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DOE OSTI2022

MOOSE framework enhancements for meshing reactor geometries

MOOSE is an open-source, parallel finite element framework designed to permit rapid development of robust multi-physics modeling capabilities. Under the DOE-NEAMS program, numerous solvers have been developed utilizing the open-source MOOSE framework for multiphysics reactor analysis. These solvers require input finite element meshes representing the discretized geometry. Typically, reactor analysts turn to licensed external tools for creation of reactor geometry meshes. Recently, enhancements have been added to the MOOSE framework to mesh common reactor geometries and improve MOOSE-based application user workflows. Support for hexagonal pins, assemblies, and cores has been added, and Cartesian support has been extended. Options for modeling static and rotating control drums within a hexagonal assembly are now available. Pin, assembly, and plane regions can be identified through automatically applied tags on the mesh called 'reporting IDs' for easier post- processing of physics results. An external open-source triangle routine has been leveraged within MOOSE to mesh core periphery zones. A set of reactor geometry builder routines further streamline the construction of hexagonal and Cartesian cores and include the ability to assign materials to regions during mesh generation. The new meshing routines are available through the MOOSE framework in the open-source 'Reactor' module, and the resulting directly within MOOSE-based applications or exported as Exodus II files for use in other finite element solvers. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Unitarity methods in AdS/CFT

We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams — we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams — in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1994

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. These algorithms are now used in the practical engineering design of devices such as cars and airplanes as well as theoretical studies of complex phenomena such as fluid turbulence. In past years, limited computer resources have motivated the development of efficient numerical methods in computational fluid dynamics (CFD) utilizing structured meshes. These meshes are comprised of systematic arrays of quadrilateral or hexahedral cells. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Structured meshes also permit the use of highly efficient solution techniques such as alternating direction implicit (ADI) iteration schemes or multigrid. Following the dramatic improvement in computing speed in recent years, emphasis has shifted towards the design of algorithms capable of treating complex geometries. The automatic generation of structured grids about complex geometries is problematic. Unstructured grids offer one promising alternative technique for treating these general geometries. Unstructured meshes have irregular connectivity and usually contain triangles and/or quadrilaterals in two dimensions and tetrahedra and/or hexahedra in three dimensions. The generation and use of unstructured grids poses new challenges in computational fluid dynamics. This is true for both grid generation as well as for the design of algorithms for flow solution. The purpose of these notes is to present recent developments in the unstructured grid generation and flow solution technology.

Barth, T. J.↗

DOE OSTI2019

Dark matter blind spots at one-loop

We evaluate the impact of one-loop electroweak corrections to the spinindependent dark matter (DM) scattering cross-section with nucleons (σ SI ), in models with a so-called blind spot for direct detection, where the leading-order prediction for the relevant DM coupling to the Higgs boson, and therefore σ SI , are vanishingly small. Adopting a simple illustrative scenario in which the DM state results from the mixing of electroweak singlet and doublet fermions, we compute the relevant higher order corrections to the scalar effective operator contributions to σ SI , stemming from both triangle and box diagrams involving the SM and dark sector fields. It is observed that in a significant region of the singlet-doublet model-space, the one-loop corrections “unblind” the tree-level blind spots and lead to detectable SI scattering rates at future multi-ton scale liquid Xenon experiments, with σ SI reaching values up to a few times 10 -47 cm 2 for a weak scale DM with O(1) Yukawa couplings. Furthermore, we find that there always exists a new SI blind spot at the next-to-leading order, which is perturbatively shifted from the leading order one in the singlet-doublet mass parameters. For comparison, we also present the tree-level spin-dependent scattering cross-sections near the SI blind-spot region, that could lead to a larger signal. Our results can be mapped to the blind-spot scenario for bino-Higgsino DM in the MSSM, with other sfermions, the heavier Higgs boson, and the wino decoupled.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Assessing Resilience in Lane Detection Methods: Infrastructure-Based Sensors and Traditional Approaches for Autonomous Vehicles

Traditional autonomous vehicle perception subsystems that use onboard sensors have the drawbacks of high computational load and data duplication. Infrastructure-based sensors, which can provide high quality information without the computational burden and data duplication, are an alternative to traditional autonomous vehicle perception subsystems. However, these technologies are still in the early stages of development and have not been extensively evaluated for lane detection system performance. Therefore, there is a lack of quantitative data on their performance relative to traditional perception methods, especially during hazardous scenarios, such as lane line occlusion, sensor failure, and environmental obstructions. We address this need by evaluating the influence of hazards on the resilience of three different lane detection methods in simulation: (1) traditional camera detection using a U-Net algorithm, (2) radar detections using infrastructure-based radar retro-reflectors (RRs), and (3) direct communication of lane line information using chip-enabled raised pavement markers (CERPMs). The performance of each of these methods is assessed using resilience engineering metrics by simulating the individual methods for each sensor technology’s response to related hazards in the CARLA simulator. Using simulation techniques to replicate these methods and hazards acquires extensive datasets without lengthy time investments. Specifically, the resilience triangle was used to quantitatively measure the resilience of the lane detection system to obtain unique insights into each of the three lane detection methods; notably the infrastructure-based CERPMs and RRs had high resistance to hazards and were not as easily affected as the vision-based U-Net. However, while U-Net was able to recover the fastest from the disruption as compared to the other two methods, it also had the most performance loss. Overall, this study demonstrates that while infrastructure-based lane keeping technologies are still in early development, they have great potential as alternatives to traditional ones.

Patil, Pritesh↗

DOE OSTI2025

Visualization techniques for the gyrokinetic tokamak simulation code

Gyrokinetic simulations of plasma microturbulence in tokamaks are challenging to visualize because the compute grid follows the magnetic field lines that spiral around the torus. We have overcome this challenge by developing three new approaches that improve visualization of gyrokinetics. Our techniques work directly with the topology of magnetic flux surfaces where the simulation stores variables in concentric rings on poloidal planes (vertical cross sections of the torus). Our visualization preview step triangulates each consecutive pair of rings to display the data on a poloidal plane. The second visualization technique follows spiral field lines around the torus and constructs polygons to visualize a flux surface. Third, the poloidal triangles are connected between planes to form prisms that compose a 3-D model of the entire torus. The visualization workflow produces detailed geometry that matches the high resolution, irregular compute grid for every time step. The surface and solid models are displayed in scientific visualization programs to effectively explore and communicate the results, including fluctuation of electron density, ion temperature, and electrostatic potential. Highly detailed renderings verify plasma behavior along magnetic field lines over time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2017

Cause and Cure-Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

In the multi-dimensional space-time conservation element and solution element16 (CESE) method, triangles and tetrahedral mesh elements turn out to be the most natural building blocks for 2D and 3D spatial grids, respectively. As such, the CESE method is naturally compatible with the simplest 2D and 3D unstructured grids and thus can be easily applied to solve problems with complex geometries. However, because (a) accurate solution of a high-Reynolds number flow field near a solid wall requires that the grid intervals along the direction normal to the wall be much finer than those in a direction parallel to the wall and, as such, the use of grid cells with extremely high aspect ratio (103 to 106) may become mandatory, and (b) unlike quadrilateral hexahedral grids, it is well-known that accuracy of gradient computations involving triangular tetrahedral grids tends to deteriorate rapidly as cell aspect ratio increases. As a result, the use of triangular tetrahedral grid cells near a solid wall has long been deemed impractical by CFD researchers. In view of (a) the critical role played by triangular tetrahedral grids in the CESE development, and (b) the importance of accurate resolution of high-Reynolds number flow field near a solid wall, as will be presented in the main paper, a comprehensive and rigorous mathematical framework that clearly identifies the reasons behind the accuracy deterioration as described above has been developed for the 2D case involving triangular cells. By avoiding the pitfalls identified by the 2D framework, and its 3D extension, it has been shown numerically.

CFD↗

DOE OSTI2024

Development of Advanced Solid Sorbents for Direct Air Capture (Final Technical Report – Unlimited)

RTI Team, proposes an approach for demonstrating carbon-neutral methanol (MeOH) produced from carbon dioxide (CO 2 ) removed from air by direct air capture (DAC) and green hydrogen (H 2 ) from water (H 2 O) electrolysis using renewable electricity. The proposed project will include completing a feasibility study that informs a conceptual design of an integrated process that meets technical and economic targets set forth.

10 SYNTHETIC FUELS↗

NASA NTRS2009

Characterization of the Effect of Wing Surface Instrumentation on UAV Airfoil Performance

Recently proposed flight research at NASA Dryden Flight Research Center (DFRC) has prompted study into the aerodynamic effects of modifications made to the surfaces of laminar airfoils. The research is focused on the high-aspect ratio, laminar-flow type wings commonly found on UAVs and other aircraft with a high endurance requirement. A broad range of instrumentation possibilities, such as structural, pressure, and temperature sensing devices may require the alteration of the airfoil outer mold line as part of the installation process. This study attempts to characterize the effect of installing this additiona1 instrumentation on key airfoil performance factors, such as transition location, lift and drag curves, and stall point. In particular, the general case of an airfoil that is channeled in the spanwise direction is considered, and the impact on key performance characteristics is assessed. Particular attention is focused on exploring the limits of channel depth and low-Reynolds number on performance and stall characteristics. To quantify the effect of increased skin friction due to premature transition caused by protruding or recessed instrumentation, two simplified, conservative scenarios are used to consider two potential sources of diaturbance: A) that leading edge alterations would cause linearly expanding areas (triangles) of turbulent flow on both surfaces of the wing upstream of the natural transition point, and B) that a channel or bump on the upper surface would trip turbulent flow across the whole upper surface upstream of the natural transition point. A potentially more important consideration than the skin friction drag increment is the change in overall airfoil performance due to the installation of instrumentation along most of the wingspan. To quantify this effect, 2D CFD simulations of the flow over a representative mid-span airfoil section were conducted in order to assess the change in lift and drag curves for the airfoil in the presence of disturbed flow due to the installed instrumentation. A discussion as to the impact on high-altitude and low-speed operation of this and similar aircraft is provided.

Ratnayake, Nalin A.↗

NASA NTRS2006

Tilt/Tip/Piston Manipulator with Base-Mounted Actuators

A proposed three-degree-of-freedom (tilt/tip/piston) manipulator, suitable for aligning an optical or mechanical component, would offer several advantages over prior such manipulators: Unlike in some other manipulators, no actuator would support the weight of another actuator: All of the actuators would be mounted on a base. Hence, there would be less manipulated weight. The basic geometry of the manipulator would afford mechanical advantage: that is, actuator motions would be larger than the motions they produce in the manipulated object. Mechanical advantage inherently increases the accuracy and resolution of manipulation. Unlike in some other manipulators, it would not be necessary to route power and/or data lines through manipulator joints. The proposed manipulator (see figure) would include three prismatic actuators (T1N1, T2N2, and T3N3) mounted on the base and operating in the same plane. Examples of suitable prismatic actuators include lead-screw mechanisms, linear hydraulic motors, piezoelectric linear drives, inchworm-movement linear stepping motors, and linear flexure drives. The actuators would control the lengths of links R1T1, R2T2, and R3T3. Three spherical joints (P1, P2, and P3) would be located at the corners of an equilateral triangle of side length q on the platform holding the object to be manipulated. Three inextensible limbs (R1P1, R2P2, and R3P3) having length r would connect the spherical joints on the platform to revolute joints (R1, R2, and R3) at the ends of the actuator-controlled links R1T1, R2T2, and R3T3. By varying the lengths of these links, one could control the tilt, tip, and piston coordinates of the platform. Closed-form equations for direct or forward kinematics of the manipulator (given the lengths of the variable links, find the tilt, tip, and piston coordinates) have been derived. The equations of inverse kinematics (find the variable link lengths needed to obtain the desired tilt, tip, and piston coordinates) have also been derived.

Tahmasebi, Farhad↗

DOE OSTI2015

Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8], [9], [19] and [21] for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair (β 0 ,β 1 ) in the numerical flux formula, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. As a result, a sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Lithiation-induced zinc clustering of Zn 3 , Zn 12 , and Zn 18 units in Zintl-like Ca ~30 Li 3+x Zn 60-x (x=0.44-1.38)

Zinc clusters are not common for binary intermetallics with relatively low zinc content, but this work shows that zinc clustering can be triggered by lithiation, as exemplified by Ca ~30 Li 3+x Zn 60-x , P6/mmm, Z = 1, which can be directly converted from CaZn 2 . Two end members of the solid solution (x = 0.44 and 1.38) were established and structurally characterized by single-crystal X-ray diffraction analyses: Ca 30 Li 3.44(6) Zn 59.56(6) , a = 15.4651(9) Å, c = 9.3898(3) Å; Ca 30.45(2) Li 4.38(6) Zn 58.62(6) , a = 15.524(3) Å, c = 9.413(2) Å. The structures of Ca ~30 Li 3+x Zn 60-x feature a condensed anionic network of Zn3 triangles, lithium-centered Zn12 icosahedra, and arachno-(Zn,Li)18 tubular clusters that are surrounded respectively by Ca 14 , Ca 20 , and Ca 30 polyhedra. These polyhedra share faces and form a clathrate-like cationic framework. The specific occupation of lithium in the structure is consistent with theoretical “coloring” analyses. Analysis by the linear muffin-tin orbital (LMTO) method within the atomic sphere approximation reveals that Ca ~30 Li 3+x Zn 60-x is a metallic, Zintl-like phase with an open-shell electronic structure. The contribution of Ca–Zn polar covalent interactions is about 41%.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Unitarity and the three flavor neutrino mixing matrix

Unitarity is a fundamental property of any theory required to ensure we work in a theoretically consistent framework. In comparison with the quark sector, experimental tests of unitarity for the 3x3 neutrino mixing matrix are considerably weaker. It must be remembered that the vast majority of our information on the neutrino mixing angles originates from v - e and v μ disappearance experiments, with the assumption of unitarity being invoked to constrain the remaining elements. New physics can invalidate this assumption for the 3x3 subset and thus modify our precision measurements. We also perform a reanalysis to see how global knowledge is altered when one refits oscillation results without assuming unitarity, and present 3σ ranges for allowed U PMNS elements consistent with all observed phenomena. We calculate the bounds on the closure of the six neutrino unitarity triangles, with the closure of the v - e and v μ triangle being constrained to be ≤0.03, while the remaining triangles are significantly less constrained to be ≤ 0.1 - 0.2. Similarly for the row and column normalization, we find their deviation from unity is constrained to be ≤ 0.2 - 0.4, for four out of six such normalizations, while for the v μ and v e row normalization the deviations are constrained to be ≤0.07, all at the 3σCL. Additionally, we emphasize that there is significant room for new low energy physics, especially in the v τ sector which very few current experiments constrain directly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Collaborative Research: Polymer Macrocycles: A novel topology to control dynamics of rubbery materials

Understanding the dynamics of polymers of different topologies is an important field of study and one of the most important unanswered questions in this field is "how do circular polymers move," particularly in the melt state. New information suggests that molecular topology, specifically circular rings, impacts the response of materials in nanometer- scale confinement. The work performed here tackles these subjects through a collaboration in which specialists in polymer synthesis, polymer rheology and scattering methods, and in the physics of nanoconfinement work together to investigate the thermophysical behavior of circular macromolecules. The project goals are to use a novel synthesis method of "green" oxidative polymerization to produce high purity macrocycles and to investigate their linear viscoelastic behavior in order to fully characterize the dynamics of circular macromolecules to sizes that correspond to linear molecule entanglement densities higher than previously obtainable with synthetic polymers. Chemical chain end characterization and critical edge fractionation coupled with direct visualization of the prepared polymers through the use of polymer amplification methods are proposed in order to quantify the numbers of circular and linear molecules in each sample. The study of the linear viscoelastic response of blends of linear and circular molecules is also to be undertaken in the project. Nonlinear viscoelastic measurements, including extensional viscosity, are to be made. Strong differences in behavior between linear chains and circular ones also provides an important opportunity for new technology to break the "magic triangle" for tires: it is believed that improving one of the three key attributes - traction, wear, rolling resistance - necessarily sacrifices at least one of the others. Rubber made from cyclic polymers has the potential to break out of this triangle by reducing the so-called Payne effect in reinforced rubbers because circular macromolecules are less sensitive to nanoconfinement than their linear counterparts. The work has as one objective to characterize the impact of nanoconfinement on the behavior of large circular macromolecules. In addition, the dynamics of carbon black filled circular macromolecules are to be studied to test the hypothesis that the resulting rubbery materials will exhibit a reduced Payne effect.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

Event Horizon Telescope imaging of the archetypal blazar 3C 279 at an extreme 20 microarcsecond resolution

3C 279 is an archetypal blazar with a prominent radio jet that show broadband flux density variability across the entire electromagnetic spectrum. We use an ultra-high angular resolution technique – global Very Long Baseline Interferometry (VLBI) at 1.3 mm (230 GHz) – to resolve the innermost jet of 3C 279 in order to study its fine-scale morphology close to the jet base where highly variable γ-ray emission is thought to originate, according to various models. The source was observed during four days in April 2017 with the Event Horizon Telescope at 230 GHz, including the phased Atacama Large Millimeter/submillimeter Array (ALMA), at an angular resolution of ∼20 μas (at a redshift of z = 0.536 this corresponds to ∼0.13 pc ∼ 1700 Schwarzschild radii with a black hole mass MBH = 8 × 108 M⊙). Imaging and model-fitting techniques were applied to the data to parameterize the fine-scale source structure and its variation. We find a multicomponent inner jet morphology with the northernmost component elongated perpendicular to the direction of the jet, as imaged at longer wavelengths. The elongated nuclear structure is consistent on all four observing days and across different imaging methods and model-fitting techniques, and therefore appears robust. Owing to its compactness and brightness, we associate the northern nuclear structure as the VLBI “core”. This morphology can be interpreted as either a broad resolved jet base or a spatially bent jet. We also find significant day-to-day variations in the closure phases, which appear most pronounced on the triangles with the longest baselines. Our analysis shows that this variation is related to a systematic change of the source structure. Two inner jet components move non-radially at apparent speeds of ∼15 c and ∼20 c (∼1.3 and ∼1.7 μas day−1, respectively), which more strongly supports the scenario of traveling shocks or instabilities in a bent, possibly rotating jet. The observed apparent speeds are also coincident with the 3C 279 large-scale jet kinematics observed at longer (cm) wavelengths, suggesting no significant jet acceleration between the 1.3 mm core and the outer jet. The intrinsic brightness temperature of the jet components are ≲1010 K, a magnitude or more lower than typical values seen at ≥7 mm wavelengths. The low brightness temperature and morphological complexity suggest that the core region of 3C 279 becomes optically thin at short (mm) wavelengths.Key words: galaxies: active / galaxies: jets / galaxies: individual: 3C 279 / techniques: interferometric⋆ The data are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/640/A69 and at https://eventhorizontelescope.org/for-astronomers/data⋆⋆ Deceased.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Advanced Model Development for Large Eddy Simulation of Oxy-Combustion and Supercritical Carbon Dioxide Power Cycles

A joint experimental and numerical study is performed to observe the characteristics of a supercritical carbon dioxide turbulent mixing layer in the presence of strong nonlinearities in the thermodynamic and transport properties. A bespoke experimental setup is designed and employed for this purpose and provides insight into macroscopic mixing behavior. The mixing is experimentally observed using two techniques: shadowgraphy and spontaneous Raman scattering. Qualitative and quantitative intensity fields obtained via these techniques yield instantaneous and mean density data. Spanwise temperature data is also collected using analogue resistance temperature detectors. These measurements are used to quantify the level of mixed material within the field. The experimental data are supplemented by a companion high-fidelity numerical study. The numerical results are obtained through fully resolved, three-dimensional direct numerical simulation. The numerical dataset permits observation of the near-field mixing characteristics, which are difficult to measure experimentally due to the rapid dynamics and sharp thermophysical gradients in this area. Qualitative field visualizations are presented, followed by quantitative mixed material results and observations regarding thermodynamic property trends at select locations within the field. One-dimensional spectra of the turbulent kinetic energy and solenoidal dissipation are provided to observe the spectral characteristics of the flow. Reynolds stress anisotropy is analyzed graphically through anisotropy invariance maps (Lumley triangles). The mixing quantification, spectral data and anisotropy analysis of a flow at these thermodynamic conditions represent the main outcomes of the work.

20 FOSSIL-FUELED POWER PLANTS↗

NASA NTRS2011

Axisymmetric Implementation for 3D-Based DSMC Codes

The primary objective in developing NASA s DSMC Analysis Code (DAC) was to provide a high fidelity modeling tool for 3D rarefied flows such as vacuum plume impingement and hypersonic re-entry flows [1]. The initial implementation has been expanded over time to offer other capabilities including a novel axisymmetric implementation. Because of the inherently 3D nature of DAC, this axisymmetric implementation uses a 3D Cartesian domain and 3D surfaces. Molecules are moved in all three dimensions but their movements are limited by physical walls to a small wedge centered on the plane of symmetry (Figure 1). Unfortunately, far from the axis of symmetry, the cell size in the direction perpendicular to the plane of symmetry (the Z-direction) may become large compared to the flow mean free path. This frequently results in inaccuracies in these regions of the domain. A new axisymmetric implementation is presented which aims to solve this issue by using Bird s approach for the molecular movement while preserving the 3D nature of the DAC software [2]. First, the computational domain is similar to that previously used such that a wedge must still be used to define the inflow surface and solid walls within the domain. As before molecules are created inside the inflow wedge triangles but they are now rotated back to the symmetry plane. During the move step, molecules are moved in 3D but instead of interacting with the wedge walls, the molecules are rotated back to the plane of symmetry at the end of the move step. This new implementation was tested for multiple flows over axisymmetric shapes, including a sphere, a cone, a double cone and a hollow cylinder. Comparisons to previous DSMC solutions and experiments, when available, are made.

Stewart, Benedicte↗

NASA NTRS1989

Application of unstructured grid methods to steady and unsteady aerodynamic problems

The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Batina, John T.↗