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At least 253 records · Page 14

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗

Variational energy principle for compressible, baroclinic flow. 1: First and second variations of total kinetic action

The case of a cold gas in the absence of external force fields is considered. Since the only energy involved is kinetic energy, the total kinetic action (i.e., the space-time integral of the kinetic energy density) should serve as the total free-energy functional in this case, and as such should be a local minimum for all possible fluctuations about stable flow. This conjecture is tested by calculating explicit, manifestly covariant expressions for the first and second variations of the total kinetic action in the context of Lagrangian kinematics. The general question of the correlation between physical stability and the convexity of any action integral that can be interpreted as the total free-energy functional of the flow is discussed and illustrated for the cases of rectillinear and rotating shearing flows.

Schmid, L. A.↗

An implicit, conservative, zonal-boundary scheme for Euler equation calculations

A zonal, or patched, grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative, zonal boundary condition that could be used with explicit schemes was extended so that it can be used with existing second order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, M. M.↗

Chaotic motion in the Jovian atmosphere

Strong nonlinear interactions among unstable waves and the mean flow occur in a simplified quasigeostrophic spectral model of the upper troposphere of Jupiter. The upper boundary of the layer inhibits vertical motion while at the lower boundary perturbations of the potential temperature are not permitted. On an infinite beta plane the forced flow of alternating zones of prograde and retrograde zonal winds, decreasing with height, are linearly unstable and it is shown that the nonlinear terms stabilize the flow by bounding the growth of the eddies. Explicit viscosity terms are not needed. This does not imply that energy would not cascade to the small scale flow but suggests that the nature of the large scale flow is independent of the viscosity at small scales. Numerical time integration shows the flow to be chaotic but, in some cases, with transient propagating features and meandering zonal flow.

Pirraglia, Joseph↗

On the viscoplastic response of a composite wafer

In the present treatment of a viscoplastic composite wafer formed from a viscoplastic matrix that is reinforced by elastic or viscoplastic fibers attached to its plane surfaces, one constitutive equation is established by considering the viscoplastic behavior of the matrix as determined by an integral-type constitutive law whose intrinsic time-measure is pertinent to endochronic viscoplasticity. Attention is given to asymptotic cases where fiber stiffnesses and the hydrostatic modulus of the wafer are much larger than the latter's shear modulus. An explicit calculation is used when the stress field is uniaxial.

Valanis, K. C.↗

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗

Time dependent supervisory control update with FARM using rolling window

This report describes improvements to the Feasible Actuator Range Modifier (FARM) component of the RAVEN-based HYBRID framework for analysis of Integrated Energy Systems (IES). FARM supports the HERON plug-in that solves the power dispatch problem. The solution to the dispatch problem involves economically optimal dispatches that satisfy limits on production variables and their rates of variation (explicit constraints) as well as process variables tied to the service life of equipment (implicit constraints). FARM serves to validate or confirm that a HERON solution for explicit constraints also satisfies the implicit constraints. FARM-alpha was released by Argonne National Laboratory in January 2021 followed by FARM-Beta in January 2022 with the latter providing increased flexibility for the user. In this report, FARM-Gamma, the latest version of the code, is described. The major improvement is the implementation of a system identification algorithm based on the Dynamic Mode Decomposition with Control (DMDc) coupled with a “Rolling Window” scheme that allows obtaining linear time-varying state-space models. This feature equips FARM with the most accurate approximation of system dynamics, and it relieves the user from the burden of performing an exhaustive off-line characterization of the dynamics. FARM-Gamma capabilities are assessed by solving the power dispatch problem for a representative IES unit. The simulation times corresponding to the different releases are estimated and compared. These values capture the increasing computational burden of the successively higher fidelity state-space models adopted by FARM-Alpha, FARM-Beta and FARM-Gamma. The code implementation provides significant flexibility, i.e., the user can always select the most suitable version of FARM according to the problem to be solved and the available computational resources. It is anticipated that FARM will play a role in addressing several future IES applications. We outline how it can support the coordinated management and safe operation of a nuclear plant coupled to industrial processes to produce hydrogen and synfuels.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

An implicit, conservative, zonal-boundary scheme for Euler equation calculations

A 'zonal', or 'patched-grid', approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal-boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. In this study a conservative, zonal-boundary condition that could be used with explicit schemes has been extended so that it can be used with existing second-order-accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time-accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, M. M.↗

An Implicit, Conservative, Zonal-Boundary Scheme for Euler Equation Calculations

A "zonal," or "patched-grid," approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal-boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. In this study a conservative, zonal-boundary condition that could be used with explicit schemes has been extended so that it can be used with existing second-order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time-accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, Man Mohan↗

Activated relaxation in supercooled monodisperse atomic and polymeric WCA fluids: Simulation and ECNLE theory

Here, we combine simulation and Elastically Collective Nonlinear Langevin Equation (ECNLE) theory to study the activated relaxation in monodisperse atomic and polymeric Weeks–Chandler–Andersen (WCA) liquids over a wide range of temperatures and densities in the supercooled regime under isochoric conditions. By employing novel crystal-avoiding simulations, metastable equilibrium dynamics is probed in the absence of complications associated with size polydispersity. Based on a highly accurate structural input from integral equation theory, ECNLE theory is found to describe well the simulated density and temperature dependences of the alpha relaxation time of atomic fluids using a single system-specific parameter, a c , that reflects the nonuniversal relative importance of local cage and collective elastic barriers. For polymer fluids, the explicit dynamical effect of local chain connectivity is modeled at the fundamental dynamic free energy trajectory level based on a different parameter, N c , that quantifies the degree of intramolecular correlation of bonded segment activated barrier hopping. For the flexible chain model studied, a physically intuitive value of N c ≈ 2 results in good agreement between simulation and theory. A direct comparison between atomic and polymeric systems reveals that chain connectivity can speed up activated segmental relaxation due to weakening of equilibrium packing correlations but can slow down relaxation due to local bonding constraints. The empirical thermodynamic scaling idea for the alpha time is found to work well at high densities or temperatures but fails when both density and temperature are low. The rich and subtle behaviors revealed from simulation for atomic and polymeric WCA fluids are all well captured by ECNLE theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of a Complete Landsat Evapotranspiration and Energy Balance Archive to Support Agricultural Consumptive Water Use Reporting and Prediction in the Central Valley, CA

Mapping evapotranspiration (ET) from agricultural areas in Californias Central Valley is critical for understanding historical consumptive use of surface and groundwater. In addition, long histories of ET maps provide valuable training information for predictive studies of surface and groundwater demands. During times of drought, groundwater is commonly pumped to supplement reduced surface water supplies in the Central Valley. Due to the lack of extensive groundwater pumping records, mapping consumptive use using satellite imagery is an efficient and robust way for estimating agricultural consumptive use and assessing drought impacts. To this end, we have developed and implemented an algorithm for automated calibration of the METRIC remotely sensed surface energy balance model on NASAs Earth Exchange (NEX) to estimate ET at the field scale. Using automated calibration techniques on the NEX has allowed for the creation of spatially explicit historical ET estimates for the Landsat archive dating from 1984 to the near present. Further, our use of spatial NLDAS and CIMIS weather data, and spatial soil water balance simulations within the NEX METRIC workflow, has helped overcome challenges of time integration between satellite image dates. This historical and near present time archive of agricultural water consumption for the Central Valley will be an extremely useful dataset for water use and drought impact reporting, and predictive analyses of groundwater demands.

valleys↗

Integration of Weather Data into Airspace and Traffic Operations Simulation (ATOS) for Trajectory- Based Operations Research

Explicit integration of aviation weather forecasts with the National Airspace System (NAS) structure is needed to improve the development and execution of operationally effective weather impact mitigation plans and has become increasingly important due to NAS congestion and associated increases in delay. This article considers several contemporary weather-air traffic management (ATM) integration applications: the use of probabilistic forecasts of visibility at San Francisco, the Route Availability Planning Tool to facilitate departures from the New York airports during thunderstorms, the estimation of en route capacity in convective weather, and the application of mixed-integer optimization techniques to air traffic management when the en route and terminal capacities are varying with time because of convective weather impacts. Our operational experience at San Francisco and New York coupled with very promising initial results of traffic flow optimizations suggests that weather-ATM integrated systems warrant significant research and development investment. However, they will need to be refined through rapid prototyping at facilities with supportive operational users We have discussed key elements of an emerging aviation weather research area: the explicit integration of aviation weather forecasts with NAS structure to improve the effectiveness and timeliness of weather impact mitigation plans. Our insights are based on operational experiences with Lincoln Laboratory-developed integrated weather sensing and processing systems, and derivative early prototypes of explicit ATM decision support tools such as the RAPT in New York City. The technical components of this effort involve improving meteorological forecast skill, tailoring the forecast outputs to the problem of estimating airspace impacts, developing models to quantify airspace impacts, and prototyping automated tools that assist in the development of objective broad-area ATM strategies, given probabilistic weather forecasts. Lincoln Laboratory studies and prototype demonstrations in this area are helping to define the weather-assimilated decision-making system that is envisioned as a key capability for the multi-agency Next Generation Air Transportation System [1]. The Laboratory's work in this area has involved continuing, operations-based evolution of both weather forecasts and models for weather impacts on the NAS. Our experience has been that the development of usable ATM technologies that address weather impacts must proceed via rapid prototyping at facilities whose users are highly motivated to participate in system evolution.

Peters, Mark↗

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges since these systems enable ever-increasing size and complexity. In recent years, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using implicit-explicit (IMEX) and low-order operator splitting schemes. However, to date there have been few performance studies that compare different classes of multirate integrators on complex application problems. In this work, we study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits prior work on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but runs at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed IMEX MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both.

97 MATHEMATICS AND COMPUTING↗

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY↗

Dynamic Control of Sodium Cold Trap Purification Temperature Using LSTM System Identification

This study investigates the dynamic regulation of the sodium cold trap purification temperature at Argonne National Laboratory’s liquid sodium test facility, employing long short-term memory (LSTM) system identification techniques. The investigation introduces an innovative hybrid approach by integrating model predictive control (MPC) based on first principles dynamic models with a multi-step time–frequency LSTM model in predicting the temperature profiles of a sodium cold trap purification system. The long short-term memory–model predictive controller (LSTM-MPC) model employs a sliding window scheme to gather training samples for multi-step prediction, leveraging historical data to construct predictive models that capture the non-linearities of the complex system dynamics without explicitly modeling the underlying physical processes. The performance of the LSTM-MPC and MPC were evaluated through simulation experiments, where both models were assessed on their capacity to maintain the cold trap temperature within predefined set-points while minimizing deviations and overshoots. Results obtained show how the data-driven LSTM-MPC model demonstrates stability and adaptability. In contrast, the traditional MPC model exhibits irregularities, particularly evident as overshoots around set-point limits, which can potentially compromise its effectiveness over long prediction time intervals. The findings obtained offer valuable insights into integrating data-driven techniques for enhancing real-time monitoring systems.

LSTM-MPC↗

Nitrate Removal Across Ecogeomorphic Zones in Wax Lake Delta, Louisiana (USA)

Human activities have increased nitrate export from rivers, degrading coastal water quality. At deltaic river mouths, the flow of water through wetlands increases nitrate removal, and the spatial organization of removal rates influences coastal water quality. To understand the spatial distribution of nitrate removal in a river-dominated delta, in this study we deployed 23 benthic chambers across ecogeomorphic zones with varying elevation, vegetation, and sediment properties in Wax Lake Delta (Louisiana, USA) in June 2018. Regression analyses indicate that normalized difference vegetation index is a useful predictor of summertime nitrate removal. Mass transfer velocity were approximately three times greater on a vegetated submerged levee (13 mm hr –1 ), where normalized difference vegetation index was greatest, compared to other locations (4.6 mm hr –1 ). Two methods were developed to upscale nitrate removal across the delta. The flooded-delta method integrates spatially explicit potential removal rates across submerged portions of the delta and suggests that intermediate elevations on the delta—including submerged levees—are responsible for 70% of potential nitrate removal despite covering only 33% of the flooded area. The channel network method treats the delta as a network of river channels and suggests that although secondary channels are more efficient than primary channels at removing received nitrate, primary channels collectively contribute more to overall removal because they convey more of the total nitrate load. The two upscaling methods predict similar rates of nitrate removal, equivalent to less than 4% of nitrate entering the delta. To protect coastal waters against high nitrate loads, management policies should aim to reduce upstream nutrient loads.

54 ENVIRONMENTAL SCIENCES↗