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All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Magnetotail Current Sheet Thinning and Magnetic Reconnection Dynamics in Global Modeling of Substorms

Magnetotail current sheet thinning and magnetic reconnection are key elements of magnetospheric substorms. We utilized the global MHD model BATS-R-US with Adaptive Mesh Refinement developed at the University of Michigan to investigate the formation and dynamic evolution of the magnetotail thin current sheet. The BATSRUS adaptive grid structure allows resolving magnetotail regions with increased current density up to ion kinetic scales. We investigated dynamics of magnetotail current sheet thinning in response to southwards IMF turning. Gradual slow current sheet thinning during the early growth phase become exponentially fast during the last few minutes prior to nightside reconnection onset. The later stage of current sheet thinning is accompanied by earthward flows and rapid suppression of normal magnetic field component $B-z$. Current sheet thinning set the stage for near-earth magnetic reconnection. In collisionless magnetospheric plasma, the primary mechanism controlling the dissipation in the vicinity of the reconnection site is non-gyrotropic effects with spatial scales comparable with the particle Larmor radius. One of the major challenges in global MHD modeling of the magnetotail magnetic reconnection is to reproduce fast reconnection rates typically observed in smallscale kinetic simulations. Bursts of fast reconnection cause fast magnetic field reconfiguration typical for magnetospheric substorms. To incorporate nongyritropic effects in diffusion regions we developed an algorithm to search for magnetotail reconnection sites, specifically where the magnetic field components perpendicular to the local current direction approaches zero and form an X-type configuration. Spatial scales of the diffusion region and magnitude of the reconnection electric field are calculated self-consistently using MHD plasma and field parameters in the vicinity of the reconnection site. The location of the reconnection sites and spatial scales of the diffusion region are updated during the simulations. Such an approach allows quantifying the interaction between large-scale global magnetospheric dynamics and microphysical processes in diffusion regions localized near reconnection sites. To clarify the role of smallscale non-MHD effects in diffusion region on the global magnetospheric dynamic and to test different models of dissipation we perform simulations with steady southward IMF driving of the magnetosphere.

Kuznetsova, M. M.↗
DOE OSTI2026

Seamlessly joining length scales: From atomistic thermal graphs to anisotropic continuum conductivity

Thermal transport in complex solids is governed by local structure, defects, and anisotropy, yet most continuum models still rely on oversimplified and homogenized conductivities. Here, we bridge atomistic and continuum descriptions by building finite element (FE) models directly from the site-projected thermal conductivity (SPTC), an atomic-level decomposition of the Green–Kubo thermal conductivity. We introduce a toolkit, the “Simulator Collection for Atomic-to-Continuum Scales (SCACS)”, which uses a graph neural network to predict SPTC on large atomic structures, coarse-grains these fields into anisotropic conductivity tensors, and embeds them into the heat-flow FE equation with a customized, anisotropy-aware adaptive mesh refinement scheme. Applied to silicon nanostructures, the resulting FE models act as representative volume elements, reproduce bulk conductivities, and capture interfacial and defect-driven anisotropy while maintaining thermodynamic consistency. Additionally, SCACS predicts experimental conductance trends and fields. This work demonstrates a general route for transferring atomistic transport information into device-scale thermal simulations with physics-based approximations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

Solution adaptivity using a triangular mesh

Solution adaptivity is discussed first from a general perspective and then from the specific viewpoint of triangular meshes. The use of a general connectivity triangular mesh is emphasized. The development of monitor surfaces and their geometric properties is discussed. Mesh point movement is addressed, as is the dynamic restructuring of the connectivity pattern among moving modes. Changes in the number of mesh nodes to obtain suitable refinement for a physical simulation is examined, and the use of locally regular structures to offset the data structure limitation of a general connectivity triangular mesh and thus to obtain an enhanced range of application is considered. To illustrate the basic features of the adaptive triangular mesh strategy, an application to the study of plasma equilibrium is briefly considered.

Eiseman, P. R.↗
NASA NTRS1995

An Adaptive Semi-Implicit Scheme for Simulations of Unsteady Viscous Compressible Flows

A numerical scheme for simulation of unsteady, viscous, compressible flows is considered. The scheme employs an explicit discretization of the inviscid terms of the Navier-Stokes equations and an implicit discretization of the viscous terms. The discretization is second order accurate in both space and time. Under appropriate assumptions, the implicit system of equations can be decoupled into two linear systems of reduced rank. These are solved efficiently using a Gauss-Seidel method with multigrid convergence acceleration. When coupled with a solution-adaptive mesh refinement technique, the hybrid explicit-implicit scheme provides an effective methodology for accurate simulations of unsteady viscous flows. The methodology is demonstrated for both body-fitted structured grids and for rectangular (Cartesian) grids.

Steinthorsson, Erlendur↗
NASA NTRS1994

Incremental triangulation by way of edge swapping and local optimization

This document is intended to serve as an installation, usage, and basic theory guide for the two dimensional triangulation software 'HARLEY' written for the Silicon Graphics IRIS workstation. This code consists of an incremental triangulation algorithm based on point insertion and local edge swapping. Using this basic strategy, several types of triangulations can be produced depending on user selected options. For example, local edge swapping criteria can be chosen which minimizes the maximum interior angle (a MinMax triangulation) or which maximizes the minimum interior angle (a MaxMin or Delaunay triangulation). It should be noted that the MinMax triangulation is generally only locally optical (not globally optimal) in this measure. The MaxMin triangulation, however, is both locally and globally optical. In addition, Steiner triangulations can be constructed by inserting new sites at triangle circumcenters followed by edge swapping based on the MaxMin criteria. Incremental insertion of sites also provides flexibility in choosing cell refinement criteria. A dynamic heap structure has been implemented in the code so that once a refinement measure is specified (i.e., maximum aspect ratio or some measure of a solution gradient for the solution adaptive grid generation) the cell with the largest value of this measure is continually removed from the top of the heap and refined. The heap refinement strategy allows the user to specify either the number of cells desired or refine the mesh until all cell refinement measures satisfy a user specified tolerance level. Since the dynamic heap structure is constantly updated, the algorithm always refines the particular cell in the mesh with the largest refinement criteria value. The code allows the user to: triangulate a cloud of prespecified points (sites), triangulate a set of prespecified interior points constrained by prespecified boundary curve(s), Steiner triangulate the interior/exterior of prespecified boundary curve(s), refine existing triangulations based on solution error measures, and partition meshes based on the Cuthill-McKee, spectral, and coordinate bisection strategies.

Wiltberger, N. Lyn↗
DOE OSTI2025

Three-dimensional modeling of hyphal fusion, branching, and nutrient transport in filamentous fungi

Fungi exhibit behaviors distinct from other microbes. Filamentous fungi grow by extending complex networks of branched filaments collectively referred to as the mycelium. These networks can expand over large distances and traverse low-nutrient areas by translocating nutrients through the filament network. This spatial characteristic makes filamentous fungi crucial for soil ecosystems, supporting stable microbial communities and promoting plant growth. However, simulating these behaviors is complex. The elongated nature of fungal compartments results in different mechanical interactions compared to the commonly modeled spherical bacteria. These detailed hyphal mechanics require specialized consideration and are often excluded from conventional fungal simulation packages. Additionally, the extensive fungal networks in nature demand computationally intensive simulations, necessitating high-performance algorithms. Therefore, realistic fungi simulations require specialized software. Here, we introduce a fungal modeling expansion to the high-performance biological modelling and interface exchange (bmx) software suite. bmx leverages adaptive mesh refinement in AMReX for chemical diffusion and incorporates a full mechanical model for bacterial cells, accelerated by GPUs. By extending bmx to model filamentous particles, we demonstrate the formation of complex filament networks through interactions like hyphal branching and fusion (anastomosis). We show that the networks produced match real-world fungal structures through various metrics. This work supports computational studies of fungal growth dynamics and can be adapted to investigate the growth of other filamentous structures in biology or materials science. The expanded-BMX package is open-sourced and is available online.

Cell mechanics↗
DOE OSTI2022

NucMesh: nuclear reactor geometry creation and mesh generation module in NEMoSys

NucMesh is a parameterized geometry and mesh generator for nuclear reactors developed within the Nuclear Energy Modeling System NEMoSys at Illinois Rocstar. NEMoSys is a platform developed for mesh generation, adaptive refinement, and solution verification. NucMesh is implemented to be generalized and extensible with a robust computer aided design engine and multiple mesh generation algorithms for unstructured triangular, quad-dominant, and structured quadrilateral meshing. In this paper, we present the geometric and meshing features of NucMesh. Geometrically objects are constructed bottom-to-top and overlaps are addressed automatically. A sophisticated object tracking algorithm prevents data from being lost for segmented objects. We discuss the primitive objects of circle and polygons that constitute the module and show how they are used with example inputs. Arrays of primitives and arrays of arrays are utilized to build large assemblies of objects. The concept of saved objects is discussed to demonstrate how repetitive objects can be reused easily and augmented in place. Three dimensional meshes can be obtained through mesh extrusion where all materials and side sets are extended to three dimensions. We show that side sets can be defined nearly anywhere within the geometry and can then be applied to the mesh. Finally, example reactor meshes are demonstrated for the Idaho National Laboratory Advanced Test Reactor and Los Alamos National Lab Empire reactor, both of which use control drums that NucMesh handles easily. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1988

Finite element Euler computations in three dimensions

A two-step explicit FEM solution algorithm for the three-dimensional compressible Euler and Navier-Stokes equations based on unstructured triangular and tetrahedral grids is described and demonstrated. The method represents an extension and refinement of the algorithms presented by Loehner et al. (1984 and 1985), Peraire et al. (1987), and Morgan et al. (1987). The formulation and numerical implementation are outlined; the mesh generation, data structures, and adaptive remeshing are explained; and results for a two-dimensional airfoil, a three-dimensional engine air intake, a B747 in landing configuration, and a generic fighter aircraft are presented in extensive graphics and discussed in detail.

Peraire, Jaime↗
NASA NTRSDate not supplied

Multiscale Mesh Adaptation for Transonic Aeroelastic Flutter Problems

This work applies multiscale mesh adaptation with refine to reduce spatial discretization error of aeroelastic computational fluid dynamics (CFD) simulations. Benchmark flutter models, such as the pitch and plunge NACA64A-010 airfoil and the benchmark supercritical wing, are studied with both a linearized frequency-domain solver and time-marching CFD coupled to a modal structural solver in FUN3D. The undeformed NASA Common Research Model (CRM), an aeroelastic jig shape variant of the CRM, is also studied with the linearized frequency-domain approach. For these cases, the adaptation process converges to comparable flutter predictions to hand-generated meshes but with smaller node counts. However the additional disciplines of the linearized frequency-domain analysis, the mesh deformation, and the unsteady finite-volume solver create robustness challenges that need to be addressed before it can be applied as a fully automated process for complex transonic aeroelastic problems. In particular, negative volumes are observed to be an issue for FUN3D’s linear elasticity mesh deformation solver when moving the adapted meshes.

Aeroelasticity↗
NASA NTRS1993

NASA Langley developments in response calculations needed for failure and life prediction

NASA Langley developments in response calculations needed for failure and life predictions are discussed. Topics covered include: structural failure analysis in concurrent engineering; accuracy of independent regional modeling demonstrated on classical example; functional interface method accurately joins incompatible finite element models; interface method for insertion of local detail modeling extended to curve pressurized fuselage window panel; interface concept for joining structural regions; motivation for coupled 2D-3D analysis; compression panel with discontinuous stiffener coupled 2D-3D model and axial surface strains at the middle of the hat stiffener; use of adaptive refinement with multiple methods; adaptive mesh refinement; and studies on quantity effect of bow-type initial imperfections on reliability of stiffened panels.

Housner, Jerrold M.↗
NASA NTRS2004

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian↗
NASA NTRS2020

A Numerical Investigation of Parachute Deployment in Supersonic Flow

A validated computational fluid-structure interaction method applied to supersonic parachute inflation is extended to consider a unique, parallel self-contact algorithm, porosity interface conditions on the canopy, improved flow field sampling procedures for obtaining quality loading on the parachute canopy, adaptive mesh refinement, and improved treatment of thin geometries in an immersed boundary framework. These extensions are discussed in detail and demonstrated individually on test problems. Finally, the developments are brought together for demonstration on a sub-scale MSL parachute geometry.

Boustani, Jonathan↗
NASA NTRS1996

A User's Guide to AMR1D: An Instructional Adaptive Mesh Refinement Code for Unstructured Grids

This report documents the code AMR1D, which is currently posted on the World Wide Web (http://sdcd.gsfc.nasa.gov/ESS/exchange/contrib/de-fainchtein/adaptive _mesh_refinement.html). AMR1D is a one-dimensional finite element fluid-dynamics solver, capable of adaptive mesh refinement (AMR). It was written as an instructional tool for AMR on unstructured mesh codes. It is meant to illustrate the minimum requirements for AMR on more than one dimension. For that purpose, it uses the same type of data structure that would be necessary on a two-dimensional AMR code (loosely following the algorithm described by Lohner).

deFainchtein, Rosalinda↗
DOE OSTI2025

Chemical timescale effects on detonation convergence

Numerical simulations of detonation-containing flows have emerged as crucial tools for designing next- generation power and propulsion devices. As these tools mature, it is important for the combustion community to properly understand and isolate grid resolution effects when simulating detonations. To this end, the objective of this work is to provide a comprehensive analysis of the numerical convergence of unsteady detonation simulations, with focus on isolating the impacts of chemical timescale modifications on convergence characteristics in the context of operator splitting. With the aid of an AMReX-based adaptive mesh refinement flow solver-which enables resolutions up to ($\mathcal{O}$ (1000) cells-per-induction length-the convergence analysis is conducted using two kinetics configurations: (1) the simplified three-step Arrhenius-based model mechanism of Short and Quirk (1997), where chemical timescales in the detonation are modified by adjusting activation energies in the initiation and branching reactions, and (2) a detailed hydrogen- air mechanism, where the chemical timescales are adjusted by varying the ambient pressure. The convergence of unsteady self-sustained detonations in one-dimensional channels is then analyzed with reference to steady-state theoretical baseline solutions using these mechanisms. The goal of the analysis is to provide a detailed comparison of the effects of grid resolution on both macroscopic (peak pressures and wave speeds) and microscopic (wave structure) quantities of interest, drawing connections between the deviations from steady-state baselines and minimum chemical timescales. In particular, chemical timescale reductions were found to have minimal impact on the convergence of macroscopic properties. Furthermore, analyses of microscopic convergence trends, particularly in the reaction front location, revealed a key insight: maintaining the induction time while eliminating prohibitive chemical timescales through mechanism simplifications and combustion modeling can significantly enhance detonation convergence properties. Ultimately, this work uncovers resolution-dependent unsteady detonation convergence regimes and highlights the important role played by not only the chemical timescales, but also the ratio between the chemical timescale and induction time on the numerical convergence of the detonation wave structure.

Adaptive mesh refinement↗
NASA NTRS2011

Overview of the Helios Version 2.0 Computational Platform for Rotorcraft Simulations

This article summarizes the capabilities and development of the Helios version 2.0, or Shasta, software for rotary wing simulations. Specific capabilities enabled by Shasta include off-body adaptive mesh refinement and the ability to handle multiple interacting rotorcraft components such as the fuselage, rotors, flaps and stores. In addition, a new run-mode to handle maneuvering flight has been added. Fundamental changes of the Helios interfaces have been introduced to streamline the integration of these capabilities. Various modifications have also been carried out in the underlying modules for near-body solution, off-body solution, domain connectivity, rotor fluid structure interface and comprehensive analysis to accommodate these interfaces and to enhance operational robustness and efficiency. Results are presented to demonstrate the mesh adaptation features of the software for the NACA0015 wing, TRAM rotor in hover and the UH-60A in forward flight.

Sankaran, Venkateswaran↗
DOE OSTI2026

High-Fidelity, Low-Dissipation/Symmetry-Preserving Numerical Scheme for Solving the Euler Equations with Unstructured, Metric-Based Mesh Adaptation

This work presents an overview of a high-fidelity compressible Euler solver that utilizes the continuous Galerkin (CG) method with added artificial numerical diffusion for stabilization to solve a variety of unsteady and steady benchmark inviscid flow problems. This work shows that discretizing the Euler equations with this CG approach and first order basis functions produces a cost-effective stencil as well as simple well-posed boundary conditions. We show through convergence testing with manufactured solutions that the reduced stencil of CG, combined with the low amount of artificial diffusion required when using the stabilization method outlined in this work, leads to stable and highly accurate results for a variety of unsteady and steady applications. When combined with the adaptive mesh refinement approach used for many of the cases in this work, our results show that the flow solver achieves even more accurate results. A variety of inviscid flow cases are presented in this work, including transient 2D cases with complex shock structures and several steady 3D airfoils sections with a constant span.

Doetsch, Kevin [ORNL] (ORCID:0000000267051705)↗
NASA NTRS1993

A solution-adaptive hybrid-grid method for the unsteady analysis of turbomachinery

A solution-adaptive method for the time-accurate analysis of two-dimensional flows in turbomachinery is described. The method employs a hybrid structured-unstructured zonal grid topology in conjunction with appropriate modeling equations and solution techniques in each zone. The viscous flow region in the immediate vicinity of the airfoils is resolved on structured O-type grids while the rest of the domain is discretized using an unstructured mesh of triangular cells. Implicit, third-order accurate, upwind solutions of the Navier-Stokes equations are obtained in the inner regions. In the outer regions, the Euler equations are solved using an explicit upwind scheme that incorporates a second-order reconstruction procedure. An efficient and robust grid adaptation strategy, including both grid refinement and coarsening capabilities, is developed for the unstructured grid regions. Grid adaptation is also employed to facilitate information transfer at the interfaces between unstructured grids in relative motion. Results for grid adaptation to various features pertinent to turbomachinery flows are presented. Good comparisons between the present results and experimental measurements and earlier structured-grid results are obtained.

Mathur, Sanjay R.↗
DOE OSTI2022

CFD simulations of electric motor end ring cooling for improved thermal management

Proper thermal management of an electric motor for vehicle applications extends its operating range. One cooling approach is to impinge Automatic Transmission Fluid (ATF) onto the rotor end ring. Increased ATF coverage correlates to enhanced heat transfer. Computational Fluid Dynamics (CFD) analytical tools provide a mechanism to assess motor thermal management prior to hardware fabrication. The complexity of the fluid flow (e.g., jet atomization, interface tracking, wall impingement) and heat transfer makes these simulations challenging. Computational costs are high when solving these flows on high-speed rotating meshes. Typically, a Volume-of Fluid (VOF) technique (i.e., two-fluid system) is used to resolve ATF dynamics within this rotating framework. Suitable numerical resolution of the relevant physics for thin films under strong inertial forces at high rotor speeds is computationally expensive, further increasing the run times. In this work, a numerical study of rotor-ring cooling by ATF is presented using a patent automated Cartesian cut-cell based method coupled with Automatic Mesh Refinement (AMR). This approach automatically creates the Cartesian mesh on-the-fly and can effectively handle complex rotating geometries by adaptively refining the mesh based on local gradients in the flow field which results in better resolution of the air-ATF interface. A Single non-inertial Reference Frame (SRF) approach is used to account for the rotating geometry and to further improve the overall computational efficiency. Quasi-steady state conditions are targeted in the analysis of the results. Important physics such as ATF jet structure, velocity detail near the air-jet interface, ATF coverage/accumulation on the ring surface, and cooling capacity are presented for a low-resolution Reynolds averaged Navier-Stokes (RANS), high-resolution RANS, and high-resolution Large-Eddy Simulation (LES) models. Computations are scaled over hundreds of cores on a supercomputer to maximize turnaround time. Each numerical approach is shown to capture the general trajectory of the oil jet prior to surface impingement. The high-resolution LES simulation, however, is superior in capturing small scale details and heat transfer between the free jet and surrounding air.

42 ENGINEERING↗