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DOE OSTI2026

PFLOTRAN modeling data and scripts associated with “Refining the Hydrogeologic Framework of a Large River Corridor Model Using Waterborne Transient Electromagnetics”

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the publication “Refining the Hydrogeologic Framework of a Large River Corridor Model Using Waterborne Transient Electromagnetics” submitted to Water Resources Research (Terry et al. 2025). The data package contains the groundwater modeling dataset from PFLOTRAN software. It includes the python script for mesh generation, boundary condition setting, PFLOTRAN input deck formation and postprocessing. It couples groundwater flow and species transport for Hanford Reach river corridor and pipelines the model generation and processing. This model can be used to easily generate the model and analysis for Hanford site. It can also be adjusted to other hydrologic area with ease. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. The data package consists of 6 folders: (1) “data” contains all necessary data as input and intermediate data for processing; (2) “mesh” contains all mesh related files to generate mesh in Hanford Reach river corridor; (3) “model_run” contains the generated script for PFLOTRAN modeling; (4) “notebooks” contains all the Python script to generate the model; (5) “output” contains all the output from the computation; (6) “postprocessing” contains the Python script to generate scientific figure for manuscript. All files are .csv (comma-separated values), .h5 (HDF5 format), .in (input files), .ipynb (Jupyter notebooks), .p (Python pickle), .png (images), .PNG (images), .py (Python scripts), .pyc (Python bytecode), .r (R scripts), .sh (shell scripts), .txt (text files), .vtu (3D mesh/visualization format), .xz (compressed archive), or .zip (compressed archive).

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1993

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 5: Unsteady counterrotation ducted propfan analysis

The primary objective of this study was the development of a time-marching three-dimensional Euler/Navier-Stokes aerodynamic analysis to predict steady and unsteady compressible transonic flows about ducted and unducted propfan propulsion systems employing multiple blade rows. The computer codes resulting from this study are referred to as ADPAC-AOAR\CR (Advanced Ducted Propfan Analysis Codes-Angle of Attack Coupled Row). This document is the final report describing the theoretical basis and analytical results from the ADPAC-AOACR codes developed under task 5 of NASA Contract NAS3-25270, Unsteady Counterrotating Ducted Propfan Analysis. The ADPAC-AOACR Program is based on a flexible multiple blocked grid discretization scheme permitting coupled 2-D/3-D mesh block solutions with application to a wide variety of geometries. For convenience, several standard mesh block structures are described for turbomachinery applications. Aerodynamic calculations are based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. Steady flow predictions are accelerated by a multigrid procedure. Numerical calculations are compared with experimental data for several test cases to demonstrate the utility of this approach for predicting the aerodynamics of modern turbomachinery configurations employing multiple blade rows.

Hall, Edward J.↗

DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

A finite element algorithm for sound propagation in axisymmetric ducts containing compressible mean flow

An accurate mathematical model for sound propagation in axisymmetric aircraft engine ducts with compressible mean flow is reported. The model is based on the usual perturbation of the basic fluid mechanics equations for small motions. Mean flow parameters are derived in the absence of fluctuating quantities and are then substituted into the equations for the acoustic quantities which were linearized by eliminating higher order terms. Mean swirl is assumed to be zero from the restriction of axisymmetry. A linear rectangular serendipity element is formulated from these equations using a Galerkin procedure and assembled in a special purpose computer program in which the matrix map for a rectangular mesh was specifically coded. Representations of the fluctuating quantities, mean quantities and coordinate transformations are isoparametric. The global matrix is solved by foreward and back substitution following an L-U decomposition with pivoting restricted internally to the blocks. Results from the model were compared with results from several alternative analyses and yielded satisfactory agreement.

Abrahamson, A. L.↗

DOE OSTI2022

Numerical analysis of soot emissions from gasoline-ethanol and gasoline-butanol blends under gasoline compression ignition conditions

In the present work, computational fluid dynamics (CFD) simulations of a single-cylinder gasoline compression ignition (GCI) engine were performed to investigate the impact of blending two biofuels, ethanol and n-butanol, with gasoline on the trade-off between combustion phasing and soot emissions under low load conditions. Here, in order to represent market gasoline (RD5-87), a four-component toluene primary reference fuel (TPRF) + ethanol (ETPRF) surrogate (with 20% ethanol by mole; E20) was formulated using a neural network based octane predictor such that the surrogate had the same ethanol content, Research Octane Number (RON) and Octane Sensitivity (S). In addition, a novel skeletal kinetic mechanism for ETPRF and TPRF + n-butanol (BTPRF) blends, incorporating polycyclic aromatic hydrocarbon (PAH) chemistry, was developed. A three-dimensional (3D) engine CFD formulation employing the skeletal mechanism, adaptive mesh refinement (AMR), finite-rate chemistry approach, and hybrid method of moments (HMOM) was adopted to capture the in-cylinder combustion phenomena and soot emissions. The engine CFD model was validated against RD5-87 experimental data for a broad range of start-of-injection (SOI) timings (-21/-27/-36/-45 crank angle degrees (CAD) after top-dead center (aTDC)), with respect to in-cylinder pressure, heat release rate, combustion phasing, and soot emissions. The closed-cycle simulation results were analyzed to elucidate the non-monotonic trend of soot emissions versus SOI timing: SOI-36 > SOI-45 > SOI-21 > SOI-27. Thereafter, the validated CFD model was employed to simulate the combustion of a gasoline-ethanol blend with 45% (by mole) ethanol (E45) and a gasoline-butanol blend with 45% (by mole) n-butanol (B45) under the same operating conditions to study the effects of fuel composition and SOI timing on combustion phasing and soot emissions. The sooting propensity followed the trend: B45 > E20 > E45 at all SOI timings. Overall, it was observed that the autoignition propensity was primarily related to fuel chemistry. On the other hand, sooting propensity showed strong coupling with both fuel chemistry and physical properties, with greater impact of fuel physical properties at advanced SOI timings.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2017

Evaluation of an Eulerian multi-material mixture formulation based on a single inverse deformation gradient tensor field

We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to Lagrangian (Benson 1992) and arbitrary Lagrangian-Eulerian (ALE) methods (Donea et al. 2004), fully Eulerian methods use grids that do not change in time. Consequently, Eulerian methods do not suffer from difficulties on account of mesh entanglement, and do not require periodic, expensive, remap operations.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Pre- and postprocessing techniques for determining goodness of computational meshes

Research in error estimation, mesh conditioning, and solution enhancement for finite element, finite difference, and finite volume methods has been incorporated into AUDITOR, a modern, user-friendly code, which operates on 2D and 3D unstructured neutral files to improve the accuracy and reliability of computational results. Residual error estimation capabilities provide local and global estimates of solution error in the energy norm. Higher order results for derived quantities may be extracted from initial solutions. Within the X-MOTIF graphical user interface, extensive visualization capabilities support critical evaluation of results in linear elasticity, steady state heat transfer, and both compressible and incompressible fluid dynamics.

Oden, J. Tinsley↗

NASA NTRS1994

A Navier-Strokes Chimera Code on the Connection Machine CM-5: Design and Performance

We have implemented a three-dimensional compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the 'chimera' approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. A parallel machine like the CM-5 is well-suited for finite-difference methods on structured grids. The regular pattern of connections of a structured mesh maps well onto the architecture of the machine. So the first design choice, finite differences on a structured mesh, is natural. We use centered differences in space, with added artificial dissipation terms. When numerically solving the Navier-Stokes equations, there are liable to be some mesh cells near a solid body that are small in at least one direction. This mesh cell geometry can impose a very severe CFL (Courant-Friedrichs-Lewy) condition on the time step for explicit time-stepping methods. Thus, though explicit time-stepping is well-suited to the architecture of the machine, we have adopted implicit time-stepping. We have further taken the approximate factorization approach. This creates the need to solve large banded linear systems and creates the first possible barrier to an efficient algorithm. To overcome this first possible barrier we have considered two options. The first is just to solve the banded linear systems with data spread over the whole machine, using whatever fast method is available. This option is adequate for solving scalar tridiagonal systems, but for scalar pentadiagonal or block tridiagonal systems it is somewhat slower than desired. The second option is to 'transpose' the flow and geometry variables as part of the time-stepping process: Start with x-lines of data in-processor. Form explicit terms in x, then transpose so y-lines of data are in-processor. Form explicit terms in y, then transpose so z-lines are in processor. Form explicit terms in z, then solve linear systems in the z-direction. Transpose to the y-direction, then solve linear systems in the y-direction. Finally transpose to the x direction and solve linear systems in the x-direction. This strategy avoids inter-processor communication when differencing and solving linear systems, but requires a large amount of communication when doing the transposes. The transpose method is more efficient than the non-transpose strategy when dealing with scalar pentadiagonal or block tridiagonal systems. For handling geometrically complex problems the chimera strategy was adopted. For multiple zone cases we compute on each zone sequentially (using the whole parallel machine), then send the chimera interpolation data to a distributed data structure (array) laid out over the whole machine. This information transfer implies an irregular communication pattern, and is the second possible barrier to an efficient algorithm. We have implemented these ideas on the CM-5 using CMF (Connection Machine Fortran), a data parallel language which combines elements of Fortran 90 and certain extensions, and which bears a strong similarity to High Performance Fortran. We make use of the Connection Machine Scientific Software Library (CMSSL) for the linear solver and array transpose operations.

Jespersen, Dennis C.↗

DOE OSTI2023

Latest developments in the MOOSE fluid properties module

The fluid properties module in MOOSE serves a variety of fluid simulation applications based on MOOSE, including the MOOSE Navier Stokes module~\cite{moose_ns}, Pronghorn~\cite{pgh}, SAM~\cite{sam}, the MOOSE thermal hydraulics module, RELAP-7~\cite{relap7} and subchannel~\cite{subchannel}. It is used for coarse mesh multi-dimensional thermal-hydraulics~\cite{pgh}, 1D systems analysis~\cite{sam,relap7} in nuclear reactor analysis, and porous flow simulations~\cite{porous} for underground gas storage and water seepage. The use of consistent fluid properties across fluid flow applications facilitates coupled simulations~\cite{anl_sam_pgh}. The module offers a consistent set of interfaces to implement to create a new fluid property. There are numerous fluid properties of interest in the entirety of all fields of fluid flow simulations, and this is exacerbated by the use of different variable sets depending on the compressibility of the fluid. For single-phase fluids, the following variable sets may be used to compute fluid properties: (pressure, temperature) and (specific volume, specific internal energy). Some properties may also be computed using the (pressure, density) or the (specific volume, specific enthalpy) variable sets. In order to reduce the challenge of adding a new fluid property, properties may be implemented partially.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Numerical Investigation of a Gasoline-Like Fuel in a Heavy-Duty Compression Ignition Engine Using Global Sensitivity Analysis

Fuels in the gasoline auto-ignition range (Research Octane Number (RON) > 60) have been demonstrated to be effective alternatives to diesel fuel in compression ignition engines. Such fuels allow more time for mixing with oxygen before combustion starts, owing to longer ignition delay. Moreover, by controlling fuel injection timing, it can be ensured that the in-cylinder mixture is “premixed enough” before combustion occurs to prevent soot formation while remaining “sufficiently inhomogeneous” in order to avoid excessive heat release rates. Gasoline compression ignition (GCI) has the potential to offer diesel-like efficiency at a lower cost and can be achieved with fuels such as low-octane straight run gasoline which require significantly less processing in the refinery compared to today’s fuels. To aid the design and optimization of a compression ignition (CI) combustion system using such fuels, a global sensitivity analysis (GSA) was conducted to understand the relative influence of various design parameters on efficiency, emissions and heat release rate. The design parameters included injection strategies, exhaust gas recirculation (EGR) fraction, temperature and pressure at intake valve closure and injector configuration. These were varied simultaneously to achieve various targets of ignition timing, combustion phasing, overall burn duration, emissions, fuel consumption, peak cylinder pressure and maximum pressure rise rate. The baseline case was a three-dimensional closed-cycle computational fluid dynamics (CFD) simulation with a sector mesh at medium load conditions. Eleven design parameters were considered and ranges of variation were prescribed to each of these. These input variables were perturbed in their respective ranges using the Monte Carlo (MC) method to generate a set of 256 CFD simulations and the targets were calculated from the simulation results. GSA was then applied as a screening tool to identify the input parameters having the most significant impact on each target. The results were further assessed by investigating the impact of individual parameter variations on the targets. Overall, it was demonstrated that GSA can be an effective tool in understanding parameters sensitive to a low temperature combustion concept with novel fuels.

Pal, Pinaki↗

NASA NTRS1996

Gear crack propagation investigations

Analytical and experimental studies were performed to investigate the effect of gear rim thickness on crack propagation life. The FRANC (FRacture ANalysis Code) computer program was used to simulate crack propagation. The FRANC program used principles of linear elastic fracture mechanics, finite element modeling, and a unique re-meshing scheme to determine crack tip stress distributions, estimate stress intensity factors, and model crack propagation. Various fatigue crack growth models were used to estimate crack propagation life based on the calculated stress intensity factors. Experimental tests were performed in a gear fatigue rig to validate predicted crack propagation results. Test gears were installed with special crack propagation gages in the tooth fillet region to measure bending fatigue crack growth. Good correlation between predicted and measured crack growth was achieved when the fatigue crack closure concept was introduced into the analysis. As the gear rim thickness decreased, the compressive cyclic stress in the gear tooth fillet region increased. This retarded crack growth and increased the number of crack propagation cycles to failure.

Lewicki, David G.↗

DOE OSTI2013

Postshock Spectral Radiance Measurements in Nickel and Nickel/Aluminum Powders [Book Chapter]

Because of complications associated with temperature heterogeneities in shocked metal powders, time-resolved radiation pyrometer measurements of shock temperatures in powders with particle sizes greater than a few tens of microns cannot be made under normal laboratory conditions with uniaxial loading durations limited to about one microsecond. Fortunately, for highly porous, reactive powders, the difference between shock and postshock temperature is negligible. For loading conditions similar to those that have yielded reaction products in recovery experiments, there is no evidence of any chemical reaction in a coarse (-325 mesh) nickel/aluminum powder mixture within the first 6 μs of shock arrival, based on constraints on postshock temperatures provided by thermal radiation measurements. This result is in contrast to that for a micron-sized nickel/aluminum mixture, for which there is evidence of significant reaction on a time scale of 100 ns under similar shock loading conditions.

42 ENGINEERING↗

DOE OSTI2023

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers

We report that in the near-future noisy intermediate-scale quantum (NISQ) era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of the number of qubits used. The need to represent numeric quantities using limited resources leads to digitization errors which must be taken into account. As a first step towards quantum simulations of realistic high-energy physics problems, we explore classically the effects of digitizing elements of the $\mathrm{SU}(2)$ gauge group to a finite set. We consider several methods for digitizing the group, finding the best performance from an action-preserving projection onto a mesh. Working in (3+1) dimensions, we find that using $\sim 7$ (qu)bits to represent each $\mathrm{SU}(2)$ gauge link induces a digitization error on the order of $10\%$ in short-distance observables and $2\%$ in long-distance observables. Promisingly, our results indicate that each $\mathrm{SU}(2)$ gauge link can be represented by $\mathcal{O}(10)$ (qu)bits, from which we estimate that a $16^3$ $\mathrm{SU}(2)$ lattice could be simulated with no more than $\mathcal{O}(10^5)$ (qu)bits. Lastly, our results on digitization are also of interest as a form of lossy compression that could be used in high-performance classical computing to alleviate communications bottlenecks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1998

A Preconditioning Method for Shape Optimization Governed by the Euler Equations

We consider a classical aerodynamic shape optimization problem subject to the compressible Euler flow equations. The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous level. The Hessian (second order derivative of the cost functional with respect to the shape variables) is approximated also at the continuous level, as first introduced by Arian and Ta'asan (1996). The approximation of the Hessian is used to approximate the Newton step which is essential to accelerate the numerical solution of the optimization problem. The design space is discretized in the maximum dimension, i.e., the location of each point on the intersection of the computational mesh with the airfoil is taken to be an independent design variable. We give numerical examples for 86 design variables in two different flow speeds and achieve an order of magnitude reduction in the cost functional at a computational effort of a full solution of the analysis partial differential equation (PDE).

Arian, Eyal↗

NASA NTRS1999

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Thomas, J. L.↗

NASA NTRSDate not supplied

Towards an Automated Unstructured Grid Adaptation Workflow with VULCAN

Early work is presented for an unstructured grid adaptation workflow with VULCAN and refine. Anisotropic simplex grids are iteratively adapted to match a Riemannian metric tensor field describing desired mesh spacing. The Riemannian metric tensor field is obtained from Hessians of CFD solution output scalar sensor fields; both Mach number and static temperature sensor fields are explored. In addition, we describe a Newton-method-based solver recently implemented in VULCAN utilizing Jacobian-Free-Newton-Krylov that can be used to increase flow solver automation on early grids in the adadptation process. Hypersonic flow solutions are presented on a high Reynolds number flat plate and wall heat flux is compared against a highly resolved structured solution. Additionally, complex shock boundary-layer interaction is explored in a high Mach number compression corner and complex 3D flow phenomena are evaluated on the Boundary Layer Transition (BOLT) vehicle.

Matthew O'Connell↗

DOE OSTI2021

Considering computational speed vs. accuracy: Choosing appropriate mesoscale RVE boundary conditions

Modeling a material’s microstructure using continuum theories allows for inspection of the relationship between coarse scale and fine scale behaviors. Computational limits generally require selection of a sub-volume from a bulk sample in order to directly model the microstructure. Boundary conditions are applied to the sub-volume to mimic the excluded bulk material. Appropriate selection of boundary conditions helps effectively determine the appropriate spatial scale required of the sub-volume. Applicable boundary conditions include direct displacement, periodic, and uniform traction. While direct displacement and periodic boundary conditions are commonly used, uniform traction boundary conditions have seen limited use due to rigid body stability issues in simulations of compression or shear deformation. A new application of uniform traction boundary conditions was developed through linear constraint equations, similar to approaches employed by direct displacement and periodic boundary conditions, to quench rigid body motions with minimal interference of the relative deformation of the model. These boundary conditions were tested by compressing several synthetically generated periodic microstructures using the finite element method. Evaluating the effective stiffness along the compression axis, the direct displacement boundary condition produced the stiffest response, whereas the uniform traction boundary condition produced the most compliant. Periodic boundary conditions produced the same response for all volumes analyzed and both the direct displacement and uniform traction boundary conditions trended toward the periodic response as the domain volume increased. Computational performance was also evaluated for each boundary condition using implicit and explicit solvers. Direct displacement boundary conditions presented the lowest computational cost of all of the boundary conditions followed by periodic then uniform traction. The computational expense of periodic and uniform traction boundary conditions limited the viable spatial scale and mesh resolutions able to be simulated. Selection of appropriate boundary conditions for specific uses need to be a balance between allowable computational expense and accuracy of the method. Techniques for evaluating which boundary conditions to use are discussed.

42 ENGINEERING↗