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DOE OSTI2024

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Openpronghorn

OpenPronghorn is a simulation tool specifically tailored for modeling thermal-hydraulic phenomena in advanced nuclear reactors. It is built on the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source platform that facilitates the development of high-performance scientific computing applications. OpenPronghorn solves the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in fluid flows, using the finite volume numerical method. The code supports a wide range of fluid flow conditions that are applicable to nuclear reactors, including incompressible and weakly compressible flows, as well as single-phase and multiphase flows. It is capable of modeling diverse flow regimes, including laminar and turbulent flows, using various turbulence models such as the standard k-epsilon models, the v2f model, and the mixing length model. For multiphase flows, OpenPronghorn employs a mixture a Eulerian modeling approach with mixture, drift-flux, and full Eulerian models, and includes open-sourced interfacial transfer correlations for drag, exchange, and heat transfer coming from the scientific literature. OpenPronghorn's modular design allows it to handle multiscale simulations, ranging from detailed Reynolds-Averaged Navier Stokes (RANS) simulations to coarse-mesh and lumped parameter models. This flexibility enables users to perform high-fidelity simulations of specific reactor components as well as system-level analyses of entire reactor circuits. The code can be coupled with other MOOSE-based tools using the MultiApp system, allowing for the transfer of coupling quantities such as mass flow rates, heat fluxes, and boundary conditions between different simulation scales. One of the main features of OpenPronghorn is the it includes built-in validation cases from the open-source scientific literature and supports the implementation of user-defined models and correlations through MOOSE's FunctorMaterial system. OpenPronghorn is designed to be computationally efficient, leveraging the SIMPLE projection method for large-scale problems, and can be run on high-performance computing systems to handle the extensive computational demands of detailed reactor simulations. Overall, OpenPronghorn is a versatile and robust tool that provides critical insights into the thermal-hydraulic behavior of advanced nuclear reactors, supporting the design, safety, and optimization of next-generation nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗

NASA NTRS2019

Quasi-Static and Dynamic Analysis of Composite Panels: Characterization and Validation

The predictive capability of a progressive damage model to simulate the quasi-static and dynamic crushing of composite specimens is evaluated in this article. The material model is commercially available within the ABAQUS finite element software package, i.e., “Damage for Fiber reinforced Composites”, and is often utilized to simulate damage progression and failure in static and dynamic failure scenarios such as crushing of a composite plate. The composite specimens used in this study consist of quasi-isotropic C-shaped and corrugated composite panels comprised of carbon fiber/epoxy braided fabric. The C-shaped panel specimen is used to calibrate the model and optimize material/model properties through comparison with experimental results. Then, using the same model parameters, the quasi-static crush response of the corrugated panel is predicted. The predictive capability of the model is further demonstrated by simulating the dynamic crushing response of both C-shaped and corrugated panels using the same material properties as in the quasi-static crush case with only minor adjustments for the dynamic elastic properties (i.e., rate dependent modulus). Results show that the in-built material model available in ABAQUS can successfully reproduce experimental results for both panels (C-shaped and corrugated) subjected to both quasi-static and dynamic loading scenarios. A small-scale parametric study on physical (experimentally measurable) and nonphysical (purely mathematical) model parameters was also conducted. It can be concluded that, achieving successful simulation results requires a more in-depth understanding of the influence of model parameter variation on the mechanical response of the composite together with the strategies and challenges of the utilized modeling methodology (e.g., FEA mesh density, etc.).

Naghipour Ghezeljeh, Paria↗

NASA NTRSDate not supplied

Toward Time Synchronization in Delay Tolerant Network based Solar System Internetworking

The expanding presence in space will place an increased dependency on networked communications– a scalable communications infrastructure; that is, the Solar System Internet (SSI). Upcoming developments towards a SSI include NASA’s upcoming LunaNet, or lunar Internet, which provides multi-hop multi-path communications using Delay Tolerant Networking (DTN). DTN has been an active area of research and development, particularly in routing, security, and optimization. DTNs are marked by mobility, disconnection, and a wide variance of latencies (propagation and processing delays). In this paper, we outline progress towards a theory of time synchronization across such a network. An underlying assumption of DTN is that the network is time synchronized already, rather than synchronization being provided as a service. While this is necessary for schedule-based routing, which is necessarily prevalent in DTNs, it is so deeply ingrained as to be built into the primary unit of data in DTNs– the bundle. Indeed, a bundle’s creation timestamp and its time to live (called the lifetime) are based on time, and there are special recommendations for systems that lack accurate clocks. The assumption of time synchronization makes sense when limiting considerations to smaller-scale and more traditional space communication. However, just as end-to-end connectivity cannot be guaranteed in DTNs, neither can access to a reference or authoritative clock. In this more general case, it might be necessary to synchronize over time-varying meshes, and perhaps even to consider relativistic effects. Moreover, by imposing synchronization restrictions in order to sustain a network, the effectiveness of the network to achieve scalability will be necessarily muted. To work towards a time synchronization theory for DTNs, we build upon past successes in modeling DTNs using time-varying graphs and sheaves. This includes error and limitation estimation, which allows one to define domains over which schedule-based routing is possible, up to some threshold sensitivity. Despite the theoretical nature of these results, the approaches taken are also algorithmic, and hence lend themselves to practical implementations. The paper concludes with comparisons of the various methods along with suggestions for future work.

Delay Tolerant Networking↗

DOE OSTI2024

Towards a NEAMS-based high-fidelity model of the MARVEL reactor

This report outlines the progress of Idaho National Laboratory in developing a high-fidelity and high-resolution model of the Microreactor Applications Research Validation and Evaluation reactor. The model was developed under the Nuclear Energy Advanced Modeling and Simulation microreactor application driver at Idaho National Laboratory. The overarching objective of this activity is the development of a high-fidelity multiphysics MARVEL model using NEAMS tools, and to verify and validate NEAMS tools against MARVEL reference simulation and experimental data, respectively. This is a unique opportunity to conduct multiphysics analysis on a soon-to-be-deployed microreactor. This multiphysics model developed under the NEAMS-funded INL microreactor application driver leverages three single-physics models coupled via the MOOSE’s MultiApp and Transfer systems. The latter systems enable in-memory data transfer between MOOSE-based and MOOSE-wrapped applications. The first single-physics model, that functions as main application, leverages Griffin to model the neutron transport in the core through the discontinuous finite element (DFEM) discrete ordinates solver (SN). Several optimization flags that were developed by the Griffin developer team were beta-tested to enhance the solver’s performance. These include the combined use of using_average_xs and update_averaged_xs_on that enable to avoid expensive on-the-fly cross sections evaluations at each linear iterations in favor of evaluations of the macroscopic cross sections at each Picard iteration. The second single-physics model uses BISON to handle solid heat transfer and asymptotic hydrogen redistribution analysis in the fuel. While the model returns consistent results for the temperature and hydrogen distribution in the fuel, a mismatch was noticed in the calculated temperature in the reflector due to the value of the gap conductance used in our model. Ongoing investigations are being performed to assess the origin of this discrepancy. Finally, the System Analysis Module (SAM) was used to model the flow of the sodium-potassium eutectic in the primary loop. A first verification was also performed showing good agreement in terms of mass flow rate and inlet temperature. All mesh files were generated using the MOOSE Reactor module, removing the need for external meshing tools. Notably, this workscope represents one of the initial applications of the MOOSE Reactor module for modeling highly irregular geometries. The use of the reactor module significantly streamlined the mesh generation process. The full multiphysics mode, that combines all the single physics models, was leveraged to conduct initial steady-state multiphysics simulations to compute power, and temperature distribution in the reactor. Initial testing was performed for transient simulations as well. In this case, the new checkpoint restart capability for eigenvalue calculations was tested showing the capability for streamlined restart of transient calculations. Future work will focus on improving the fidelity of the model by performing comprehensive code-to-code comparisons. For instance, the full-core Griffin neutronics model will be benchmarked against MCNP reference results, that were provided by the MARVEL design team. Additionally, the SAM T/H model will be verified against reference RELAP-5 results for selected accident scenarios. Besides code-to-code verification exercises, the model fidelity will be improved by replacing the single-channel SAM model with a more complex SAM-Pronghorn coupled model, in which the sub-channel capability is deployed to obtain radial temperature resolution in the coolant. This model will be developed in synergy with the NEAMS thermal hydraulics team.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

DS-GL: Advancing Graph Learning via Harnessing the Power of Nature within Dynamic Systems

With the rapid digitization of the world, an increasing number of real-world applications are turning to nonEuclidean data, modeled as graphs. Due to their intrinsic high complexity and irregularity, learning from graph data demands tremendous computational power. Recently, CMOS-compatible Ising machines, i.e., dynamic systems composed of CMOS components, have emerged as a new approach that harnesses the inherent power of natural annealing within dynamic systems to efficiently resolve binary optimization problems and have been adopted for traditional graph computation, such as max-cut. However, when performing complex Graph Learning (GL) tasks, Ising machines face significant hurdles: (i) they are inherently binary and thus ill-suited for real-valued problems; (ii) their expensive all-to-all coupling network that guarantees effective natural annealing poses daunting scalability concerns. To address these challenges, this paper proposes a nature-powered graph learning framework dubbed DS-GL, which is the first effort to transform the process of solving graph learning problems into the natural annealing process within a parameterized dynamic system embodied as a CMOS chip. To tackle the two major hurdles, DS-GL first augments the Ising machine architecture to modify the self-reaction term of its Hamiltonian function from linear to quadratic, effectively serving as an energy regulator. This adjustment maintains the system’s original physical interpretation while enabling it to process continuous, real-valued data. Second, to address the scaling issue, DS-GL further upgrades the real-valued dense Ising machine by decomposing it into a mesh-based multi-PE dynamic system that supports efficient distributed spatial-temporal co-annealing across different PEs through sparse interconnects. By exploiting the inherent sparsity and component structures in real-world graphs, DS-GL is able to map complex graph learning tasks onto the scalable dynamic system while maintaining high accuracy. Evaluations with three diverse GL applications across six real-world datasets, including traffic flow and COVID-19 prediction, show that DS-GL can deliver from 102× to 106× speedups and 500× energy reduction over Graph Neural Networks on GPUs, with 5% - 20% accuracy enhancement.

Song, Ruibing↗

NASA NTRS1999

Solving Upwind-Biased Discretizations: Multigrid Solver Using Semicoarsening - 2

This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation obtained by AMA is always better than the required accuracy; the computational complexity of the AMA algorithm is (nearly) optimal (comparable with the complexity of the FMG algorithm applied to solve the problem on the optimally spaced target grid).

Diskin, Boris↗

NASA NTRS2004

Experimentation Toward the Analysis of Gear Noise Sources Controlled by Sliding Friction and Surface Roughness

In helicopters and other rotorcraft, the gearbox is a major source of noise and vibration (N&V). The two N&V excitation mechanisms are the relative displacements between mating gears (transmission errors) and the friction associated with sliding between gear teeth. Historically, transmission errors have been minimized via improved manufacturing accuracies and tooth modifications. Yet, at high torque loads, noise levels are still relatively high though transmission errors might be somewhat minimal. This suggests that sliding friction is indeed a dominant noise source for high power density rotorcraft gearboxes. In reality, friction source mechanism is associated with surface roughness, lubrication regime properties, time-varying friction forces/torques and gear-mesh interface dynamics. Currently, the nature of these mechanisms is not well understood, while there is a definite need for analytical tools that incorporate sliding resistance and surface roughness, and predict their effects on the vibro- acoustic behavior of gears. Toward this end, an experiment was conducted to collect sound and vibration data on the NASA Glenn Gear-Noise Rig. Three iterations of the experiment were accomplished: Iteration 1 tested a baseline set of gears to establish a benchmark. Iteration 2 used a gear-set with low surface asperities to reduce the sliding friction excitation. Iteration 3 incorporated low viscosity oil with the baseline set of gears to examine the effect of lubrication. The results from this experiment will contribute to a two year project in collaboration with the Ohio State University to develop the necessary mathematical and computer models for analyzing geared systems and explain key physical phenomena seen in experiments. Given the importance of sliding friction in the gear dynamic and vibro-acoustic behavior of rotorcraft gearboxes, there is considerable potential for research & developmental activities. Better models and understanding will lead to quiet and reliable gear designs, as well as the selection of optimal manufacturing processes.

Asnani, Vivake M.↗

NASA NTRSDate not supplied

Using XR for Improving Scientific Discovery With Numerical Weather Models

Earth science (ES) digital twins will help us understand the complex interactions and interrelationships that make up our Earth system and the impacts of earth science phenomena on it. Our work addresses two underdeveloped areas in current ES digital twin work: improving the understanding and interaction with ES model outputs by using Virtual and Mixed Reality (XR) tools and improving the non-intuitive mapping of continuous ES natural phenomena to gridded reference frames in current numerical models. Traditionally, scientists working on ES view and analyze the results of calculated or measured observables with static 1-dimensional (1D), 2D or 3D plots displayed on flat computer screens or paper. Using such limited mediums, it can be very difficult to identify, track and understand the evolution of key features due to poor viewing angles and the nature of flat computer screens. In addition, numerical models, such as the NASA Goddard Earth Observing System (GEOS) ES model, are almost exclusively formulated, visualized and analyzed in an Eulerian reference frame with fixed grid points in space and time. However, ES phenomena such as convective clouds, hurricanes and wildfire smoke plumes are visualized and analyzed in a Lagrangian reference frame: therefore it is often difficult and unnatural to understand these phenomena in relation to each other, visualized either in an Eulerian or Lagrangian context. In 3D visualizations, data generally takes one of three forms: gridded (e.g., voxelized) data, where space is divided into regions; point clouds, where data is represented as a set of points; and meshes, where objects are rendered as surfaces composed of small polygons (usually triangles). A gridded, Eulerian reference frame has been the default representation for the 2D visual analysis of atmospheric data in part because the numerical methods used to generate atmospheric model data in the first place use a gridded approach, with equations defining the relationships between the physical variables in each of a grid's cells across successive timesteps. In our work, we are particularly interested in data from GEOS. Another reason why gridded representations tend to be used for visualizing data from such models is because trajectories are difficult to interpret from representations on 2D surfaces, due to line-of-sight ambiguity. Instead of a fixed grid from GEOS, we embed a trajectory model to simulate particles' movement throughout a GEOS run. We then ingest these particle trajectories as animated point clouds with a NASA open source XR toolkit, the Mixed Reality Exploration Toolkit (MRET), and merge GEOS data with ES phenomena data onto one combined visualization that the user can intuitively interact with. Efficient rendering of arbitrarily large point clouds is an ongoing challenge being addressed by the computer science community, with the GPU-based optimizations and efficient GPU memory utilization a common theme of recent advances, especially for XR, where sustained high frame rate is mandatory to save the user from suffering due to simulation sickness. In this work, we describe and evaluate our progress in choosing and implementing appropriate methods for rendering arbitrarily large point clouds within MRET for XR. While tracking the XR headset enables the immersion of a user within a 3D scene of a data visualization, tracking of XR handheld controllers or user’s hands enables us to implement intuitive user interactions with the visualized datasets. Conventional tools require a user working with an ES visualization to conduct many interactions to commit their intended selections or manipulations with a visualized dataset; for example to specify a set of points in 3D space. Doing so in a 2D flat screen interface has traditionally required specifying a set of points in three distinct 2D coordinate systems (XY, XZ, and YZ), which is cumbersome. In other scientific domains, it has been shown that specifying or selecting a location or volume in XR using handheld controllers or tracked hands allows for greater speed and accuracy. We anticipate the same will hold true for atmospheric data, and we will share initial results of measuring the utility of such an interface. Notably, as the data being visualized is generated by GEOS as a prediction based on initial conditions, an intended application of our tool is to serve as part of an iterative feedback loop. Through XR, a scientist will review and manipulate a GEOS model run, modifying the conditions as needed to do subsequent runs of GEOS. Thereby, XR-based improvements to speed and accuracy of 3D tagging of points minimizes the effort required by both the scientist and the computer cluster conducting the necessary calculations.

Thomas Grubb↗

NASA NTRS1993

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗

NASA NTRS2012

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗

NASA NTRS2016

Improving Fidelity of Launch Vehicle Liftoff Acoustic Simulations

Launch vehicles experience high acoustic loads during ignition and liftoff affected by the interaction of rocket plume generated acoustic waves with launch pad structures. Application of highly parallelized Computational Fluid Dynamics (CFD) analysis tools optimized for application on the NAS computer systems such as the Loci/CHEM program now enable simulation of time-accurate, turbulent, multi-species plume formation and interaction with launch pad geometry and capture the generation of acoustic noise at the source regions in the plume shear layers and impingement regions. These CFD solvers are robust in capturing the acoustic fluctuations, but they are too dissipative to accurately resolve the propagation of the acoustic waves throughout the launch environment domain along the vehicle. A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed to improve such liftoff acoustic environment predictions. The framework combines the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin (DG) solver, Loci/THRUST, developed in the same computational framework. Loci/THRUST employs a low dissipation, high-order, unstructured DG method to accurately propagate acoustic waves away from the source regions across large distances. The DG solver is currently capable of solving up to 4th order solutions for non-linear, conservative acoustic field propagation. Higher order boundary conditions are implemented to accurately model the reflection and refraction of acoustic waves on launch pad components. The DG solver accepts generalized unstructured meshes, enabling efficient application of common mesh generation tools for CHEM and THRUST simulations. The DG solution is coupled with the CFD solution at interface boundaries placed near the CFD acoustic source regions. Both simulations are executed simultaneously with coordinated boundary condition data exchange.

Liever, Peter↗

NASA NTRS2013

Influence of Computational Drop Representation in LES of a Droplet-Laden Mixing Layer

Multiphase turbulent flows are encountered in many practical applications including turbine engines or natural phenomena involving particle dispersion. Numerical computations of multiphase turbulent flows are important because they provide a cheaper alternative to performing experiments during an engine design process or because they can provide predictions of pollutant dispersion, etc. Two-phase flows contain millions and sometimes billions of particles. For flows with volumetrically dilute particle loading, the most accurate method of numerically simulating the flow is based on direct numerical simulation (DNS) of the governing equations in which all scales of the flow including the small scales that are responsible for the overwhelming amount of dissipation are resolved. DNS, however, requires high computational cost and cannot be used in engineering design applications where iterations among several design conditions are necessary. Because of high computational cost, numerical simulations of such flows cannot track all these drops. The objective of this work is to quantify the influence of the number of computational drops and grid spacing on the accuracy of predicted flow statistics, and to possibly identify the minimum number, or, if not possible, the optimal number of computational drops that provide minimal error in flow prediction. For this purpose, several Large Eddy Simulation (LES) of a mixing layer with evaporating drops have been performed by using coarse, medium, and fine grid spacings and computational drops, rather than physical drops. To define computational drops, an integer NR is introduced that represents the ratio of the number of existing physical drops to the desired number of computational drops; for example, if NR=8, this means that a computational drop represents 8 physical drops in the flow field. The desired number of computational drops is determined by the available computational resources; the larger NR is, the less computationally intensive is the simulation. A set of first order and second order flow statistics, and of drop statistics are extracted from LES predictions and are compared to results obtained by filtering a DNS database. First order statistics such as Favre averaged stream-wise velocity, Favre averaged vapor mass fraction, and the drop stream-wise velocity, are predicted accurately independent of the number of computational drops and grid spacing. Second order flow statistics depend both on the number of computational drops and on grid spacing. The scalar variance and turbulent vapor flux are predicted accurately by the fine mesh LES only when NR is less than 32, and by the coarse mesh LES reasonably accurately for all NR values. This is attributed to the fact that when the grid spacing is coarsened, the number of drops in a computational cell must not be significantly lower than that in the DNS.

Bellan, Josette↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2010

NASA's Soil Moisture Active and Passive (SMAP) Mission

The Soil Moisture Active-Passive (SMAP) Mission is one of the first Earth observation satellites being formulated by NASA in response to the 2007 National Research Council s Decadal Survey. SMAP will make global measurements of soil moisture at the Earth's land surface and its freeze-thaw state. These measurements will allow significantly improved estimates of water, energy and carbon transfers between the land and atmosphere. Soil moisture measurements are also of great importance in assessing flooding and monitoring drought. Knowledge gained from SMAP observations can help mitigate these natural hazards, resulting in potentially great economic and social benefits. SMAP observations of soil moisture and freeze/thaw timing over the boreal latitudes will also reduce a major uncertainty in quantifying the global carbon balance and help to resolve an apparent missing carbon sink over land. The SMAP mission concept will utilize an L-band radar and radiometer sharing a rotating 6-meter mesh reflector antenna flying in a 680 km polar orbit with an 8-day exact ground track repeat aboard a 3-axis stabilized spacecraft to provide high-resolution and high-accuracy global maps of soil moisture and freeze/thaw state every two to three days. In addition, the SMAP project will use these surface observations with advanced modeling and data assimilation to provide estimates of deeper root-zone soil moisture and net ecosystem exchange of carbon. SMAP recently completed its Phase A Mission Concept Study Phase for NASA and transitioned into Phase B (Formulation and Detailed Design). A number of significant accomplishments occurred during this initial phase of mission development. The SMAP project held several open meetings to solicit community feedback on possible science algorithms, prepared preliminary draft Algorithm Theoretical Basis Documents (ATBDs) for each mission science product, and established a prototype algorithm testbed to enable testing and evaluation of the performance of candidate algorithms. SMAP conducted an Applications Workshop in September 2009 to coordinate with potential application users interested in the mission data. A draft Applications Plan describing the Project s planned outreach to potential applications users has been prepared and will be updated during Phase B. SMAP made a significant evaluation of the potential terrestrial radio frequency interference (RFI) source environment and established radiometer and radar flight hardware and ground processing mitigation approaches. SMAP finalized its science orbit and orbit injection approach to optimize launch mass and prepared launch and commissioning scenarios and timeline. A science data communications approach was developed to maximize available science data volume to improve science margins while maintaining moderately short data product latencies to support many potential applications using existing ground assets and with minimum impact to the flight system. SMAP developed rigid multi-body and flexible body dynamics and control models and system designs for the 6-meter rotating instrument reflector-boom assembly (RBA) and flight system to confirm pointing and control performance, and devised strategies to efficiently implement on-orbit balancing if needed. Industry partners were selected for the spin mechanism assembly (SMA) and RBA. Preliminary designs for the radar and radiometer were initiated, including constructing breadboards of key assemblies.

Kellogg, Kent↗

NASA NTRSDate not supplied

Simplified Applied Loads of a Transonic Truss-Braced Wing Derived from Computational Fluid Dynamics

The transonic truss-braced wing (TTBW) concept is under consideration by the NASA Advanced Air Transport Technology (AATT) project due to its potential to reduce fuel consumption of transport aircraft. To properly evaluate the TTBW concept, detailed structural modeling and subsequent test planning is underway, which requires a simplified set of discrete applied loads that simulate the distributed aerodynamic pressures. Given the unique architecture of the TTBW and its intended operation in the transonic regime, computational fluid dynamics (CFD) is the ideal approach to employ to ensure the aerodynamics of this configuration are sufficiently captured. To convert aerodynamic results into input for structural models, application of a data transfer tool, Discrete Data Transfer Between Dissimilar Meshes (DDTBDM), is presented to resolve aerodynamic pressures from CFD into single load vectors at hardpoints along both the wing and the strut. Evaluation of mapping the aerodynamic forces to hardpoints at rib and spar intersections in a structural model is performed, and the results are also compared with a linear static aeroelastic analysis. The structural responses indicate that distributing forces along only the wing and strut forward spars is insufficient for simulating the distributed aerodynamic loads. Adding moments along the forward spars improved the global response of the wing, but the point moments created unrealistic local rotations within the structure. When distributing loads along both the forward and aft spars of the wing and strut, the global response was less sensitive to the inclusion of point moments, which indicated the arrangement of point forces alone was sufficient input for structural design work and testing and provided a more continuous loading profile.

Finite Element↗

NASA NTRSDate not supplied

Simplified Applied Loads of a Transonic Truss-Braced Wing Derived from Computational Fluid Dynamic

Finite Element↗

DOE OSTI2024

CG-Kit: Code Generation Toolkit for performant and maintainable variants of source code applied to Flash-X hydrodynamics simulations

CG-Kit is a new Code Generation tool-Kit that we have developed as a part of the solution for portability and maintainability for multiphysics computing applications. The development of CG-Kit is rooted in the urgent need created by the shifting landscape of high-performance computing platforms and the algorithmic complexities of a particular large-scale multiphysics application: Flash-X. To efficiently use computing resources on a heterogeneous node, an application must have a map of computation to resources and a mechanism to move the data and computation to the resources according to the map. Most existing performance portability solutions are focussed on abstracting the expression of computations so that a unified source code can be specialized to run on different resources. However, such an approach is insufficient for a code like Flash-X, which has a multitude of code components that can be assembled in various permutations and combinations to form different instances of applications. Similar challenges apply to any code that has composability, where a single specified way of apportioning work among devices may not be optimal. Additionally, use cases arise where the optimal control flow of computation may differ for different devices while the underlying numerics remain identical. This combination leads to unique challenges including handling an existing large code base in Fortran and/or C/C++, subdivision of code into a great variety of units supporting a wide range of physics and numerical methods, different parallelization techniques for distributed and shared memory systems and accelerator devices, and heterogeneity of computing platforms requiring coexisting variants of parallel algorithms. All of these challenges demand that scientific software developers apply existing knowledge about domain applications, algorithms, and computing platforms to determine custom abstractions and granularity for code generation. There is a critical lack of tools to tackle those problems. CG-Kit is designed to fill this gap by providing a user with the ability to express their desired control flow and computation-to-resource map in the form a pseudocode-like recipe. It consists of standalone tools that can be combined into highly specific and, we argue, highly effective portability and maintainability toolchains. Here we present the design of our new tools: parametrized source trees, control flow graphs, and recipes. The tools are implemented in Python. They are agnostic to the programming language of the source code targeted for code generation. In conclusion, we demonstrate the capabilities of the toolkit with two examples, first, multithreaded variants of the basic AXPY operation, and second, variants of parallel algorithms within a hydrodynamics solver, called Spark, from Flash-X that operates on block-structured adaptive meshes.

Algorithmic portability↗