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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A comparison of Eulerian and semi-Lagrangian approaches for modeling stream water quality

This paper describes and compares some of the advantages and limitations of Eulerian and Lagrangian approaches to water quality modeling and introduces a mixed Eulerian-Lagrangian (or semi-Lagrangian) methodology that captures the strengths of both approaches. The semi-Lagrangian modeling approach is applied to advection-dominated rivers, and flexibly ensures unconditional stability for all time step durations and grid segmentations. The semi-Lagrangian modeling approach is demonstrated by applying it to estimate the dissolved oxygen concentrations in the Sava River in Slovenia, focusing on aspects of the methodology and findings that would be of broad interest to managers of water quality in fluvial water bodies. Results of comparisons of the semi-Lagrangian model with the Eulerian-based QUAL2K model in steady and non-steady scenarios demonstrate that while both models are fully capable of producing satisfactory results when optimally configured, the semi-Lagrangian approach offers accuracy and stability without sensitivity to the interaction of time step size and computational grid segmentation scheme.

Sava River↗
DOE OSTI2024

Stabilized bases for high-order, interpolation semi-Lagrangian, element-based tracer transport

In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A semi-Lagrangian method for detecting and tracking deep convective clouds in geostationary satellite observations

Automated methods for the detection and tracking of deep convective clouds in geostationary satellite imagery have a vital role in both the forecasting of severe storms and research into their behaviour. Studying the interactions and feedbacks between multiple deep convective clouds (DCC), however, poses a challenge for existing algorithms due to the necessary compromise between false detection and missed detection errors. We utilise an optical flow method to determine the motion of deep convective clouds in GOES-16 ABI imagery in order to construct a semi-Lagrangian framework for the motion of the cloud field, independently of the detection and tracking of cloud objects. The semi-Lagrangian framework allows severe storms to be simultaneously detected and tracked in both spatial and temporal dimensions. For the purpose of this framework we have developed a novel Lagrangian convolution method and a number of novel implementations of morphological image operations that account for the motion of observed objects. These novel methods allow the accurate extension of computer vision techniques to the temporal domain for moving objects such as DCCs. By combining this framework with existing methods for detecting DCCs (including detection of growing cores through cloud top cooling and detection of anvil clouds using brightness temperature), we show that the novel framework enables reductions in errors due to both false and missed detections compared to any of the individual methods, reducing the need to compromise when compared with existing frameworks. The novel framework enables the continuous tracking of anvil clouds associated with detected deep convection after convective activity has stopped, enabling the study of the entire life cycle of DCCs and their associated anvils. Furthermore, we expect this framework to be applicable to a wide range of cases including the detection and tracking of low-level clouds and other atmospheric phenomena. In addition, this framework may be used to combine observations from multiple sources, including satellite observations, weather radar and reanalysis model data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields

Here, we extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chacón et al., J. Comput. Phys ., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ $\ggg$ 1 (with $\mathcal{X}$∥, $ \mathcal{X}$⟂ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. Further, the implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ~ (NΔt) 1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ = 10 10 ) .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimization-based, property-preserving algorithm for passive tracer transport

Here we present a new optimization-based property-preserving algorithm for passive tracer transport. The algorithm utilizes a semi-Lagrangian approach based on incremental remapping of the mass and the total tracer. However, unlike traditional semi-Lagrangian schemes, which remap the density and the tracer mixing ratio through monotone reconstruction or flux correction, we utilize an optimization-based remapping that enforces conservation and local bounds as optimization constraints. In so doing we separate accuracy considerations from preservation of physical properties to obtain a conservative, second-order accurate transport scheme that also has a notion of optimality. Moreover, we prove that the optimization-based algorithm preserves linear relationships between tracer mixing ratios. We illustrate the properties of the new algorithm using a series of standard tracer transport test problems in a plane and on a sphere.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

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

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

Chen, Jiajie↗
DOE OSTI2023

Control of Fractional Diffusion Problems via Dynamic Programming Equations

In this study, we explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation, we use the Hamilton–Jacobi–Bellman equation. It is well known that this approach suffers from the curse of dimensionality, and to mitigate this problem we couple semi-Lagrangian schemes for the discretization of the dynamic programming principle with the use of Shepard approximation. This coupling enables approximation of high-dimensional problems. Numerical convergence toward the solution of the continuous problem is provided together with linear and nonlinear examples. The robustness of the method with respect to disturbances of the system is illustrated by comparisons with an open-loop control approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Comparison of atmospheric radionuclide dispersion models for a risk-informed consequence-driven advanced reactor licensing framework

Current nuclear facility emergency planning zones (EPZs) are based on outdated distance-based criteria, predating comprehensive dose and risk-informed frameworks. Recent advancements in simulation tools have permitted the development of site-specific, dose, and risk-based consequence-driven assessment frameworks. This study investigated the computation of advanced reactor (AR) EPZs using two atmospheric dispersion models: a straight-line Gaussian plume model (GPM) and a semi-Lagrangian Particle in Cell (PIC). Two case studies were conducted: (1) benchmarking the NRC SOARCA study for the Peach Bottom Nuclear Generating Station and (2) analyzing an advanced INL Heat Pipe Design A microreactor's end-of-cycle inventory. The dose criteria for both cases were 10 mSv at mean weather conditions and 50 mSv at 95th percentile weather conditions at 96 h post-release. Results demonstrated that GPM and PIC estimated similar mean peak dose levels for large boiling water reactors in the farfield case, placing EPZ limits beyond current regulations. For ARs with source terms remaining in the nearfield, PIC modeling without specific nearfield considerations could result in excessively high doses and inaccurate EPZ designations. PIC dispersion demonstrated an order of magnitude higher estimate of nearfield inhalation dose contribution when compared to GPM results. Furthermore, both models significantly reduced EPZ sizing within the nearfield. Thus, reductions in the AR source term may eliminate the need for a separate EPZ.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2026

Quantum kinetic modeling of KEEN waves in a warm-dense regime

We report the first fully kinetic, quantum study of kinetic electrostatic electron nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrows harmonic locking to the fundamental, and hastens post-drive decay. Electrons are evolved with a second-order Strang-split 1D1V Wigner–Poisson solver that couples conservative semi-Lagrangian WENO advection to an analytic Fourier space update for the non-local Wigner term, while ions remain classical. We focus on collisionless dynamics in a weakly coupled regime, providing a controlled baseline before collisional extensions. Short, frequency-tuned ponderomotive pulses drive KEEN formation in a uniform Maxwellian plasma; as the dimensionless quantum parameter H rises from the classical limit to values relevant to warm-dense matter, doped semiconductors, and 2D electron systems, the drive threshold increases, higher harmonics are damped, trapped electron vortices diffuse, and the subplasma electrostatic energy relaxes to a lower stationary level, as confirmed by continuous wavelet analysis. These microscopic changes carry macroscopic weight. Ignition-scale capsules now compress matter to regimes where the electron de Broglie wavelength rivals the Debye length, making classical kinetic descriptions insufficient. By extending KEEN physics into this quantum domain, our results offer a potential diagnostic of non-equilibrium electron dynamics for next-generation inertial-confinement designs and high-energy-density platforms, indicating that predictive fusion modeling may benefit from the integration of kinetic fidelity with quantum effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Energy Exascale Earth System Model v2.1.0

First release of version 2.1 of the Energy Exascale Earth System Model. [ATM] The atmosphere component remains EAM. There are no major changes in the default configuration since 2.0. New features include: A semi-lagrangian tracer transport for theta-l dycore, a new algorithm for finding the tropopause, new RRM mesh configurations. Add and update SSP370 and SSP585 cases. Restore the FIDEAL case. [LAND] The land component is ELM. There are no major changes in the default configuration since 2.0. Several option features have been added including: implementation of topography-based subgrid structure (topounits) and accompanying parameterizations and atmospheric forcing downscaling methods; a new plant hydraulics scheme; two-way land-river hydrological coupling through the infiltration of floodplain water; an implementation of perennial crops; updates to the SNICAR-AD snow radiative transfer model; and implementation of soil erosion and sediment yield in ELM-Erosion. Each of these new changes is modular in design and can be turned on or off as the user specifies; they are currently being tested in different “BGC” configurations. [OCEAN] The ocean component remains MPAS-Ocean. Major change since version 2.0 include the addition of the Fox-Kemper et al. 2011 parameterization for submesocale eddies, a correction for barotropic thickness consistency that reduces divergence noise, and the addition of an ocean carbon conservation analysis member. [SEAICE] The sea-ice component remains MPAS-Seaice. Major changes since version 2.0 include: A correction to how shortwave parameters are interpolated in the snicar-ad 5-band radiation scheme, the addition of a sea ice carbon conservation analysis member, updates to the default sea ice biogeochemistry namelist parameters to be consistent with version 2.0 improvements to nitrogen cycling and a correction in the ice-ocean dissolved organic nitrogen coupling. [LAND ICE] The land-ice component remains MPAS-Albany-landIce (MALI). Major changes since 2.0 include an update to the MALI version and the Greenland mesh.[RIVER] The river model is MOSART. There are no major changes in the default configuration since 2.0. A major new optional feature is two-way river-ocean hydrological coupling between MOSART and MPAS-O. This change can be turned on or off as the user specifies, and is being tested in different configurations. [COUPLER] The coupler remains cpl7/MCT. Major changes since version 2.0 include: Carbon budget calculated when heat/water budgets active. Fix a bug in land-atm fluxes for tri-grid configurations. [OTHER] a small bug in the zenith angle calculation was fixed in the data models.

ECP↗
DOE OSTI2022

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

Abstract The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed $$u$$ u – $$p$$ p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

Baek, Jonghyuk↗