that anticyclonic synoptic patterns during the summer months (June–September) favor GBC/BBC formation and the associated convective cloud development, representing 74% of cases. The main Tracking Aerosol Convection Interactions Experiment (TRACER) site located close to the Galveston Bay is influenced by both GBC and BBC, with nearly half of the cases showing evident BBC features. The site experiences early frontal passages ranging from 1040 to 1630 local time (LT), with 1300 LT being the most frequent. These fronts are stronger than those observed at the ancillary site which is located further inland from the Galveston Bay, including larger changes in surface temperature, moisture, and wind speed. Furthermore, these fronts trigger boundary layer updrafts, likely promoting isolated convective precipitating cores that are short lived (average convective lifetime of 63 min) and slow moving (average propagation speed of 5 m s −1 ), primarily within 20–40 km from the coast.

54 ENVIRONMENTAL SCIENCES↗