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DOE OSTI2025

Fast and Invertible Simplicial Approximation of Magnetic‐Following Interpolation for Visualizing Fusion Plasma Simulation Data

We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root-finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X-Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7-X (W7-X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet.

Ren, Congrong [The Ohio State Univ., Columbus, OH ↗

NASA NTRS1993

Unsteady fluid and optical simulation of transonic aero-windows

The time-varying fluid and optical fields of several cavity configurations have been computed on overset mesh systems using the Reynolds-averaged Navier-Stokes equations and geometric optics. Comparisons between numerical results and Airborne Optical Adjunct (AOA) flight data are made in two-dimensions for a quieted cavity geometry with two lip-blowing rates. In three-dimensions, two proposed aero-window locations for the Stratospheric Observatory For Infrared Astronomy (SOFIA) are discussed. The simulations indicate that convection of large shear layer structures across the aperture cause the blur circle diameter to be three times the diffraction-limited diameter in the near-infrared band.

Atwood, Christopher A.↗

NASA NTRS1998

A Domain-Decomposed Multi-Level Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.

Aftosmis, M. J.↗

NASA NTRS2017

Strategies Toward Automation of Overset Structured Surface Grid Generation

An outline of a strategy for automation of overset structured surface grid generation on complex geometries is described. The starting point of the process consists of an unstructured surface triangulation representation of the geometry derived from a native CAD, STEP, or IGES definition, and a set of discretized surface curves that captures all geometric features of interest. The procedure for surface grid generation is decomposed into an algebraic meshing step, a hyperbolic meshing step, and a gap-filling step. This paper will focus primarily on the high-level plan with details on the algebraic step. The algorithmic procedure for the algebraic step involves analyzing the topology of the network of surface curves, distributing grid points appropriately on these curves, identifying domains bounded by four curves that can be meshed algebraically, concatenating the resulting grids into fewer patches, and extending appropriate boundaries of the concatenated grids to provide proper overlap. Results are presented for grids created on various aerospace vehicle components.

overset↗

NASA NTRS2019

Analytical Techniques for Assessing Gateway and Other Spacecraft Antenna Line-of-Sight

NASA’s Artemis program is committed to landing the next man and the first woman on the Moon by 2024. A critical piece of infrastructure for the mission, the Gateway will inaugurate a sustainable crewed presence beyond low-Earth orbit in cis-lunar space and serve as a staging point for a lunar landing system. The Near Rectilinear Halo Orbit of the Gateway offers numerous operational benefits in terms of its Earth access via the Orion Multipurpose Crew Vehicle, the degree of lunar visibility and surface access it provides, and favorable conditions for station-keeping. To minimize burns during station-keeping and conserve propellant, the Gateway will continually align itself to a solar pressure equilibrium attitude with the Sun; this is convenient for solar array orientation and power generation, but causes difficulties in terms of communication line-of-sight with the Earth, Moon, and visiting vehicles, which appear to be continually rotating about the Gateway’s local frame. A fixed antenna on the Gateway is continually subject to a moving target and can find itself obstructed by the Gateway’s own geometry frequently if not placed carefully. To understand the performance of either Earth-pointing or Moon-pointing antenna placements for a given Gateway geometry, a transient solar system simulation of the Gateway is used to step through orbital ephemeris data and determine the periods in which line-of-sight to a chosen target is achieved and lost. Antenna placements can be tested in the simulation and optimized to increase the average line-of-sight exposure to the target, while also minimizing the maximum duration cut-out in line-of-sight communication experienced; long durations without a successful communication link could pose threats to operations, safety, and mission success. It may be necessary to deviate from the Gateway’s solar pressure equilibrium attitude for short periods of time in order to continue a successful line-of-sight link to a chosen target. Communication coverage spheres can offer insight into what these necessary attitude adjustments may be and are generated by using a 3D mesh of the Gateway and an implementation of the Möller-Trumbore intersection algorithm. This paper outlines the analytical techniques used to perform such antenna placements on the Gateway, offering examples of how line-of-sight strength can be enhanced with an understanding of the Gateway geometry and attitude constraints. These techniques have had direct impact on the writing of communication requirements for NASA and international partner-owned Gateway elements.

Kennedy, William J.↗

NASA NTRS2019

Analytical Techniques for Assessing Gateway and Other Spacecraft Antenna Line-of-Sight

Kennedy, William J.↗

NASA NTRSDate not supplied

2020 International Astronautical Congress Conference Presentation - ANALYTICAL TECHNIQUES FOR ASSESSING GATEWAY AND OTHER SPACECRAFT ANTENNA LINE-OF-SIGHT FOR THE ARTEMIS PROGRAM

NASA’s Artemis program is committed to landing the next man and the first woman on the Moon by 2024. The Gateway, a critical piece of infrastructure for the long-term Artemis mission profiles, will inaugurate a sustainable crewed presence beyond low-Earth orbit in cis-lunar space and serve as a staging point for a lunar landing system. The Near Rectilinear Halo Orbit of the Gateway offers numerous operational benefits in terms of its Earth access via the Orion Multipurpose Crew Vehicle, its degree of Earth and lunar visibility, the versatile surface access it provides, and favorable conditions for station-keeping. To minimize burns during station-keeping and conserve propellant, the Gateway will continually align itself to a solar pressure equilibrium attitude with the Sun; this is convenient for solar array orientation and power generation, but causes difficulties in terms of communication line-of-sight with the Earth, Moon, and visiting vehicles, which appear to be continually rotating about the Gateway’s local frame. A fixed antenna on the Gateway is continually subject to a moving target and can find itself obstructed by the Gateway’s own geometry frequently if not placed carefully. To understand the performance of either Earth-pointing or Moon-pointing antenna placements for a given Gateway geometry, a transient solar system simulation of the Gateway is used to step through orbital ephemeris data and determine the periods in which line-of-sight to a chosen target is achieved and lost. Antenna placements can be tested in the simulation and optimized to increase the average line-of-sight exposure to the target, while also minimizing the maximum duration drop-out in line-of-sight communication experienced; long durations without a successful communication link could pose threats to operations, safety, and mission success. It may be necessary to deviate from the Gateway’s solar pressure equilibrium attitude for short periods of time in order to continue a successful line-of-sight link to a chosen target. Communication coverage spheres can offer insight into what these necessary attitude adjustments may be and are generated by using a 3D mesh of the Gateway and an implementation of the Möller-Trumbore intersection algorithm. This paper outlines the analytical techniques used to perform such antenna placements on the Gateway, offering examples of how line-of-sight strength can be enhanced with an understanding of the Gateway geometry and attitude constraints. These techniques have had direct impact on the writing of communication requirements for NASA and international partner-owned Gateway elements.

Gateway↗

DOE OSTI2024

Approaches for the Simulation of Coupled Processes in Evolving Fractured Porous Media Enabled by Exascale Computing

Models have historically represented fractured porous media with continuum descriptions that characterize the media using bulk parameters. The impact of small-scale features is not captured in these models, although they may be controlling the performance of subsurface applications. Pore-scale models can simulate processes in small-scale features by representing the pore space geometry explicitly but are computationally expensive for large domains. The alternative multiscale approach entails the combination of pore-scale and continuum-scale descriptions in a single framework. We use Chombo-Crunch, a computational capability that discretizes complex geometries with an adaptive, embedded boundary method to contrast these two approaches. Chombo-Crunch takes advantage of recent computational performance and memory bandwidth improvements resulting from the emergence of exascale computing resources. These combined improvements enable the efficient simulation of reactive transport in fractured media with a high degree of fidelity and the ability to capture the control small-scale processes exert on the overall medium evolution.

42 ENGINEERING↗

NASA NTRS1985

A 3-D chimera grid embedding technique

A three-dimensional (3-D) chimera grid-embedding technique is described. The technique simplifies the construction of computational grids about complex geometries. The method subdivides the physical domain into regions which can accommodate easily generated grids. Communication among the grids is accomplished by interpolation of the dependent variables at grid boundaries. The procedures for constructing the composite mesh and the associated data structures are described. The method is demonstrated by solution of the Euler equations for the transonic flow about a wing/body, wing/body/tail, and a configuration of three ellipsoidal bodies.

Benek, J. A.↗

NASA NTRS2003

High Energy Boundary Conditions for a Cartesian Mesh Euler Solver

Inlets and exhaust nozzles are common place in the world of flight. Yet, many aerodynamic simulation packages do not provide a method of modelling such high energy boundaries in the flow field. For the purposes of aerodynamic simulation, inlets and exhausts are often fared over and it is assumed that the flow differences resulting from this assumption are minimal. While this is an adequate assumption for the prediction of lift, the lack of a plume behind the aircraft creates an evacuated base region thus effecting both drag and pitching moment values. In addition, the flow in the base region is often mis-predicted resulting in incorrect base drag. In order to accurately predict these quantities, a method for specifying inlet and exhaust conditions needs to be available in aerodynamic simulation packages. A method for a first approximation of a plume without accounting for chemical reactions is added to the Cartesian mesh based aerodynamic simulation package CART3D. The method consists of 3 steps. In the first step, a components approach where each triangle is assigned a component number is used. Here, a method for marking the inlet or exhaust plane triangles as separate components is discussed. In step two, the flow solver is modified to accept a reference state for the components marked inlet or exhaust. In the third step, the flow solver uses these separated components and the reference state to compute the correct flow condition at that triangle. The present method is implemented in the CART3D package which consists of a set of tools for generating a Cartesian volume mesh from a set of component triangulations. The Euler equations are solved on the resulting unstructured Cartesian mesh. The present methods is implemented in this package and its usefulness is demonstrated with two validation cases. A generic missile body is also presented to show the usefulness of the method on a real world geometry.

Pandya, Shishir↗

NASA NTRS2000

DRAGON Grid: A Three-Dimensional Hybrid Grid Generation Code Developed

Because grid generation can consume 70 percent of the total analysis time for a typical three-dimensional viscous flow simulation for a practical engineering device, payoffs from research and development could reduce costs and increase throughputs considerably. In this study, researchers at the NASA Glenn Research Center at Lewis Field developed a new hybrid grid approach with the advantages of flexibility, high-quality grids suitable for an accurate resolution of viscous regions, and a low memory requirement. These advantages will, in turn, reduce analysis time and increase accuracy. They result from an innovative combination of structured and unstructured grids to represent the geometry and the computation domain. The present approach makes use of the respective strengths of both the structured and unstructured grid methods, while minimizing their weaknesses. First, the Chimera grid generates high-quality, mostly orthogonal meshes around individual components. This process is flexible and can be done easily. Normally, these individual grids are required overlap each other so that the solution on one grid can communicate with another. However, when this communication is carried out via a nonconservative interpolation procedure, a spurious solution can result. Current research is aimed at entirely eliminating this undesired interpolation by directly replacing arbitrary grid overlapping with a nonstructured grid called a DRAGON grid, which uses the same set of conservation laws over the entire region, thus ensuring conservation everywhere. The DRAGON grid is shown for a typical film-cooled turbine vane with 33 holes and 3 plenum compartments. There are structured grids around each geometrical entity and unstructured grids connecting them. In fiscal year 1999, Glenn researchers developed and tested the three-dimensional DRAGON grid-generation tools. A flow solver suitable for the DRAGON grid has been developed, and a series of validation tests are underway.

Liou, Meng-Sing↗

DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Medial axis and local thickness computation using the Fast Sweeping Method

This report describes an efficient and robust voxel-based methodology for computing the medial axis, local thickness, and distance-to-skeleton of arbitrary three-dimensional geometries. It is assumed that the object can be represented by an exact or approximate signed distance function on a discrete grid. The gradient of such function is used to formulate a hyperbolic partial differential equation (PDE) that models the collapse of the position vector in space. By exploiting the causality property of the PDE, the Fast Sweeping Method is able to obtain the solution in a finite number of sweeps independent of the mesh resolution. The intersection of characteristic lines leads to the formation of shocks and a discrete bisector function is used to identify the medial axis. The same PDE approach is used to compute the local thickness inside the object and obtain the distance-to-skeleton field. Multiple examples are given in two and three dimensions along with a resolution study. The methodology has optimal complexity and yields subsecond computational times for geometries with over a million zones on a single core. The methodology is also capable of parallelization across shared and distributed memory architectures.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

A flexible grid embedding technique with application to the Euler equations

An automated grid embedding procedure for solution of flows about complex geometries is described. The physical domain is subdivided into regions that can accommodate easily generated grids. The grids are organized in a hierarchical structure, and communication among grids is accomplished by interpolation of the flow variables at mesh boundaries. Algorithms for locating embedded boundaries, special treatment of the embedded grids, and the data structures required for manipulating the solution data are described. The method is demonstrated by solution of the Euler equations for transonic flow about a supercritical airfoil and a flapped airfoil.

Benek, J. A.↗

NASA NTRS2026

Development and Experimental Validation of a Path-Dependent Spin Forming Finite Element Model

Spin forming is an advanced manufacturing process widely used in the aerospace and defense sectors to produce lightweight, high-strength cylindrical components with tight dimensional tolerances. This study explores the applicability of the path-dependent Mechanical Threshold Stress (MTS) constitutive model by simulating the evolution of geometry, machining forces, and plastic deformation during the spin forming of a 10-mm thick 6061-O aluminum cylinder. While numerical modeling of spin forming has advanced substantially over the past decade, systematic verification and experimental validation of material models remain limited, particularly in predicting through-thickness process evolution. The MTS model, incorporating a Voce hardening rule, is employed for its ability to represent cyclic loading, rapidly varying temperature fields, and strain rates characteristic of spin forming. Numerical convergence analysis indicates discretization uncertainties between 0.3% and 9.2% for key quantities of interest. Experimental validation demonstrates that the MTS model, when implemented with a verified mesh, accurately reproduces both elastic and plastic behavior of 6061-O aluminum, predicting peak roller loads within 11–18% of measurements, geometric tolerances within 3%, and plastic strain distributions within 10% of experimental values. Collectively, these results establish a validated computational framework for predictive spin-forming simulations with quantified confidence, providing a foundation for extension to other alloys, geometries, and forming conditions.

Spin forming↗

NASA NTRS1974

An analytical study of reduced-gravity propellant settling

Full-scale propellant reorientation flow dynamics for the Centaur D-1T fuel tank were analyzed. A computer code using the simplified marker and cell technique was modified to include the capability for a variable-grid mesh configuration. Use of smaller cells near the boundary, near baffles, and in corners provides improved flow resolution. Two drop tower model cases were simulated to verify program validity: one case without baffles, the other with baffles and geometry identical to Centaur D-1T. Flow phenomena using the new code successfully modeled drop tower data. Baffles are a positive factor in the settling flow. Two full-scale Centaur D-1T cases were simulated using parameters based on the Titan/Centaur proof flight. These flow simulations indicated the time to clear the vent area and an indication of time to orient and collect the propellant. The results further indicated the complexity of the reorientation flow and the long time period required for settling.

Bradshaw, R. D.↗

DOE OSTI2026

FIREFLY: heat load and particle exhaust approximations for rapid evaluation of divertor designs

The divertor in a magnetic confinement fusion reactor is an essential component for power dissipation and particle removal. The FIREFLY package for rapid evaluation of divertor designs is presented as an extension of the FLARE code for field line reconstruction from a flux tube mesh. First, divertor loads are approximated with a simplified heat transport model. Neutralized particles are then sampled from the resulting load distribution, and the EIRENE code is used to track molecules and atoms in a plasma background while accounting for dissociation, charge exchange and ionization. Particles are removed on pumping surfaces in order to estimate the exhaust efficiency for a given divertor geometry. Optimization of the divertor geometry for more efficient particle exhaust is explored by using W7-X as an example, and the sensitivity to model parameters for the plasma background in the proxy calculations is evaluated.

mesh generation, magnetic field lines, scrape-off ↗

NASA NTRS1989

Involute composite design evaluation using global design sensitivity derivatives

An optimization capability for involute structures has been developed. Its key feature is the use of global material geometry variables which are so chosen that all combinations of design variables within a set of lower and upper bounds correspond to manufacturable designs. A further advantage of global variables is that their number does not increase with increasing mesh density. The accuracy of the sensitivity derivatives has been verified both through finite difference tests and through the successful use of the derivatives by an optimizer. The state of the art in composite design today is still marked by point design algorithms linked together using ad hoc methods not directly related to a manufacturing procedure. The global design sensitivity approach presented here for involutes can be applied to filament wound shells and other composite constructions using material form features peculiar to each construction. The present involute optimization technology is being applied to the Space Shuttle SRM nozzle boot ring redesigns by PDA Engineering.

Hart, J. K.↗