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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems

In the hyperbolic community, discontinuous Galerkin (DG) approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many researchers a favorable property in case of hyperbolic balance laws. On the contrary, continuous Galerkin methods appear to be unsuitable for hyperbolic problems and there exists still the perception that continuous Galerkin methods are notoriously unstable. To remedy this issue, stabilization terms are usually added and various formulations can be found in the literature. However, this perception is not true and the stabilization terms are unnecessary, in general. In this paper, we deal with this problem, but present a different approach. We use the boundary conditions to stabilize the scheme following a procedure that are frequently used in the finite difference community. Here, the main idea is to impose the boundary conditions weakly and specific boundary operators are constructed such that they guarantee stability. This approach has already been used in the discontinuous Galerkin framework, but here we apply it with a continuous Galerkin scheme. No internal dissipation is needed even if unstructured grids are used. Further, we point out that we do not need exact integration, it suffices if the quadrature rule and the norm in the differential operator are the same, such that the summation-by-parts property is fulfilled meaning that a discrete Gauss Theorem is valid. This contradicts the perception in the hyperbolic community that stability issues for pure Galerkin scheme exist. In numerical simulations, we verify our theoretical analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2024

Failure investigation and mitigation after experimental research reactor fuel plate deformation in an irradiation device

Experimental research reactor fuel testing is conducted in the Belgian Reactor 2 (BR2) of the Belgian Nuclear Research Centre (SCK CEN) in dedicated irradiation vehicles or rigs. One such vehicle allows flat full-size fuel plates to be irradiated by inserting them into slotted baskets that captures a narrow portion of the longitudinal edges of the plates. The motion of the fuel plates within the baskets is possible within the narrow slots and thus, the plate is considered to be unattached. The design intentionally omits fixing mechanisms of the fuel plates to the baskets to facilitate the inspection and repositioning of the plates between the irradiation cycles and the accommodation of thermal expansion of the plates in the lateral direction. However, loosely inserted fuel plates have weak structural boundary conditions allowing for larger out-of-plane deflections caused by hydrodynamic loads exerted by the flowing coolant, as compared to those of fixed plates. Unexpected large deformations of plates occurred in several irradiation cycles that further resulted in a loss of cladding integrity. These deformations could not be attributed to a single source. This triggered a series of thermal hydraulic, structural, and fluid-structure interaction analyses aiming at understanding the observed phenomenon. The analyses revealed that, for a certain combination of unfavorable manufacturing and assembly tolerances, fuel plate edges could escape out of the slots in the irradiation basket due to the hydrodynamic load. Subsequently, the plate could become wedged inside the basket coolant channel opening. This resulted in reduced coolant flow and accelerated temperature increase and thermal expansion of the plate while under irradiation. This unfavorable feedback loop could then lead to excessive plate surface temperatures, deformed plates and cladding failure, as was observed in the experiments. These analyses not only provided a probable cause of the fuel plate failures, but also resulted in a new and improved design of the irradiation basket to avoid these issues in the future. In conclusion, a series of recent successful irradiations confirm that the sources of failures were identified correctly, and the implemented mitigations were adequate.

BR2↗
DOE OSTI2020

Advanced Methods for Immersed Domain Multi-physics Computations

This is the final report on the project, and describes the main accomplishments in the development of the Shifted Boundary Method (SBM), a new computational framework for embedded/immersed computational mechanics applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability

In the hyperbolic research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series, the application of simultaneous approximation terms for linear problems is investigated where the boundary conditions are imposed weakly. By applying this technique, the authors demonstrate that a pure continuous Galerkin scheme is indeed linearly stable if the boundary conditions are imposed in the correct way. In this work, we extend this investigation to the nonlinear case and focus on entropy conservation. Here, by switching to entropy variables, we provide an estimation of the boundary operators also for nonlinear problems, that guarantee conservation. In numerical simulations, we verify our theoretical analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Unavoidable multilevel biaxial symmetry breaking in chiral hybrid liquid crystals

Chiral nematic or cholesteric liquid crystals (LCs) are fluid mesophases with long-ranged orientational order featuring a quasilayered periodicity imparted by a helical director configuration but lacking long-range positional order. Doping molecular cholesteric LCs with strongly anisotropic uniaxial colloidal particles adds another level of complexity because of the interplay between weak surface-anchoring boundary conditions and bulk-based elastic distortions near the particle-LC interface. Using cylindrical colloidal disks and rods with different geometric shapes and surface conditions, we demonstrate that these colloidal inclusions generically exhibit biaxial orientational probability distributions which may impart anomalously strong local biaxiality onto the hybrid cholesteric LC structure. Unlike nonchiral hybrid molecular-colloidal LCs, where biaxial order emerges only at critical colloid volume fractions exceeding some uniaxial-biaxial transition value, the orientational probability of the colloidal inclusions immersed in chiral nematic hosts is unambiguously biaxial even at infinite dilution. We demonstrate that the colloids induce local biaxial perturbations within the molecular orientational order of the LC host medium which strongly enhances the weak but native biaxial order of chiral nematic LC induced by the chiral symmetry breaking of the director field. With the help of analytical modeling and computer simulations based on the Landau–de Gennes free energy of the host LC around the colloids, we rationalize the observed multilevel biaxial order and conclude that it is not only unavoidable but also strongly enhanced compared to both achiral hybrid LCs and purely molecular cholesteric LCs.

biaxial liquid crystals↗
DOE OSTI2026

Zooming in: SCREAM at 100 m using regional refinement over the San Francisco Bay Area

Pushing global climate models to large-eddy simulation (LES) scales over complex terrain has remained a major challenge. This study presents the first known implementation of a global model – SCREAM (Simple Cloud-Resolving E3SM Atmosphere Model) – at 100 m horizontal resolution using a regionally refined mesh (RRM) over the San Francisco Bay Area. Two hindcast simulations were conducted to test performance under both strong synoptic forcing and weak, boundary-layer-driven conditions. We demonstrate that SCREAM can stably run at LES scales while realistically capturing topography, surface heterogeneity, and coastal processes. The 100 m SCREAM-RRM substantially improves near-surface wind speed, temperature, humidity, and pressure biases compared to the baseline 3.25 km simulation, and better reproduces fine-scale wind oscillations and boundary-layer structures. These advances leverage SCREAM's scale-aware SHOC turbulence parameterization, which transitions smoothly across scales without tuning. Performance tests show that while CPU-only simulations remain costly, GPU acceleration with SCREAMv1 on NERSC's Perlmutter system enables two-day hindcasts to complete in under two wall-clock days. Our results open the door to LES-scale studies of orographic flows, boundary-layer turbulence, and coastal clouds within a fully comprehensive global modeling framework.

Geosciences↗
DOE OSTI2026

Idealized simulations of wind farm interactions with intermittent turbulence in stable boundary layer conditions

Stable atmospheric boundary layer conditions typically correspond to weak turbulence levels, but intermittent periods of elevated turbulence can occur during otherwise quiescent conditions. The interaction between intermittent turbulence and wind turbines is not well understood because of sparse observations, as well as the difficulty in realistically resolving small-scale turbulence during strongly stable conditions with numerical simulations. In this study, an explicit filtering and reconstruction approach for large-eddy simulation (LES) is used to simulate weakly and strongly stable conditions, with surface cooling rates of −0.2 and −2.0 K h −1 , respectively. This approach can sustain resolved background turbulence at relatively coarse grid spacing and stronger stratification compared to conventional closures, permitting more realistic intermittent stable boundary layer (SBL) turbulence. The idealized LES capability of the Weather Research and Forecasting model is employed with turbine rotors parameterized using generalized actuator disks to examine (1) how the presence of turbine wakes affects SBL evolution and (2) the effect of intermittent turbulence on power production and wake recovery. Wakes increase mixing and deepen the SBL, with a stronger effect under strongly stable conditions, primarily because the SBL is shallower and closer to the top of the wind turbine rotor layer. Intermittent turbulence does not have a significant impact on mean power generation and wake recovery because the relevant intermittent turbulent structures in this study only affect the bottom half of the rotor disk. Power production is, however, more variable during periods of elevated turbulence, demonstrating the impact of SBL intermittency. This study uses an idealized configuration, focusing on LES model performance and physical understanding, with the goal of informing future simulations of the conditions observed during the American Wake Experiment.

Energy - Wind↗
DOE OSTI2020

Weak scaling of the contact distance between two fluctuating interfaces with system size

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ* depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ* scales weakly with system size, i.e., the dependence of ℓ* on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim L→∞ (ℓ*/L) = 0. In particular, for (2+1)-dimensional interfaces ℓ* is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. Overall, this weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the “NIMROD benchmark” problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Progress on Demonstration of a MOOSE-Based Coupled Capability for Hot Channel Factors in Fast Reactors

Hot channel factors (HCFs) are computed values that account for the impact on predicted peak fuel, cladding, and coolant temperatures due to uncertainties in the as-built reactor’s material properties and geometry as well as uncertainties due to modeling approximations. Reduction in computed HCF values via reduction or elimination of modeling approximations may translate to significant economic savings if the reactor power can be raised due to the extra temperature margin gained. While limited historical datasets exist for sodium-cooled fast reactors (SFRs), there are no available HCF data for lead-cooled fast reactors (LFRs) outside of work generated previously within NEAMS. The computation of HCFs involves insights from reactor physics, thermal fluids and heat conduction calculations to determine how the peak temperatures respond to various uncertainties in the design. Due to the significant advantages for multi-physics coupling offered by the MOOSE framework, Griffin (MOOSE-based reactor physics code), MOOSE Heat Conduction Module, and Cardinal (MOOSE-wrapped multi-physics application which includes the NekRS thermal fluids code) are being coupled together using the MOOSE MultiApp System to develop a highfidelity multi-physics modeling capability for HCF simulations. This high-fidelity coupling workflow may also be beneficial for other fast reactor applications in the future. In previous work, Griffin and NekRS were individually assessed to ensure the necessary capabilities were in place. This work describes initial efforts to couple the codes (including folding in the MOOSE Heat Conduction Module) and determining the workflow for the perturbed calculations which will leverage the Stochastic Tools Module (STM). To our knowledge, this is the first coupling of Griffin and NekRS as well as the first exploratory use of Stochastic Tools Module for Cardinal. In this report, the neutronics code Griffin, the heat conduction solver in MOOSE, and the MOOSE-wrapped application containing NekRS (Cardinal) are linked together to demonstrate the coupled capability. Griffin and Cardinal are linked dynamically by specifying shared libraries. Different coupling hierarchies are tested for selecting the most appropriate coupling strategy. A coupling scheme is selected based on the efficiency of calculation and ease of data communication. Multiple tests are performed to choose suitable mesh structure, model configurations, scheme setup and boundary conditions to avoid loss of energy due to data interpolation between different modules or weak imposition of fluxes in finite element codes. Computational experiments are performed to study the tolerance control of each type of iteration to avoid false convergence. The coupled capability is demonstrated in both single pin and 7-pin models based on LFR materials and geometry. The study finds that the use of too large a time step size in the heat conduction module can lead to temperature oscillation even though the heat conduction equation does not have a time-derivative kernel, but only the time-dependent boundary condition. A 7-pin model without duct region achieved good convergence in the coupled calculation while a 7 pin model with duct region experienced data communication issues which need to be resolved.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Modeling Microstructural Effects on Heterogeneous Temperature Fields within Polycrystalline Explosives

The paper addresses the role of crystal anisotropy on the evolution of heterogeneous temperature fields in plastic-bonded explosives (PBXs) under conditions of weak shock. The modeling approach is based on simplified idealizations of PBX microstructure including RDX grains and estane binder regions subjected to velocity boundary conditions representative of impact conditions in situ. The constitutive description of the microstructure constituents includes a dislocation-based, anisotropic, single crystal plasticity model for the explosive grains and a linear viscoelastic model to represent the estane binder. Large suites of simulations were used to systematically study the correlation in heating of the grains with local wave dynamics, crystal orientation, and the microstructural neighborhood. These correlations were identified through the selection of characteristics of crystal anisotropy including oriented wave speeds and Taylor factor. A key observation is that the wave dispersion within a certain distance from the impact interface plays a dominant role in the temperature field. Beyond this distance, individual crystal orientations play a more dominant role, but cannot entirely account for the observed heterogeneity without consideration of the local microstructure neighborhood.

42 ENGINEERING↗
DOE OSTI2022

Dimensionless parameters for cloudy Rayleigh-Bénard convection: Supersaturation, Damköhler, and Nusselt numbers

In steady-state Rayleigh-Bénard convection, heat is transported by turbulent thermal convection from the bottom, hot surface to the top, cold surface, leading to a height-independent sensible heat flux. When water vapor is present and cloud formation occurs, there is also an additional latent heat flux. Heat transport in cloudy Rayleigh-Bénard convection depends on turbulent flow as well as the microphysical state of the clouds: specifically, whether substantial supersaturations exist and whether cloud liquid water is removed through sedimentation/precipitation. In this article we bridge between the Rayleigh-Bénard convection literature and the atmospheric literature. We express the governing equations for cloudy convection in dimensionless form, thereby explicitly identifying the governing parameters relevant to the cloudy case, including Schmidt, Damköhler, supersaturation, and sedimentation numbers. We further connect to the atmospheric literature by obtaining a Nusselt number (dimensionless heat flux) for a cloud-convection system, directly from the conservation equations for temperature and water vapor. This flux has the same form as that identified by Zhang et al. [L. Zhang, K. L. Chong, and K.-Q. Xia, J. Fluid Mech. 874, 1041 (2019)] for convection with water vapor, but is extended to the cloudy case. For equal thermal and water vapor diffusivities, the flux corresponds to the widely used atmospheric quantities equivalent temperature and moist static energy. Using large eddy simulation (LES) of an idealized cloudy Rayleigh-Bénard convection system with fixed boundary conditions, we find that the equivalent heat flux (Nusselt number) is only weakly dependent on the microphysical details of the system, such as liquid water mixing ratio and cloud droplet number concentration. Finally, from the results, we show the vertical profiles of sensible and latent heat fluxes depend on the liquid water content, whereas the equivalent heat flux remains a constant throughout the height of the chamber.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Attribution of NAO Predictive Skill Beyond 2 Weeks in Boreal Winter

Weeks 3–6 averaged winter North Atlantic Oscillation (NAO) predictive skill in a state-of-the-art coupled climate prediction system is attributed to two principle sources: upper and lower boundary conditions linked to the stratosphere and El Niño-Southern Oscillation (ENSO), respectively. A 20-member ensemble of 45-day reforecasts over 1999–2015 is utilized, together with uninitialized simulations with the atmospheric component of the prediction system forced with observed radiative forcing and lower boundary conditions. NAO forecast skill for lead times out to 6 weeks is higher following extreme stratospheric polar vortex conditions (weak and strong vortex events) compared to neutral states. Enhanced weeks 3-6 NAO predictive skill for weak vortex events results primarily from stratospheric downward coupling to the troposphere, while enhanced skill for strong vortex events can be partly attributed to lower boundary forcing related to the ENSO phenomenon. Implications for forecast system development and improvement are discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Building a new multiphysics workflow in MOOSE: application to tritium migration, trapping and advection in TMAP8

Fusion devices are anticipated to produce and consume several kilograms of tritium per year. This rare fuel resource is both highly mobile and radioactive, making tracking inventories a priority for operation and safety. The fusion safety program at the Idaho National Laboratory has been developing the Tritium Migration and Analysis Program (TMAP), of which the latest version is a MOOSE-based application. TMAP8 is verified against its predecessors and possesses additional multi-dimensional tritium migration modeling capabilities. As we extend its capabilities towards both whole device (in multiple dimensions) and whole plant (with multiple components) simulations, the syntax of inputs must become compact, descriptive, compatible with quality assurance processes, and as error-proof as achievable. The new Physics system developed MOOSE can set up equations and instantiating them on plant components. The system permits the automatic definition of complex discretization with a consistency between object parameters achieved programmatically. The Physics system can currently instantiate the equations for heat conduction and Navier Stokes weakly compressible flow. In MOOSE-terms, it automates the definition of kernels, boundary conditions, and several core and helper materials and fields. As part of this effort, Physics classes were developed for tritium migration, trapping and advection within either a multi-dimensional Navier Stokes fluid dynamics simulation, or a 1D thermal hydraulics piping system. In this presentation, we will showcase the new syntax, its application to several verification and validation cases which were already studied using the classical TMAP8 syntax, and a demonstration of the new coupling capabilities for the migration of tritium into blanket coolant channels and the subsequent advection into the coolant loop.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Atmospheric Turbulent Intermittency Over the Arctic Sea‐Ice Surface During the MOSAiC Expedition

Turbulent motions in the Arctic stable boundary layer are characterized by intermittency, but they are rarely investigated due to limited observations, in particular over the sea‐ice surface. In the present study, we explore the characteristics of turbulent intermittency over the Arctic sea‐ice surface using data collected during the Multidisciplinary drifting Observation for the Study of Arctic Climate expedition from October 2019 to September 2020. We first develop a new algorithm, which performs well in identifying the spectral gap over the Arctic sea‐ice surface. Then the characteristics of intermittency are investigated. It is found that the strength of intermittency increases under the conditions of light surface wind speed, small surface wind speed gradient, and strong surface air temperature gradient. The momentum flux, sensible heat flux, and latent heat flux calculated by raw eddy‐covariance fluctuations are overestimated by 3%, 10%, and 24%, respectively, because submesoscale motions are included. Furthermore, the characteristics of the atmospheric boundary layer structure under various intermittency conditions reveal that strong low‐level jets are favorable to surface turbulent motions that result in weak intermittency, while strong temperature inversions above the surface layer suppress surface turbulent motions and lead to strong intermittency.

54 ENVIRONMENTAL SCIENCES↗