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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Integrated Neutronics Modeling for Inertial Fusion Energy Systems: Development and Application to LD-FIRST

Lawrence Livermore National Laboratory (LLNL) is proposing a new Laser Driven Fusion Integration Research and Science Test Facility (LD-FIRST) with the goal of providing an experimental testbed for future Inertial Fusion Energy (IFE) systems. However, IFE systems require detailed and accurate multiphysics modeling to quantify material damage, thermal loading, and tritium breeding within complex chamber environments. This article presents the first step in an integrated multiphysics framework that couples meshed CAD-based geometry within Monte Carlo neutronic simulations to enable high-fidelity analysis of IFE chamber concepts, with future coupling to external codes. The neutronics workflow utilizes OpenMC and its third-party capability to use CAD-based geometries through DAGMC and tally on unstructured meshes with Libmesh to evaluate neutron transport behavior, geometric fidelity, and material performance under reactor-relevant conditions. The use of tailored tallies on unstructured meshes in this framework allows direct transfer without interpolating to CFD simulation tools. Two IFE chambers were evaluated, both conceived by LLNL: HYLIFE-II and Laser IFE (LIFE). This work produced high-fidelity conformal surface and volumetric meshes of the HYLIFE-II and LIFE chambers with mapped spatial insight into material damage, thermal loading, and tritium breeding. The HYLIFE-II model was built utilizing available resources and used as a test case to verify that the neutronics framework can handle complex geometries. The LIFE chamber CAD was provided by LLNL and was the main focus of this work. This work analyzes multiple ternary alloy breeding materials for the LIFE chamber, across different 6 Li enrichments to produce data relevant to the LD-FIRST project. This work also investigates the level of model fidelity for the LIFE chamber, and results show that inclusion of detailed first wall and coolant structures increased the predicted tritium breeding ratio (TBR) by ~30%, highlighting the sensitivity of tritium breeding and the need for a high-fidelity simulation framework for IFE chambers. These developments provide a scalable toolset for the design and optimization of next-generation IFE chambers, forming a solid foundation for future coupled multiphysics analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Preparing an Incompressible-Flow Fluid Dynamics Code for Exascale-Class Wind Energy Simulations

The U.S. Department of Energy has identified exascale-class wind farm simulation as critical to wind energy scientific discovery. A primary objective of the ExaWind project is to build high-performance, predictive computational fluid dynamics (CFD) tools that satisfy these modeling needs. GPU accelerators will serve as the computational thoroughbreds of next-generation, exascale-class supercomputers. Here, we report on our efforts in preparing the ExaWind unstructured mesh solver, Nalu-Wind, for exascale-class machines. For computing at this scale, a simple port of the incompressible-flow algorithms to GPUs is insufficient. To achieve high performance, one needs novel algorithms that are application aware, memory efficient, and optimized for the latest-generation GPU devices. The result of our efforts are unstructured-mesh simulations of wind turbines that can effectively leverage thousands of GPUs. In particular, we demonstrate a first-of-its-kind, incompressible-flow simulation using Algebraic Multigrid solvers that strong scales to more than 4000 GPUs on the Summit supercomputer.

algebraic multigrid↗
DOE OSTI2020

Co-Extrusion (CoEx) for Cost Reduction of Advanced High-Energy-and-Power Battery Electrode Manufacturing

Co-Extrusion (CoEx) is a deposition technology developed at PARC that uses engineered fluidic channels to cause multiple streams of dissimilar fluids to impart shape to one another. Here, we describe the use of CoEx to produce structured cathode electrode films to improve electrochemical performance of thick electrode films. CoEx enables us to create structured electrode films that have periodic regions of enhanced ionic conductivity, enabling higher utilization of thicker cathode films at high discharge rates. While increasing electrode thickness is a known method for increasing energy density of battery electrodes, this increase in energy density typically also results in reduced power density. This project, a collaboration between the Palo Alto Research Center, Oak Ridge National Laboratories, and Ford Motor Company, seeks to first validate the benefits of CoEx at the coin cell level, before performing the necessary R&D effort to scale production up to large (10+ Ah) pouch cells that will show increased energy density without a reduction in power density. We used conventional battery materials (commercially available NMC, PVDF, carbon black, and graphite) to produce structured electrodes via CoEx and compared them to thick and thin conventionally produced (unstructured) battery electrodes. CoEx electrodes show improved high rate performance compared to unstructured electrodes, resulting in higher energy density pouch cells compared to the baseline electrode of 7 and 11% in volumetric and gravimetric energy density, respectively. These electrodes also showed substantially improved electrochemical performance at high discharge rates compared to thick conventional electrodes.

25 ENERGY STORAGE↗
DOE OSTI2020

Survey of Current State of the Art Entity-Relation Extraction Tools

In the area of information extraction from text data, there exists a number of tools with the capability of extracting entities, topics, and their relationships with one another from both structured and unstructured text sources. Such information has endless uses in a number of domains, however, the solutions to getting this information are still in early stages and has room for improvement. The topic has been explored from a research perspective by academic institutions, as well as formal tool creation from corporations but has not made much advancement since the early 2000's. Overall, entity extraction, and the related topic of entity linking, is common among these tools, though with varying degrees of accuracy, while relationship extraction is more difficult to find and seems limited to same sentence analysis. In this report, we take a look at the top state of the art tools currently available and identify their capabilities, strengths, and weaknesses. We explore the common algorithms in the successful approaches to entity extraction and their ability to efficiently handle both structured and unstructured text data. Finally, we highlight some of the common issues among these tools and summarize the current ability to extract relationship information.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗
DOE OSTI2021

Evaluation of Attila and MCNP computational methods for dose and exposure estimation

Radiation transport calculations are often used to estimate dose or exposure to components and personnel surrounding a radiation source. The sources for these calculations are decaying radionuclides within various nuclear materials. Historically, dose calculations use MCNP (Monte Carlo N-Particle) transport code as the primary particle transport tool without a secondary computational tool to validate the results from the MCNP simulations [1]. The goal of this study is to make an independent check of the Monte Carlo solution from MCNP6 Version 6.2.1 with the discrete ordinates solution from Attila 10.2.0 Beta 3. As an example problem for this study, water-filled, stainless-steel vessels, modeled with an unstructured mesh (UM) with both MCNP and Attila [2], are exposed to 252Cf and 60Co point sources. This report also includes a discussion of the limitations of unstructured mesh in a MCNP calculation.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Performance Results on CPU/GPU Exascale Architectures for OMEGA: The Ocean Model for E3SM Global Applications

The US Department of Energy (DOE) conducts climate simulations on some of the world’s largest supercomputers. These exascale machines use heterogeneous architectures with both CPUs and GPUs, and scientific codes must adapt to make full use of this computing power. Los Alamos National Lab is developing Omega: The Ocean Model for E3SM Global Applications, which is specifically designed for modern exascale computers. It uses external libraries that have been optimized for a variety of architectures to run on different supercomputers. Omega is an unstructured-mesh ocean model based on TRiSK numerical methods. It will be the new ocean component of the DOE’s Energy Exascale Earth System Model (E3SM). The algorithms in Omega follow those of the current ocean component, MPAS-Ocean, but it will be written in C++ rather than Fortran to take advantage of the Kokkos performance portability library. Omega spatial operators are written as Kokkos kernels to run efficiently on both CPUs and GPUs. Work on Omega began in 2023 with a new C++ framework for unstructured mesh partitioning, halo exchanges, parallel IO, and Kokkos interfaces. The current version, Omega-0, is being developed to solve the shallow water equations and at present includes all of the tendency terms but not time stepping. Here we share the results of Omega-0 verification and performance testing. Verification includes unit tests implemented with CTest as well as convergence tests in Polaris, an in-house python package with a large suite of test problems. Performance tests compare simulations conducted on CPUs versus GPUs and across different architectures: tests are run on Frontier, which has AMD “Optimized 3rd Gen EPYC” CPUs and AMD MI250X GPUs, as well as Perlmutter, which is composed of AMD EPYC 7763 CPUs and NVIDIA A100 GPUs.

58 GEOSCIENCES↗
DOE OSTI2024

Application of Modified Meshgraphnets for Subsurface Prediction during CO2 Sequestration

In the face of the increasingly dire consequences of anthropogenic climate change, capturing and storing carbon dioxide is paramount. However, several impediments exist to the safe and effective subsurface storage of CO2, such as cost of transport, identification of suitable sites for subsurface storage, and assessment of long-term risk from storage in subsurface aquifers. Accurate subsurface modeling is necessary to ensure that CO2 storage is both safe and effective. Still, such modeling has traditionally required either substantial time and computational power (numerical simulation) or a substantial amount of pre-existing data for training (machine learning models). Additionally, these models lack flexibility in dealing with both changes in discretization of the input data and generalizability beyond the data on which they are trained. In order to address these issues, this research applies graph neural networks (GNNs) to predict subsurface saturation and pressure during CO₂ injection in a model of the Illinois Basin-Decatur Project (IBDP). GNNs provide a flexible, intuitive method for representing and manipulating complex unstructured data, which is often found in many practical domain problems such as fluid flow and subsurface characterization. These unstructured grids are easily represented in GNNs by representing spatially-localized features such as permeability, porosity, saturation, and pressure as nodes in a graph and relationships between these properties as edges connecting these nodes. This research applies a specific GNN model called MeshGraphNets (MGN) to model the change in CO2 saturation and pressure over a 50-month time period (36 months of injection, 14 months post-injection). The MGN model leverages a message passing process that allows the network to learn both the spatial and temporal dynamics of this system simultaneously. Additionally, training on a limited dataset (64 realizations, 20 time points each) resulted in a high degree of accuracy in saturation prediction both within the same timeframe as the training (20 months, 0.039 average RMSE) and when projecting out to the end of injection (36 months, 0.053 average RMSE). Temporal predictions such as those generated by MGNs and other similar models are prone to accumulated error over time; in order to address this, a multi-step rollout (MSR) training process was applied to calculate training loss. This method mimics the forward prediction during inference by “rolling out” multiple time points in a single training step using the previous prediction as input to the MGN model. By calculating the loss several time steps forward from the current prediction, the model is forced to find a more stable state over time. Application of MSR to the MGN model resulted in an average 15% reduction in inference error over time during forward prediction. This study showcases the immense potential of GNNs as a game-changing methodology for predicting pressure and saturation evolution in CCS projects, ultimately paving the way for more sustainable and effective carbon storage solutions. Presentation prepared for the 2024 AiChE Annual Meeting, October 27 to November 1 2024, San Diego, CA.

Holcomb, Paul↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2025

AI-Assisted Conceptual Development of a Pre-Geometric Cosmological Model - An Exercise in AI-Assisted Conceptual Framework Generation, Paper I: Foundations and Replication Dynamics

We develop a pre-geometric cosmological framework in which existence is identified with a finite amount of unstructured energy possessing vibration as its only intrinsic property. This vibrational substrate occupies an open, bounded spectral interval $(\omega_{\min},\omega_{\max})$, ensuring finiteness of total energy and excluding infinitely stable configurations. The substrate evolves under two fundamental and competing tendencies---excitation, which amplifies coherence, and randomization, which scrambles it. Their balance produces a metastable unstructured regime in which rare fluctuations may form long-lived self-consistent spectral configurations. Because the substrate is finite and subject to competing order--disorder dynamics, no coherent configuration can be perpetually stable. We show that the only mechanism capable of sustaining long-lived organization is a replication instability: a coherent unit may reproduce into multiple offspring according to a general $1\!\to n$ rule. Replication consumes energy from the finite substrate, breaks the metastable symmetry, and induces a discrete notion of event time through the replication tick $\Delta\tau$. Temporal succession is defined through correlation ordering of spectral microstates, producing an intrinsic pre-causal structure. The compactness of the spectral domain imposes minimal and maximal timescales, bounds the internal coherence of emergent units, and limits their proliferation. These spectral constraints serve as precursors for the emergence of geometry, adjacency, and a limiting propagation speed, developed in subsequent papers of this series. Paper I provides the foundational axioms (PG1--PG9) governing the spectral substrate, its metastable dynamics, the formation of coherent units, and the necessity of replication, establishing a fully pre-geometric stage from which causal and geometric structure naturally emerge.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Synthetic Digital Environments for Training Robots on Earth & Beyond [Poster]

Creating physical replicas of real-world environments to train robots for challenging outdoor tasks, whether constructing energy infrastructure like solar farms on Earth or on the Moon and Mars, is prohibitively expensive. This project will prototype a high-fidelity digital twin framework using NVIDIA IsaacSim to create realistic digital representations of robotic systems and their operating conditions, including varied terrains and environmental factors, allowing robots to learn and adapt in a faster, safer, and more affordable way to tackle unpredictable challenges in terrestrial and extraterrestrial applications. The Robotic Space Exploration (RoSE) Lab at Colorado School of Mines focused on the development and testing of synthetic digital twins to explore multi-physics interactions between robots and unstructured environments, with emphasis on lunar conditions such as deformable regolith, reduced gravity, and terrain-robot contact dynamics. The Industrialized Construction Innovation (ICI) team at National laboratory of the Rockies (NLR), simulated robotic apparatus and construction workflows using synthetic digital twins to inform real-world deployment, targeting application-driven use cases such as robotic construction of a scaled prototype of a photovoltaic energy infrastructure. Joint efforts between RoSE and ICI are continuing to explore how environment-scale multi-physics modeling and application-level robotic system simulation could be integrated to support robotic construction of energy infrastructure in highly unstructured environments, including scenarios relevant to the Lunar South Pole.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

FPGA Acceleration of GCN in Light of the Symmetry of Graph Adjacency Matrix

Graph Convolutional Neural Networks (GCNs) are widely used to process large-scale graph data. Different from deep neural networks (DNNs), GCNs are sparse, irregular, and unstructured, posing unique challenges to hardware acceleration with regular processing elements (PEs). In particular, the adjacency matrix of a GCN is extremely sparse, leading to frequent but irregular memory access, low spatial/temporal data locality and poor data reuse. Furthermore, a realistic graph usually consists of unstructured data (e.g., unbalanced distributions), creating significantly different processing times and imbalanced workload for each node in GCN acceleration. To overcome these challenges, we propose an end-to-end hardware-software co-design to accelerate GCNs on resource-constrained FPGAs with the features including: (1) A custom dataflow that leverages symmetry along the diagonal of the adjacency matrix to accelerate feature aggregation for undirected graphs. We utilize either the upper or the lower triangular matrix of the adjacency matrix to perform aggregation in GCN to improve data reuse. (2) Unified compute cores for both aggregation and transform phases, with full support to the symmetry-based dataflow. These cores can be dynamically reconfigured to the systolic mode for transformation or as individual accumulators for aggregation in GCN processing. (3) Preprocessing of the graph in software to rearrange the edges and features to match the custom dataflow. This step improves the regularity in memory access and data reuse in the aggregation phase. Moreover, we quantize the GCN precision from FP32 to INT8 to reduce the memory footprint without losing the inference accuracy. We implement our accelerator design in Intel Stratix10 MX FPGA board with HBM2, and demonstrate 1.3x-110.5x improvement in end-to-end GCN latency as compared to the state-of the-art FPGA implementations, on the graph datasets of Cora, Pubmed, Citeseer and Reddit.

Nair, Gopikrishnan R.↗
NASA NTRS1985

Tree-oriented interactive processing with an application to theorem-proving, appendix E

The concept of unstructured structure editing and ted, an editor for unstructured trees, is described. Ted is used to manipulate hierarchies of information in an unrestricted manner. The tool was implemented and applied to the problem of organizing formal proofs. As a proof management tool, it maintains the validity of a proof and its constituent lemmas independently from the methods used to validate the proof. It includes an adaptable interface which may be used to invoke theorem provers and other aids to proof construction. Using ted, a user may construct, maintain, and verify formal proofs using a variety of theorem provers, proof checkers, and formatters.

Hammerslag, David↗
NASA NTRS1985

Recent developments in FEM-CFD

The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large three-dimensional problems involving flow past arbitrary geometries are developed. Adaptive mesh refinement strategy is reviewed, and domain splitting or local time-stepping are briefly addressed. The development of search algorithms of optimal order, variable time-stepping Jacobi smoothers for elliptic problems, and transport concepts for hyperbolics to help achieve good performance for unstructured multigrid processes is discussed. As examples, transient supersonic flow in a channel, regular shock reflection of a wall, viscous flow past a protruberance, potential flow past a cylinder, and Burgers equation are considered.

Loehner, R.↗
NASA NTRS1988

Adaptive mesh generation for viscous flows using Delaunay triangulation

A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

Mavriplis, Dimitri J.↗
NASA NTRS1987

Knowledge-based vision for space station object motion detection, recognition, and tracking

Computer vision, especially color image analysis and understanding, has much to offer in the area of the automation of Space Station tasks such as construction, satellite servicing, rendezvous and proximity operations, inspection, experiment monitoring, data management and training. Knowledge-based techniques improve the performance of vision algorithms for unstructured environments because of their ability to deal with imprecise a priori information or inaccurately estimated feature data and still produce useful results. Conventional techniques using statistical and purely model-based approaches lack flexibility in dealing with the variabilities anticipated in the unstructured viewing environment of space. Algorithms developed under NASA sponsorship for Space Station applications to demonstrate the value of a hypothesized architecture for a Video Image Processor (VIP) are presented. Approaches to the enhancement of the performance of these algorithms with knowledge-based techniques and the potential for deployment of highly-parallel multi-processor systems for these algorithms are discussed.

Symosek, P.↗
NASA NTRS1989

Multigrid solution of the Navier-Stokes equations on triangular meshes

A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. The convergence efficiency of the present method is shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗
NASA NTRS1989

Two-dimensional Euler computations on a triangular mesh using an upwind, finite-volume scheme

A numerical procedure was developed for the finite-volume solution of the Euler equations on unstructured triangular meshes based on a flux-difference split upwind method. Techniques for implementing Roe's (1985) approximate Reimann solver together with the preprocessing MUSCL differencing on unstructured grids are presented. Applications and comparisons with structured grid problems are carried out for a supersonic shock reflection problem, the supersonic flow over a blunt body, the transonic flow over NACA 0012 and RAE 2822 airfoils, and the flow about a double element Karman-Trefftz airfoil.

Whitaker, D. L.↗