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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Rigidity of MHD equilibria to smooth incompressible ideal motion near resonant surfaces

In ideal MHD, the magnetic flux is advected by the plasma motion, freezing flux-surfaces into the flow. An MHD equilibrium is reached when the flow relaxes and force balance is achieved. We ask what classes of MHD equilibria can be accessed from a given initial state via smooth incompressible ideal motion. It is found that certain boundary displacements are formally not supported. This follows from yet another investigation of the Hahm–Kulsrud–Taylor (HKT) problem, which highlights the resonant behaviour near a rational layer formed by a set of degenerate critical points in the flux-function. When trying to retain the mirror symmetry of the flux-function with respect to the resonant layer, the vector field that generates the volume-preserving diffeomorphism vanishes at the identity to all order in the time-like path parameter.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Dyn$\mathrm{AMO}$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Here we introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

Algebraic Nonoverlapping Domain Decomposition Methods for Stabilized FEM and FV Discretizations

We consider preconditioning methods for convection dominated fluid flow problems based on a nonoverlapping Schur complement domain decomposition procedure for arbitrary triangulated domains. The triangulation is first partitioned into a number of subdomains and interfaces which induce a natural 2 x 2 partitioning of the p.d.e. discretization matrix. We view the Schur complement induced by this partitioning as an algebraically derived coarse space approximation. This avoids the known difficulties associated with the direct formation of an effective coarse discretization for advection dominated equations. By considering various approximations of the block factorization of the 2 x 2 system, we have developed a family of robust preconditioning techniques. A computer code based on these ideas has been developed and tested on the IBM SP2 using MPI message passing protocol. A number of 2-D CFD calculations will be presented for both scalar advection-diffusion equations and the Euler equations discretized using stabilized finite element and finite volume methods. These results show very good scalability of the preconditioner for various discretizations as the number of processors is increased while the number of degrees of freedom per processor is fixed.

Barth, Timothy J.↗
NASA NTRS1986

Higher-order flux difference splitting schemes for the Euler equations using upstream interpolations

A class of explicit two time-level, 2p + 1 space-point, (2p 1)-th order, upwind-biased flux difference splitting schemes are proposed for the numerical advection based on Lagrange's interpolation, and the method is an accord with the physical domain of dependence. A normalized Jacobian coefficient matrix is introduced to convert the schemes to hyperbolic systems of conservation laws, and approaches to make the higher-order schemes total variation stable are discussed. Accuracy and stability of the present schemes are examined, and implicit total variation diminishing schemes are developed for steady-state calculations.Application to gasdynamic problems for both steady and unsteady flows covering a wide range of Mach numbers is considered, and results for a blast wave passing a cylinder, and head-on collision of two blast waves over a circular arc, are presented. The flow patterns were found to be symmetric, and good resolution of flow structures was obtained.

Yang, J. Y.↗
DOE OSTI2025

Integrated Molten Salt Reactor Modeling Capabilities in NEAMS Thermal Hydraulics Tools

The DOE neams program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad range of advanced reactor concepts. The research and development approach under the thermal fluids technical area synergistically combines three length and time scales in a hierarchical multi-scale approach. To enable multi-scale thermal fluids capability using these codes, a key joint effort has been underway to develop an integrated system- and engineering-scale thermal fluids analysis capability, through integration of SAM and Pronghorn codes, both based on the MOOSE framework. This report summarizes recent advances in developing an integrated system- and engineering-scale modeling capability for the msr concept, which has gained significant interest in recent years. A consistent framework was established by coupling Pronghorn and SAM through the Saline interface, with thermophysical properties provided by the Molten Salt Thermal Property Database (MSTDB-TP). Further improvements were made to the coupling schemes and domain-overlapping strategies, enhancing the stability and robustness of multi-code simulations. Verification and validation efforts demonstrate the accuracy of this integration across a range of benchmark problems, including one-dimensional heated pipe flows, three-dimensional natural convection loops with evolving isotopic compositions, and \gls{msre} demonstration cases. Within Pronghorn, new capabilities were introduced to model corrosion and noble-metal plating phenomena, supported by an extended thermal-hydraulics framework and refined turbulence treatments. To capture two-phase flow behavior, a multiphase Euler–Euler model was implemented in Pronghorn, including advanced closure relations, high-resolution advection techniques, and capillary force reconstruction. Preliminary verification cases confirm the fidelity of the approach, while planned validation efforts target canonical multiphase benchmarks and application to msr components such as the msre pump bowl. Finally, updates to SAM’s msr mass transfer modeling were extended to consider noble gas migration into porous structures like graphite. The point kinetics model was updated to include reactivity feedback contributions from any defined species, such as xenon. The gas transport model was expanded for applicability to gas mixtures, bubble efflux phenomena, and species transport between liquid and gas phases. A selection of multi-scale Sherwood number correlations from MOSCATO/NekRS and multi-phase correlations from literature have been added for improved accuracy in calculating mass transfer coefficients. A companion effort on developing system-level redox corrosion has also been incorporated into SAM. Collectively, these enhancements strengthen the predictive capability of SAM and Pronghorn for simulating MSR thermal-hydraulics, corrosion, multiphase behavior, and fission-product transport, providing a more complete toolset for design, safety analysis, and licensing support of next-generation \gls{msr}s.

42 - ENGINEERING↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Radiological Performance Modeling: Platform Comparison

Zapadnoe Uranium Mill Tailings Site, Pridneprovsky Chemical Plant Ukraine: Two exposure scenarios were utilized to develop performance assessment models in GoldSim and NORMALYSA. The first scenario is an onsite worker exposed to radioactivity through external ground irradiation as well as radon and radioactive dust inhalation. The second being an offsite Resident 300 years after institutional control exposed through the ingestion of garden vegetables irrigated by contaminated ground water, ingestion of fish from Konoplyanka River, and agricultural activities in contaminated garden. NORMALYSA utilizes a modular interface to connect extensive pre-created modules to develop contaminant transport and risk assessment models for safety assessments and performance assessments at NORM and legacy sites. Developed by Facilia AB, the program was tested with the creation of the Zapadnoe model under the International Atomic Energy Agency MODARIA Il Working Group 1 (WG1). Default values are provided for input parameters where site specific data and distributions lack. Probabilistic simulations and inputs are limited to parameters with assigned Gaussian probability functions. Similar results for transient worker inhalation dose were found in comparison with the Zapadnoe GoldSim model. However, the NORMALYSA model has results larger by an order of magnitude for external radiation in the transient worker and for aquatic food ingestion, inhalation, and garden food ingestion to the resident. Performance Assessment Modeling: Radiological performance models promote good management and support in remediation and environmental decision making by optimizing radioactive waste disposal site performance. a performance assessment model of the Zapadnoe uranium mill tailings site and a model for calculating authorized limits at Los Alamos National Laboratory are created to demonstrate and highlight the respective capabilities of three modeling platforms: GoldSim, NORMALYSA, and RESRAD-Onsite. GoldSim is a general-purpose modeling platform with the ability to simulate site-specific FT radionuclide transport and risk assessment using a graphical interface to create and link elements that act as indivisible building blocks of the model. The Zapadnoe performance assessment model created in GoldSim is composed of input parameters collected from site specific parameters from WG1 as well as standard assumptions seen in the Generic PA Model from Neptune and Company. The multivariate Zapadnoe simulation contains both deterministic and probabilistic simulation capabilities with the ability to quantitatively represent the uncertainty and associated risks of the site via the Monte Carlo simulation method. Model parameters, documentation, and assumptions are built directly into the model creating a transparent, reproducible, and more purposeful site specific model. To demonstrate this, an ingestion of water pathway was included in addition to the exposure pathways included in the NORMALYSA model. GoldSim offers a wide variety of probability distributions to choose from as well as many tools to visualize the uncertainty of the models and explore which pathways and radionuclides dominate dose. In contrast to the NORMALYSA model, the GoldSim model uses dynamic simulation to calculate tritium concentrations. Authorized limits support the evaluation of radiological health effects from radionuclides present in bulk contaminated soil in order to assist in the process of clearing land for release under different uses. Calculations of authorized limits in RESRAD-Onsite and GoldSim models support the evaluation for 15 radionuclides using a residential exposure scenario, indoor and outdoor inhalation of dust and vapor phase radionuclides (tritium), incidental soil ingestion, and ingestion grown fruits and Vegetables. RESRAD-Onsite, developed by Argonne National Laboratory is a dedicated computer code for calculating radiation doses and cancer risks to an individual located on top of radioactively contaminated soils. It can also be used to provide guidelines for deriving radionuclide soil levels corresponding to a specific dose criterion. The menu driven user interface facilitates selection of radionuclides and soil concentrations, as well as defines parameter values related to materials, environmental factors, and exposure pathways. The program contains radionuclide-specific data such as dose conversion factors and risk coefficients, as well as soil-water partition coefficients and transfer factors for biotic media. The GoldSim model successfully emulates the RESRAD-Onsite code using identical radiological decay and ingrowth factors, radiation dose conversion factors, and other input parameters. DE EEDE ETS Each model supports dynamic modeling of radionuclide ingrowth and decay over time, and integrate this capability with the transport of radionuclides in the environment via processes such as advection and/or diffusion in fluids, or within porous solid media, The applicability of each program is heavily dependent on project context. In the context of developing Authorized Limits, RESRAD-Onsite may be a more desirable option as it was developed for this particular application. For simple disposal or legacy sites or sites that do not need site-specific model structure, NORMALYSA may be a desirable modeling platform, GoldSim can be used to model any problem for which RESRAD or NORMALYSA is applicable, but its strength lies in its flexibility, analytical, and probabilistic capabilities.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

A Comparison of RESRAD and GoldSim Models for Assessing Radiological Dose for a RCRA Landfill - 20418

US Ecology Idaho (USEI) operates a Resource Conservation and Recovery Act (RCRA) Subtitle C, Hazardous Waste Treatment, Storage, and Disposal (TSD) Facility on a 640-acre property in Owyhee County, Idaho. USEI accepts a wide variety of RCRA-exempt low activity radioactive wastes, including naturally occurring radioactive material (NORM) and technologically enhanced NORM (TENORM) (USEI 2009). The performance of the landfill with regard to radiological operating permit requirements was previously assessed using a model constructed with the residual radioactivity (RESRAD) computer program, developed by Argonne National Laboratory for the U.S. Department of Energy (DOE). RESRAD supports the evaluation of several environmental transport pathways related to a radionuclide-contaminated soil source term, but it was not conceived as a model for the evaluation of landfill radiological performance. A more comprehensive and realistic model is desired in order to better support submissions to both the State of Idaho's Department of Environmental Quality as well as the U.S. Nuclear Regulatory Commission. A Performance Assessment (PA) computer model was developed using GoldSim software for the USEI RCRA Subtitle C landfill. The RESRAD computer model was specifically developed for calculating soil cleanup criteria and radiological dose and cancer risk from residual radioactive material in soil. To evaluate site-specific conditions, users may select from among a number of available environmental transport and exposure pathways and modify 'default' parameter values. In GoldSim, a user must construct the model 'from scratch.' However, this modeling is facilitated by a number of specialized elements available in GoldSim to support a radiological mass transport model. These include elements for defining radiological decay and ingrowth, container failure and radiological release, advective and diffusive transport, and other processes. Advantages afforded by the use of RESRAD for modeling radiological dose for a RCRA Subtitle C landfill include ease of use and reasonable flexibility in specifying site-specific conditions. GoldSim allows for considerably more flexibility and site-specificity than RESRAD, including evaluation of potentially relevant environmental transport processes not supported in RESRAD. The probabilistic modeling capabilities of GoldSim also far exceed those of RESRAD. The pros and cons of RESRAD and GoldSim for this modeling problem are explored with a focus on identifying approaches and critical factors in identifying the appropriate platform. The capabilities of RESRAD and GoldSim for mathematically modeling the disposal system will be contrasted and compared. For example, the existing RESRAD radiological safety assessment evaluated potentially complete exposure pathways related to infiltration to groundwater and upwards diffusion of radon. Additional transport pathways identified in the USEI Idaho facility Conceptual Site Model include deposition of radon decay products in cover material, root uptake of radionuclides in disposed wastes by native plants, and mixing of cover material by burrowing animals. Results of the two models and how the different transport and dose pathways affect results will be discussed. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

Influence of 3D plasmoid dynamics on the transition from collisional to kinetic reconnection

Within the resistive magnetohydrodynamic model, high-Lundquist number reconnection layers are unstable to the plasmoid instability, leading to a turbulent evolution where the reconnection rate can be independent of the underlying resistivity. However, the physical relevance of these results remains questionable for many applications. First, the reconnection electric field is often well above the runaway limit, implying that collisional resistivity is invalid. Furthermore, both theory and simulations suggest that plasmoid formation may rapidly induce a transition to kinetic scales, due to the formation of thin current sheets. Here, this problem is studied for the first time using a first-principles kinetic simulation with a Fokker-Planck collision operator in 3D. The low-β reconnecting current layer thins rapidly due to Joule heating before the onset of the oblique plasmoid instability. Linear growth rates for standard (k y = 0) tearing modes agree with semicollisional boundary layer theory, but the angular spectrum of oblique (|k y |>0) modes is significantly narrower than predicted. In the nonlinear regime, flux-ropes formed by the instability undergo complex interactions as they are advected and rotated by the reconnection outflow jets, leading to a turbulent state with stochastic magnetic field. In a manner similar to previous 2D results, super-Dreicer fields induce a transition to kinetic reconnection in thin current layers that form between flux-ropes. These results may be testable within new laboratory experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Use of satellite data and modeling to assess the influence of stratospheric processes on the troposphere

Over the past forty years, numerous linear stability studies have been performed in order to explain the origin and structure of observed waves in the atmosphere. Of these studies, only a small fraction have considered the stability of time-dependent, zonally varying flow or the influence of radiative-photochemical feedbacks on the stability of zonally uniform flow. The stability of such flows is described, and these flows may yield important information concerning the origin, structure, and transient time scales of free waves in the atmosphere. During the period 1990 to 1991, a beta-plane model that couples radiative transfer, ozone advection, and ozone photochemistry with the quasigeostrophic dynamical circulation was developed in order to study the diabatic effects of Newtonian cooling and ozone-dynamics interaction on the linear stability of free planetary waves in the atmosphere. The stability of a basic state consisting of a westward-moving wave and a zonal mean jet was examined using a linearized, nondivergent barotropic model on sphere. The sensitivity of the stability of the flow to the strength and structure of the zonal jet was emphasized. The current research is focused on the following problems: (1) examination of the finite amplitude interactions among radiation, ozone, and dynamics; and (2) examination of the role of seasonal forcing in short-term climate variability. The plans for next year are presented.

Nathan, Terrence↗
DOE OSTI2021

Science & Technology Review: The Road to Exascale Computing

At Lawrence Livermore National Laboratory, we focus on science and technology research to ensure our nation’s security. We also apply that expertise to solve other important national problems in energy, bioscience, and the environment. Science & Technology Review is published eight times a year to communicate, to a broad audience, the Laboratory’s scientific and technological accomplishments in fulfilling its primary missions. The publication’s goal is to help readers understand these accomplishments and appreciate their value to the individual citizen, the nation, and the world. The Department of Energy’s Exascale Computing Project (ECP) and Lawrence Livermore’s RADIUSS (Rapid Application Development via an Institutional Universal Software Stack) initiative benefit from strategically developed software tools. The front cover shows a simulation of advection under twisting rotation that uses high-order finite elements from Livermore’s Modular Finite Element Methods (MFEM) software library and GLVis visualization tool. On the back cover, the logo (also created with GLVis) for the MFEM project illustrates the curved mesh and sub-element resolution used in high-order simulations. MFEM and GLVis are key components of the ECP’s co-design Center for Efficient Exascale Discretizations (CEED) and RADIUSS. MFEM is also part of ECP’s Extreme-Scale Scientific Software Development Kit (xSDK).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Role of Intense Arctic Storm in Accelerating Summer Sea Ice Melt: An In Situ Observational Study

Abstract Intense storms have been more frequently observed in the Arctic during recent years, in coincidence with extreme sea ice loss events. However, it is still not fully understood how storms drive such events due to deficient observations and modeling discrepancies. Here we address this problem by analyzing in situ observations acquired during an Arctic expedition, which uniquely captured an intense storm in summer 2016. The result shows a pronounced acceleration of sea ice loss during the storm process. Diagnostic analysis indicates a net energy loss at the ice surface, not supporting the accelerated melting. Although the open water surface gained net heat energy, it was insufficient to increase the mixed‐layer temperature to the observed values. Dynamic analysis suggests that storm‐driven increase in ocean mixing and upward Ekman pumping of the Pacific‐origin warm water tremendously increased oceanic heat flux. The thermal advection by the Ekman pumping led to a warmed mixed layer by 0.05°C–0.12°C and, in consequence, an increased basal sea ice melt rate by 0.1–1.7 cm day −1 .

58 GEOSCIENCES↗
DOE OSTI2026

Optimal Transfer Operators in Algebraic Two-Level Methods for Nonsymmetric and Indefinite Problems

Consider an algebraic two-level method applied to the 𝑛-dimensional linear system 𝐴⁢𝒙 = 𝒃 using fine-space preconditioner (i.e., “relaxation” or “smoother”) 𝑀, with 𝑀 ≈ 𝐴, restriction and interpolation 𝑅 and 𝑃, and algebraic coarse-space operator 𝐴 𝑐 : = 𝑅 ∗ ⁢𝐴⁢𝑃. Then, what are the best possible transfer operators 𝑅 and 𝑃 of a given dimension 𝑛 𝑐 < 𝑛? Brannick et al. [12] showed that when 𝐴 and 𝑀 are Hermitian positive definite (HPD), the optimal interpolation is such that its range contains the 𝑛 𝑐 smallest generalized eigenvectors of the matrix pencil (𝐴, 𝑀). Recently, in Ali et al. [5] we generalized this framework to the non-HPD setting, by considering both right (interpolation) and left (restriction) generalized eigenvectors of (𝐴, 𝑀) and defining corresponding nonsymmetric transfer operators {𝑅#, 𝑃#}. Tight convergence bounds for {𝑅#, 𝑃#} are derived in spectral radius, as well as a proof of pseudo-optimality. Note, {𝑅#, 𝑃#} are typically complex valued, which is not practical for real-valued problems. Here, in this work, we build on [5], first characterizing all inner products in which the coarse-space correction defined by {𝑅#, 𝑃#} is orthogonal. We then develop tight two-level convergence bounds in these norms, and prove that the underlying transfer operators {𝑅#, 𝑃#} are genuinely optimal. As a special case, our theory both recovers and extends the HPD results from [12]. Finally, we show how to construct optimal, real-valued transfer operators in the case of that 𝐴 and 𝑀 are real valued, but are not HPD. Numerical examples arising from a discretized advection-reaction equation, wave-equation, and Stokes equations are used to verify and illustrate the theory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Synoptic/planetary-scale interactions and blocking over the North Atlantic Ocean

Work was completed on the height tendency diagnoses of two extratropical cyclones that occurred upstream from the blocking event studied previously. One developed explosively over water 60 to 36 hours before the block first appeared, while the second developed explosively over the southeastern United States during the time of block formation. In both cases, both vorticity and temperature advection were consistently important forcing mechanisms. This is in contrast to the block itself, in which vorticity advection was easily the dominant forcing mechanism. Latent heat release was also significant, accounting for about 50 percent of the total height falls in the cyclone below 850 mb. Estimates of latent heat release were greatly enhanced by coupling parameterized estimates with values derived from GOES IR data using an algorithm developed by Marshall's F. R. Robertson. Among the difficulties encountered in this work was the identification of an appropriate lower boundary condition for the solution of the height tendency equation. The zero value currently used tends to yield underestimates of the lower troposphere height tendencies. To address this problem a new diagnostic technique was developed in cooperation with Dr. Peter Zwack of the University of Quebec at Montreal. Based on an equation Dr. Zwack had previously developed (the Zwack-Okossi development equation), researchers now have a relationship that is completely consistent with the height tendency equation and provides estimates of lower boundary geostrophic vorticity or height tendencies. Finally, comparison of the SAT (satellite data) and NOSAT (no satellite data) analyses is progressing well. The present focus is on both the new diagnostic technique and the SAT/NOSAT comparisons. The former is being tested on the southeastern United States cyclone case previously mentioned and compared with the height tendency diagnoses already completed. The latter are being examined for the blocking case described in the publications cited in this summary. In addition to obtaining statistics that will allow general comparison of the two analyses, it will be possible to determine whether conclusions about the dynamics of the block development are influenced by the analysis set used.

Smith, Phillip J.↗
DOE OSTI2025

High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. Further, these solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.

42 ENGINEERING↗
NASA NTRS1985

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Engquist, B. E.↗
NASA NTRS1987

Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

Osher, Stanley↗
DOE OSTI2024

Hybridized Discontinuous Galerkin Methods for Computational Fluid Dynamics

Hybridizable Discontinuous Galerkin (HDG) methods hold promise for any applications with significant advection character, including thermal hydraulics in light water reactors and advanced reactor concepts and fluid models of plasmas in magnetic confinement fusion. Its features include natural upwinding, local element conservation, and extensibility to arbitrarily high order accuracy. In the last fiscal year we have implemented HDG in the Multiphysics Object-Oriented Simulation Environment (MOOSE). We developed a first-of-its-kind automatic static condensation system in MOOSE’s underlying finite element library libMesh which can condense out arbitrarily many internal variables. Finally, we developed the first preconditioner for HDG discretizations of the Navier-Stokes equations which shows robust performance across a wide range of problem sizes and Reynolds numbers. This preconditioner yields solution times that are equivalent to the fastest developed for industry standard finite volume methods. Moreover, the arbitrarily high-order nature of HDG makes it a prime candidate for acceleration via graphical processing units (GPUs). We believe these developments will hold significant importance for future DOE Nuclear Energy (NE) and Fusion Energy Science (FES) programs.

97 MATHEMATICS AND COMPUTING↗