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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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NASA NTRS2018

Sensitivity Analysis for Multidisciplinary Systems (SAMS)

This report describes the research conducted under an interagency collaboration agreement between the Aerospace Systems Directorate of the Air Force Research Laboratory (AFRL/RQ) and the Computational AeroSciences Branch of NASA Langley (NASA LaRC). Both organizations have a long-term goal of developing a modular computational system for coupling fluids and structures to enable both analysis and optimization of aerospace vehicles. Ultimately, the system should support multiple solvers within the fluid and structure domains to allow the best combination for the task at hand, as well as to allow for institutional preferences of specific software components. Towards this goal, the current research was focused on enhancing the existing modal aeroelastic analysis in the NASA FUN3D (Fully-UNstructured three-dimensional CFD (Computational Fluid Dynamics) code) software (Biedron et al. 2018), as well as developing new aeroelastic analysis and optimization capabilities based on a non-linear finite-element method. The methods and enhancements described in this document pertain to FUN3D Version 13.4.

Biedron, Robert T.↗
DOE OSTI2025

Surrogate models for linear response

Linear response theory is a well-established method in physics and chemistry for exploring excitations of many-body systems. In particular, the quasiparticle random-phase approximation (QRPA) provides a powerful microscopic framework by building excitations on top of the mean-field vacuum; however, its high computational cost limits model calibration and uncertainty quantification studies. Here, we present two complementary QRPA surrogate models and apply them to study response functions of finite nuclei. One is a reduced-order model that exploits the underlying QRPA structure, while the other utilizes the recently developed parametric matrix model algorithm to construct a map between the system’s Hamiltonian and observables. Our benchmark applications, the calculation of the electric dipole polarizability of 180 Yb and the 𝛽-decay half-life of 80 Ni, show that both emulators can achieve 0.1%–1% accuracy while offering a 6–7 orders of magnitude speedup compared to state-of-the-art QRPA solvers. These results demonstrate that the developed QRPA emulators are well positioned to enable Bayesian calibration and large-scale studies of computationally expensive physics models describing the properties of many-body systems.

Beta decay↗
NASA NTRS2014

Comparison of Computational Approaches for Rapid Aerodynamic Assessment of Small UAVs

Computational Fluid Dynamic (CFD) methods were used to determine the basic aerodynamic, performance, and stability and control characteristics of the unmanned air vehicle (UAV), Kahu. Accurate and timely prediction of the aerodynamic characteristics of small UAVs is an essential part of military system acquisition and air-worthiness evaluations. The forces and moments of the UAV were predicted using a variety of analytical methods for a range of configurations and conditions. The methods included Navier Stokes (N-S) flow solvers (USM3D, Kestrel and Cobalt) that take days to set up and hours to converge on a single solution; potential flow methods (PMARC, LSAERO, and XFLR5) that take hours to set up and minutes to compute; empirical methods (Datcom) that involve table lookups and produce a solution quickly; and handbook calculations. A preliminary aerodynamic database can be developed very efficiently by using a combination of computational tools. The database can be generated with low-order and empirical methods in linear regions, then replacing or adjusting the data as predictions from higher order methods are obtained. A comparison of results from all the data sources as well as experimental data obtained from a wind-tunnel test will be shown and the methods will be evaluated on their utility during each portion of the flight envelope.

Shafer, Theresa C.↗
DOE OSTI2025

Implementation of a Mesh refinement algorithm into the quasi-static PIC code QuickPIC

Plasma-based acceleration (PBA) has emerged as a promising candidate for the accelerator technology used to build a future linear collider and/or an advanced light source. In PBA, a trailing or witness particle beam is accelerated in the plasma wave wakefield (WF) created by a laser or particle beam driver. The WF is often nonlinear and involves the crossing of plasma particle trajectories in real space and thus particle-in-cell methods are used. The distance over which the drive beam evolves is several orders of magnitude larger than the wake wavelength. This large disparity in length scales is amenable to the quasi-static approach. Three-dimensional (3D), quasi-static (QS), particle-in-cell (PIC) codes, e.g., QuickPIC, have been shown to provide high fidelity simulation capability with 2-4 orders of magnitude speedup over 3D fully explicit PIC codes. In PBA, the witness beam needs to be matched to the focusing forces of the WF to reduce the emittance growth. In some linear collider designs, the matched spot size of the witness beam can be 2 to 3 orders of magnitude smaller than the spot size (and wavelength) of the wakefield. Such an additional disparity in length scales is ideal for mesh refinement where the WF within the witness beam is described on a finer mesh than the rest of the WF. A mesh refinement scheme is described that has been implemented into the 3D QS PIC code, QuickPIC. Very fine (high) resolution is used in a small spatial region that includes the witness beam and progressively coarser resolutions in the rest of the simulation domain. A fast multigrid Poisson solver has been implemented for the field solve on the refined meshes and a Fast Fourier Transform (FFT) based Poisson solver is used for the coarse mesh. The code has been parallelized with both MPI and OpenMP, and the parallel scalability has also been improved by using pipelining. A preliminary adaptive mesh refinement technique is described to optimize the computational time for simulations with an evolving witness beam size. Several test problems are used to verify that the mesh refinement algorithm provides accurate results. Additionally, the results are benchmarked against highly resolved simulations exhibiting near-azimuthal symmetry, performed using QPAD—a novel hybrid QS PIC code that uses a PIC description in the coordinates (r, ct – z) and a gridless description in the azimuthal angle, Φ.

Linear collider↗
NASA NTRS2010

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗
DOE OSTI2025

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗
NASA NTRS2011

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗
DOE OSTI2025

SAGIPS: a physics-inspired scalable asynchronous generative inverse-problem solver

Abstract Solving large-scale inverse problems using deep-learning algorithms have become an essential part of modern research and industrial applications. The complexity of the underlying inverse problem may require the utilization of high performance computing systems which poses a challenge on the algorithmic design of the inverse problem solver. Most deep learning algorithms require, due to their design, custom parallelization techniques in order to be resource efficient while showing a reasonable convergence. In this paper we introduce a S calable A synchronous G enerative I nverse P roblem S olver (SAGIPS) on high-performance computing systems. We present a workflow that utilizes an asynchronous ring-allreduce algorithm to transfer the gradients of the generator network across multiple GPUs. Experiments with a scientific proxy application demonstrate that SAGIPS shows near linear weak scaling, together with a convergence quality that is comparable to traditional methods. The approach presented here allows leveraging Generative Adverserial Network across multiple GPUs, promising advancements in solving complex inverse problems at scale.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Barth, Timothy↗
NASA NTRS1988

Three-dimensional elliptic grid generation technique with application to turbomachinery cascades

Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.

Chen, S. C.↗
NASA NTRS1996

Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems

Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.

Vanek, Petr↗
NASA NTRS2011

Turbulence Modeling for Shock Wave/Turbulent Boundary Layer Interactions

Accurate aerodynamic computational predictions are essential for the safety of space vehicles, but these computations are of limited accuracy when large pressure gradients are present in the flow. The goal of the current project is to improve the state of compressible turbulence modeling for high speed flows with shock wave / turbulent boundary layer interactions (SWTBLI). Emphasis will be placed on models that can accurately predict the separated region caused by the SWTBLI. These flows are classified as nonequilibrium boundary layers because of the very large and variable adverse pressure gradients caused by the shock waves. The lag model was designed to model these nonequilibrium flows by incorporating history effects. Standard one- and two-equation models (Spalart Allmaras and SST) and the lag model will be run and compared to a new lag model. This new model, the Reynolds stress tensor lag model (lagRST), will be assessed against multiple wind tunnel tests and correlations. The basis of the lag and lagRST models are to preserve the accuracy of the standard turbulence models in equilibrium turbulence, when the Reynolds stresses are linearly related to the mean strain rates, but create a lag between mean strain rate effects and turbulence when nonequilibrium effects become important, such as in large pressure gradients. The affect this lag has on the results for SWBLI and massively separated flows will be determined. These computations will be done with a modified version of the OVERFLOW code. This code solves the RANS equations on overset grids. It was used for this study for its ability to input very complex geometries into the flow solver, such as the Space Shuttle in the full stack configuration. The model was successfully implemented within two versions of the OVERFLOW code. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWBLI assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced.

Lillard, Randolph P.↗
DOE OSTI2026

Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂⁡(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂⁡(𝑁⁢log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.

58 GEOSCIENCES↗
NASA NTRS2020

Multigrid Preconditioning for a Space-Time Spectral-Element Discontinuous-Galerkin Solver

In this work we examine a multigrid preconditioning approach in the context of a high- order tensor-product discontinuous-Galerkin spectral-element solver. We couple multigrid ideas together with memory lean and efficient tensor-product preconditioned matrix-free smoothers. Block ILU(0)-preconditioned GMRES smoothers are employed on the coarsest spaces. The performance is evaluated on nonlinear problems arising from unsteady scale- resolving solutions of the Navier-Stokes equations: separated low-Mach unsteady ow over an airfoil from laminar to turbulent ow. A reduction in the number of ne space iterations is observed, which proves the efficiency of the approach in terms of preconditioning the linear systems, however this gain was not reflected in the CPU time. Finally, the preconditioner is successfully applied to problems characterized by stiff source terms such as the set of RANS equations, where the simple tensor product preconditioner fails. Theoretical justification about the findings is reported and future work is outlined.

Franciolini, Matteo↗
DOE OSTI2026

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2015

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

Mazaheri, Alireza↗
DOE OSTI2025

A self-consistent electrostatic electrified shallow water model for charged liquid surface dynamics

The dynamics of an electrified liquid surface are investigated using a shallow water model that is self-consistently coupled with an electrostatic solver. To account for the spatiotemporal variation of a curved liquid surface, the electric field on curved surfaces is calculated by solving a two-dimensional electrostatic equation using the weighted least squares (WLSQ) interpolation method. First, the WLSQ implementation is verified with analytical theory obtained from a Laplace solution assuming a half-cylinder liquid surface profile. Then, the coupled electrified shallow water model is used to study the instability of liquid surface perturbation as a function of the potential drop between an electrode and conducting liquid, surface tension, and gravity. We present a linear dispersion theory of liquid surface instability for long-wavelength perturbations, including the effects of liquid viscosity. Furthermore, the effects of multiple sinusoidal surface perturbations on the electrified liquid surface instability are investigated.

Capillary waves↗
NASA NTRS1993

Accurate upwind methods for the Euler equations

A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

Huynh, Hung T.↗