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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗
DOE OSTI2021

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2022

On the Response of a Herschel–Bulkley Fluid Due to a Moving Plate

In this paper, we study the boundary-layer flow of a Herschel–Bulkley fluid due to a moving plate; this problem has been experimentally investigated by others, where the fluid was assumed to be Carbopol, which has similar properties to cement. The computational fluid dynamics finite volume method from the open-source toolbox/library OpenFOAM is used on structured quad grids to solve the mass and the linear momentum conservation equations using the solver “overInterDyMFoam” customized with non-Newtonian viscosity libraries. The governing equations are solved numerically by using regularization methods in the context of the overset meshing technique. The results indicate that there is a good comparison between the experimental data and the simulations. The boundary layer thicknesses are predicted within the uncertainties of the measurements. The simulations indicate strong sensitivities to the rheological properties of the fluid.

36 MATERIALS SCIENCE↗
DOE OSTI2024

One-shot omnidirectional pressure integration through matrix inversion

In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now 'fast-forwarded' to the 'infinity' iteration, leading to a different matrix equation that can be solved in a single step, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of ~10 6 when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of ~10 9 points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a boundary condition where the boundary points are treated as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

SWinzip v. 2.0

SWinzip is a Matlab and C++ library for scientific lossy data compression and reconstruction using compressed sensing and tree-wavelets transforms. These methods are known for their large compression and usefulness in data analytics such as features extraction. Compressed sensing and wavelets methods rely heavily on sparse and dense linear algebra operations implemented through the Boost codes in our library. SWinzip accommodates data represented on both regular grids (e.g. image data) and point-clouds (e.g. unstructured meshes). In SWinzip v2.0, there is more focus on wavelet compression and the following features are added: - The matrix-free (direct) wavelet transform is implemented in both C++ and Matlab. A threshold-based compression can now be used. Examples for distributed compression are also added. - Python implementation of Alpert wavelet transforms - Field data comparison using wavelets in Matlab with global and local metrics

Solloum, Maher↗
DOE OSTI2026

CHESS 2025: Orthorectified airborne RGB imagery from NEON AOP surveys

This dataset provides Level 1 (L1) and Level 3 (L3) orthorectified Red-Green-Blue (RGB) imagery collected for the 2025 Colorado Headwaters Ecological Spectroscopy Study (CHESS). This high-resolution imagery is a photographic record of red, green, and blue visible light from sunlight reflected off of the Earth’s surface. The data comprise full-color images of the ground surface and are primarily intended to provide context to imaging spectroscopy and light detection and ranging (LiDAR) data. The data were acquired over three study domains in the Upper Gunnison river basin: the upper East River watershed (CRBU); Almont Triangle and Taylor Canyon (ALMO); and Upper Taylor River watershed (UPTA) between 2025-06-13 and 2025-07-15. RGB images were acquired using the PhaseOne IXM-RS150F high-resolution digital camera onboard the National Ecological Observatory Network (NEON) Airborne Observation Platform (AOP). The package data include both an L1 product comprising one camera frame per file and an L3 mosaic aligned to the Universal Transverse Mercator (UTM) Zone 13N grid and the World Geodetic System (WGS) 84 projection. Both products are provided in geotif (.tif) format at 0.1 m ground resolution. The bulk of the imagery was collected during the main CHESS field campaign from June 13 to July 15, 2025. Additional images of a portion of the Upper Taylor (UPTA) domain were collected on September 18, 2025, to fill gaps in imagery identified after the main campaign was complete. RGB camera imagery is not radiometrically calibrated, and therefore pixel values should not be exploited for scientific analysis. Pixel values have undergone a manual adjustment to enhance feature identification. The imagery is rigorously geolocated which does allow for reliable geometric information to be retrieved. To generate the orthorectified imagery, the NEON AOP camera captured visible spectrum in red, green, and blue bands. The raw images were then processed using NEON’s camera orthorectification workflow. A boresight calibration flight was made to build a complete camera, distortion, and alignment model. Color balance/white balance and exposure correction were applied to the raw RGB images. The corrected images were orthorectified by ray-tracing image pixels to a lidar-derived digital surface model (DSM) mesh using the refined camera model, outputting orthorectified raster pixels on a regular grid. Flightline-level data were mosaicked by selecting per-pixel contributions from overlapping orthorectified images using line-of-sight (LOS) zenith angle minimization to reduce edge distortions. CHESS Project Description: The Colorado Headwaters Ecological Spectroscopy Study (CHESS) comprised a multi-week airborne remote sensing and field observation campaign in the Upper Gunnison Basin, Colorado, conducted in June and July of 2025. Airborne remote sensing was conducted by the National Ecological Observatory Network Airborne Observation Platform (NEON AOP), concurrent with a field campaign run by the Rocky Mountain Biological Laboratory (RMBL), the Lawrence Berkeley National Laboratory (LBNL) and SLAC National Accelerator Laboratory Watershed Function Science Focus Area (SFA), and NASA-JPL (Jet Propulsion Laboratory) Earth Surface Mineral Dust Source Investigation (EMIT) program. Between June 10 and July 18, 2025, the NEON AOP flight team collected high-resolution aerial imaging spectroscopy and Light Detection and Ranging (LiDAR) data over three domains: the Upper East River (CRBU), Almont Triangle (ALMO), and the Upper Taylor Basin (UPTA). In coordination with the flights, a field campaign acquired ground-truth observations, including observations of vegetation composition, foliar traits, forest demography, and subsurface properties in 18 core sampling areas within the domains. Additional surface water observations were taken at over 380 point locations. All CHESS campaign datasets can be found within the CHESS ESS-DIVE data portal: https://data.ess-dive.lbl.gov/portals/chess. Funding Acknowledgement: Field and remote-sensing data acquisition was performed under a grant from the National Aeronautics and Space Administration (80NSSC24K1005). This work was also supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

2018 NEON and 2025 CHESS Campaigns↗
DOE OSTI2025

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Fast, Nondestructive and Precise Biomass Measurements Are Possible Using Lidar-Based Convex Hull and Voxelization Algorithms

Light detection and ranging (lidar) scanning tools are available that can make rapid digital estimations of biomass. Voxelization and convex hull are two algorithms used to calculate the volume of the scanned plant canopy, which is correlated with biomass, often the primary trait of interest. Voxelization splits the scans into regular-sized cubes, or voxels, whereas the convex hull algorithm creates a polygon mesh around the outermost points of the point cloud and calculates the volume within that mesh. In this study, digital estimates of biomass were correlated against hand-harvested biomass for field-grown corn, broom corn, and energy sorghum. Voxelization (r = 0.92) and convex hull (r = 0.95) both correlated well with plant dry biomass. Lidar data were also collected in a large breeding trial with nearly 900 genotypes of energy sorghum. In contrast to the manual harvest studies, digital biomass estimations correlated poorly with yield collected from a forage harvester for both voxel count (r = 0.32) and convex hull volume (r = 0.39). However, further analysis showed that the coefficient of variation (CV, a measure of variability) for harvester-based estimates of biomass was greater than the CV of the voxel and convex-hull-based biomass estimates, indicating that poor correlation was due to harvester imprecision, not digital estimations. Overall, results indicate that the lidar-based digital biomass estimates presented here are comparable or more precise than current approaches.

Environmental Sciences & Ecology↗
DOE OSTI2020

Wavelet-based local mesh refinement for rainfall–runoff simulations

A wavelet-based local mesh refinement (wLMR) strategy is designed to generate multiresolution and unstructured triangular meshes from real digital elevation model (DEM) data for efficient hydrological simulations at the catchment scale. The wLMR strategy is studied considering slope- and curvature-based refinement criteria to analyze DEM inputs: the slope-based criterion uses bed elevation data as input to the wLMR strategy, whereas the curvature-based criterion feeds the bed slope data into it. The performance of the wLMR meshes generated by these two criteria is compared for hydrological simulations; first, using three analytical tests with the systematic variation in topography types and then by reproducing laboratory- and real-scale case studies. The bed elevation on the wLMR meshes and their simulation results are compared relative to those achieved on the finest uniform mesh. Repeated analytical tests show that the slope- and curvature-based criteria are equally effective with the wLMR strategy, and that it is easier to decide which criterion to take in relation to the (regular) shape of the topography. For the realistic case studies: (i) slope analysis provides a better metric to assess the correlation of a wLMR mesh to the fine uniform mesh and (ii) both criteria predict outlet hydrographs with a close predictive accuracy to that on the uniform mesh, but the curvature-based criterion is found to slightly better capture the channeling patterns of real DEM data.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Boundary-consistent B-spline filtering schemes and application to high-fidelity simulations of turbulence

A filtering operation, based on B-spline discretizations, is introduced to target weakly growing mesh-scale oscillations that can arise in high-fidelity turbulence simulations. This is a spectral regularization that can be described using the singular values of a banded matrix operator, with the filtering strength set by a scalar- or vector-valued penalty parameter. The penalty parameter can be specified though it can also be advantageously selected to minimize the generalized cross validation (GCV) measure of distance between the pre- and post-filtered solutions. Efficient algorithms are developed to compute both the scalar and vector penalty parameters. The B-spline filter has a sharper localization to high-wavenumber than compact or explicit filters of the same stencil width and is demonstrated for solutions of the Burgers' equation, decaying Burgers' turbulence, and compressible Navier–Stokes turbulent channel flow. Furthermore, these simulations confirm the scheme's numerical stability and ability to narrowly target the high wavenumber components of numerical solutions. An advantage over finite-difference filters is that these B-spline filters are stable on bounded domains and even preserve formal order of accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A $C^1$-Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-Field Equation

We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-field (HOPF) equation relies on the design of an arbitrary-order accurate, virtual element space with $C^1$ global regularity. Such regularity is guaranteed by taking the values of the virtual element functions and their full gradient at the mesh vertices as degrees of freedom. Attaining high-order accuracy requires also edge polynomial moments of the trace of the virtual element functions and their normal derivatives. In this work, we detail the scheme construction, and prove its convergence by deriving error estimates in different norms. A set of representative test cases allows us to assess the behavior of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Meshfree Methods

Meshfree methods have undergone substantial development and have received much attention in the last two decades. This new family of numerical methods is designed to inherit the main advantages of the finite element method such as compact supports of shape functions and good approximation properties while, at the same time, overcome the main disadvantages of the finite element method caused by the mesh dependence. The meshfree methods share a common feature that no mesh is needed and shape functions are constructed from sets of points, thus eliminating the need for time consuming mesh generation. The most significant advantage of meshfree methods is the flexibility in customizing approximation functions for desired regularity and for capturing essential physics and features of the particular problems of interest. Adaptivity formulation and multiple-scale solution strategies also can be implemented with relative ease. It has become clear that the meshfree methods provide considerable advantages over the conventional finite element methods in solving problems involving moving discontinuities, evolving material interfaces, multiple-scale phenomena, large material distortion and structural deformation, and fracture and damage processes. This Chapter gives an overview of many classes of meshfree methods, with more detailed discussions on Smoothed Particle Hydrodynamics (SPH), the Reproducing Kernel Particle Method (RKPM), Peridynamics (PD), the Material Point Method (MPM), as well as their applications in various challenging engineering problems.2

Chen, Jiun-Shyan↗
DOE OSTI2023

Wassersplines for Neural Vector Field-Controlled Animation

Much of computer-generated animation is created by manipulating meshes with rigs. While this approach works well for animating articulated objects like animals, it has limited flexibility for animating less structured free-form objects. Here we introduce Wassersplines, a novel trajectory inference method for animating unstructured densities based on recent advances in continuous normalizing flows and optimal transport. The key idea is to train a neurally-parameterized velocity field that represents the motion between keyframes. Trajectories are then computed by advecting keyframes through the velocity field. We solve an additional Wasserstein barycenter interpolation problem to guarantee strict adherence to keyframes. Our tool can stylize trajectories through a variety of PDE-based regularizers to create different visual effects. We demonstrate our tool on various keyframe interpolation problems to produce temporally-coherent animations without meshing or rigging.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

MOOSE Optimization Module Overview: Application to Residual Stress Inversion in Nuclear Fuel Plates

Manufacturing methods, material selections and unique plate geometries used in low enriched uranium plate fuels for the High Performance Research Reactor (HPRR) have led to concerns about the residual stresses effect on bond strength of the fuel/cladding interfaces and overall fuel performance under irradiation. The current HPRR plate fuel test program performed residual stress calculations using the contour method with experimental displacement data obtained by incrementally cutting the plate fuel. In this work, we use a gradient based inverse optimization module developed within the MOOSE framework to estimate normal and shear residual stresses within the plate fuels using displacement data taken from a cut placed in the HPRR fuel plate. These results are verified against residual stress calculations obtained from the contour method. The inversion protocol used in this work utilizes two meshes to separately discretize the physics and parameter space. This allows a fine mesh to be used to fully resolve the physics and geometry of the forward problem. A coarser mesh is used to resolve the parameter space with spatially varying mesh density determined from a sensitivity analysis. The adaptive resolution of the parameter space essentially has the effect of regularization as it is designed to achieve the bias-variance tradeoff.

42 ENGINEERING↗