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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

High-fidelity wind farm simulation methodology with experimental validation

The complexity and associated uncertainties involved with atmospheric-turbine-wake interactions produce challenges for accurate wind farm predictions of generator power and other important quantities of interest (QoIs), even with state-of-the-art high-fidelity atmospheric and turbine models. A comprehensive computational study was undertaken with consideration of simulation methodology, parameter selection, and mesh refinement on atmospheric, turbine, and wake QoIs to identify capability gaps in the validation process. For neutral atmospheric boundary layer conditions, the massively parallel large eddy simulation (LES) code Nalu-Wind was used to produce high-fidelity computations for experimental validation using high-quality meteorological, turbine, and wake measurement data collected at the Department of Energy/Sandia National Laboratories Scaled Wind Farm Technology (SWiFT) facility located at Texas Tech University’s National Wind Institute. The wake analysis showed the simulated lidar model implemented in Nalu-Wind was successful at capturing wake profile trends observed in the experimental lidar data.

17 WIND ENERGY↗
DOE OSTI2024

DNS of Flame Stabilization Dynamics of a Swirl-Stabilized Spray Burner Using Sustainable Aviation Fuels

Concern for emission reduction has motivated the development of new cost-effective alternative sustainable aviation fuels (SAFs). Drop-in SAFs with blends of the certified and the alternative fuels are beneficial because they do not require engine modifications for use in current aviation engines. Combustion characteristics are of particular concern when comparing a new fuel with Jet-A. Lean blow-off and flame stabilization have been identified to be governed by the fuel propensity to autoignition, i.e. derived cetane number. However, fundamental investigation is required to identify the impact of derived cetane number on the combustion mode of flame stabilization in a realistic combustor. The combustion mode has also a direct impact on turbulent combustion modeling closures. DNS simulations are performed in the low-Mach solver of the Pele Suite called PeleLMeX. Lagrangian multi-phase modeling is used to capture the liquid spray injection of Jet-A (reference fuel) and C1 as a representative of a low cetane number SAF. Adaptive Mesh Refinement (AMR) is used to enable a more efficient simulation of a more realistic domain size and embedded boundary treatment is used to model a bluff-body geometry. Local extinction and edge flame propagation were observed for both fuels. The edge flame propagation mode was quantified in terms of a Damkohler number defined as the ratio between progress variable reaction rate and its diffusive flux. Initial analysis suggests that a mixed mode combustion occurs for the edge flame propagation, with flame propagation assisted by ignition and autoignition co-existing for both Jet-A and C1 flames. The analysis of the extinction region shows a larger progress variable for Jet-A which can further increase the local displacement speed and present a faster reignition of the stoichiometric mixture fraction.

adaptive mesh refinement↗
DOE OSTI2023

High-Fidelity Simulations of Plasma-Assisted Oxidation of Hydrocarbon Fuels Using Nanosecond Pulsed Discharges

Next, a robust and efficient framework for simulating NSPD in multiple dimensions is developed. The reactive Navier-Stokes equations are extended to include a drift-diffusion plasma-fluid model with a local field approximation (LFA) in a finite-volume solver, which uses an adaptive mesh refinement (AMR) strategy to address the wide separation of length scales in the problem. A two-way coupling strategy is used whereby the plasma-fluid model and reactive Navier-Stokes equations are integrated simultaneously. The oxidation of ethylene/air mixtures mediated by NSPD is simulated in a pin-to-pin configuration. All phases of the plasma discharge are simulated explicitly (including streamer ignition, propagation, and connection, as well as the subsequent spark phase), along with the evolution of the plasma during the inter-pulse period. Temporally and spatially-resolved results are presented, with an emphasis on the analysis of heating and energy deposition, as well as of the evolution of the concentration of active particles generated during the NSPD and their influence on ignition.

adaptive mesh refinement↗
DOE OSTI2026

A GPU-based compressible combustion solver for applications exhibiting disparate space and time scales

High-speed chemically active flows pose significant computational challenges due to their disparate space and time scales, with stiff chemistry often dominating simulation time. While modern scientific computing programs achieve exascale performance by leveraging graphics processing units (GPUs), existing GPU-based compressible combustion solvers face critical limitations in memory management, load balancing, and handling the highly localized nature of chemical reactions. To this end, we present a high-performance compressible reacting flow solver built on the AMReX framework and optimized for multi-GPU settings. Here, our approach addresses three GPU performance bottlenecks: memory access patterns through column-major storage optimization, computational workload variability via a bulk-sparse integration strategy for chemical kinetics, and multi-GPU load distribution for adaptive mesh refinement applications. The solver adapts existing matrix-based chemical kinetics formulations to multi-grid contexts. Using representative combustion applications, including 2D and 3D detonations and a 3D jet-in-crossflow configuration, we demonstrate 1.4–5× performance improvements over initial implementations on an in-house cluster of NVIDIA H100 GPUs, and near-ideal weak scaling on the Frontier supercomputer (Oak Ridge Leadership Computing Facility) with up to 1024 AMD Instinct MI250X GPUs. Roofline analysis reveals substantial improvements in arithmetic intensity for both convection (∼ 10 ×) and chemistry (∼ 4 ×) routines, confirming efficient utilization of GPU memory bandwidth and computational resources.

42 ENGINEERING↗
DOE OSTI2024

Scalable Implicit Solvers with Dynamic Mesh Adaptation for a Relativistic Drift-Kinetic Fokker–Planck–Boltzmann Model

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. Here, we develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Numerical Analysis of Combustion Dynamics in a Full-Scale Rotating Detonation Rocket Engine using Large Eddy Simulations

Large eddy simulations (LES) using detailed chemistry and leveraging adaptive mesh refinement (AMR) are performed to gain insights into the combustion dynamics within a full-scale methane-oxygen non-premixed rotating detonation rocket engine (RDRE) employing impinging discrete injection schemes. In particular, a comparative analysis of two operating conditions corresponding to the same global equivalence ratio but different mass flow rates is carried out to investigate the resultant impact on detonation wave characteristics and RDRE global performance. Multiple co-rotating detonation waves with spatially-distributed wave structure and preferential alignment with the inner wall of the annulus (due to asymmetry in fuel distribution) are encountered under both conditions. Both cases exhibit pre-detonation deflagrative burning in the fill region, while one of the cases shows higher susceptibility to backflow into the feed plenums due to lower plenum pressures. Furthermore, heat release analysis shows that the thrust obtained from the RDRE is closely linked to the distribution of total heat release between detonative and deflagrative combustion. On the other hand, combustion efficiency is associated with the fraction of heat release occurring in fuel-rich versus fuel-lean regions within the RDRE.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Adaptive Space-Time Methods for Large Scale Optimal Design

When modeling complex physical systems with advanced dynamics, such as shocks and singularities, many classic methods for solving partial differential equations can return inaccurate or unusable results. One way to resolve these complex dynamics is through r-adaptive refinement methods, in which a fixed number of mesh points are shifted to areas of high interest. The mesh refinement map can be found through the solution of the Monge-Ampére equation, a highly nonlinear partial differential equation. Due to its nonlinearity, the numerical solution of the Monge-Ampére equation is nontrivial and has previously required computationally expensive methods. In this report, we detail our novel optimization-based, multigrid-enabled solver for a low-order finite element approximation of the Monge-Ampére equation. This fast and scalable solver makes r-adaptive meshing more readily available for problems related to large-scale optimal design. Beyond mesh adaptivity, our report discusses additional applications where our fast solver for the Monge-Ampére equation could be easily applied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Numerical Study on the Effect of Methane Doping in Hydrogen-Air Rotating Detonation Engines for Various Temperatures and Pressures

Rotating detonation engines (RDEs) have gained attention as a promising technology for future aviation engines. However, the numerical studies of these systems pose severe challenges due to the broad range of spatial and temporal scales. In this study, we use an adaptive mesh refinement based compressible, reactive solver PeleC to resolve the broad range of scales and accurately capture shock and detonation waves using high-resolution numerical schemes. Multi- species transport along with compressible Navier-Stokes equations are solved in the model along with a finite-rate based chemistry model. Embedded boundary method is used to model the complex geometry consisting of discrete fuel nozzles and the combustion chamber. The fuel consisting predominantly of hydrogen is doped with varying levels of methane while air is used as the oxidizer. For a specified total pressure and temperature, the number of stable detonation waves is found to decrease with increasing methane concentration in the fuel mixture. Additionally, no stable detonation solutions are observed for methane composition higher than 20% by volume for the range of operating conditions studied (300-900K, 10 Atm). The increased presence of high temperature zones is also indicative of higher thermal NOx emissions at low methane concentrations. The effect of fuel-air mixture composition and temperature on the detonability, detonation wave structure, mode transitions and their stability are analyzed in this study in addition to their implication on NOx emission.

automatic mesh refinement↗
DOE OSTI2022

Computation of conventional and alternative jet fuel sensitivity to lean blowout

Large Eddy Simulations (LES) are performed to compute the sensitivity of a conventional (A-2) and an alternate bio-jet (C-1) fuel to Lean Blowout (LBO). A realistic aviation gas turbine engine combustor configuration is considered. Reliable experimental LBO data and OH* chemiluminescence data for the conventional and alternate jet fuel in the combustor configuration have recently become available. The present work utilizes a highly automated, on-the-fly meshing strategy, along with adaptive mesh refinement, to demonstrate the feasibility of capturing the realistic combustion processes. A Lagrangian framework, with initial conditions specified using measurements of spray statistics, is used to model the fuel spray. Newly developed compact reaction mechanisms based on fuel surrogates are validated for the A-2 and the C-1 fuels. The compact reaction mechanisms are implemented using a detailed finite rate chemistry solver. Spray statistics computed by the present LES simulations compare well with available measurements at stable flame conditions near the lean blowout limit. The computed shape of the stable flame as represented by line integrated OH concentrations compares well with the experimental OH* chemiluminescence data. Lean blowout is reached by gradually decreasing the fuel flow rate in the computations, similar to that in the experiments. The results of the LES simulations effectively capture the fuel composition effects and estimate the sensitivity of the LBO limits to the fuel type. The computed trends in LBO limits agree within engineering accuracy with the experimental results for conventional and alternative aviation fuels. The methodology for predicting the fuel composition effects on the lean blowout limits in a fully resolved realistic, complex combustor is established for the first time.

Adaptive mesh refinement↗
DOE OSTI2022

The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven Hohlraums

Hohlraums are hollow cylindrical cavities with high-Z material walls used to convert laser energy into uniform x-ray radiation drives for inertial confinement fusion capsule implosions and high energy density physics experiments. Credible computational modeling of hohlraums requires detailed modeling and coupling of laser physics, hydrodynamics, radiation transport, heat transport, and atomic physics. We report on improvements to Los Alamos National Laboratory's xRAGE radiation-hydrodynamics code in order to enable hohlraum modeling. xRAGE's Eulerian hydrodynamics and adaptive mesh refinement make it uniquely well suited to study the impacts of multiscale features in hohlraums. In order to provide confidence in this new modeling capability, we demonstrate xRAGE's ability to produce reasonable agreement with data from several benchmark hohlraum experiments. We also use xRAGE to perform integrated simulations of a recent layered high density carbon capsule implosion on the National Ignition Facility in order to evaluate the potential impacts of the capsule support tent, mixed cell conductivity methodologies, plasma transport, and cross-beam energy transfer (XBT). We find that XBT, seeded by plasma flows in the laser entrance hole (LEH), causes a slight decrease in energy coupling to the capsule and that all of these impact the symmetry of the x-ray drive such that they have an appreciable impact on the capsule implosion shape.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Detonation structure in the presence of mixture stratification using reaction-resolved simulations

Many investigations of detonation-based combustors have identified reactant mixture inhomogeneity as having a leading-order impact on wave dynamics and combustion efficiency. To examine this phenomenon in a simplified context, an array of two- and three-dimensional channel detonation simulations are conducted in the present work. The reactant mixture consists of stratified fuel and air, wherein the randomly distributed equivalence ratio field features a characteristic stratification length scale. Detailed chemical kinetics are implemented in an adaptive mesh refinement solution framework where the region near the shock front is resolved with Ο (100) cells per representative ZND induction length. The results show that in comparison to baseline cases with uniform reactant mixtures, reactant stratification has a marked impact on the detonation structure. Increasing the stratification length scale increases the size and irregularity of the detonation cells, yielding larger variations in wave speed. Triple point collisions in fuel-rich regions lead to local wave speeds above the notional mean CJ speed, but wave passage through inert regions causes the local wave speed and strength to diminish. Further, conditional statistics show that increasing the stratification length scale increases the variance in pressure and temperature in the primary reaction zone, as well as the variance in heat release over a range of mixture conditions. In addition to the reactant mixture, the impact of the boundary condition behind the detonation is also investigated. The results show that an inflow boundary condition acts to over-drive the wave, leading to higher peak pressures, smaller detonation cells, and increased reactant consumption. On the other hand, cases with a wall behind the wave exhibit weaker waves with lower peak pressures and heat release rates, as well as greater variance in conditional quantities. Comparisons between complementary two- and three-dimensional simulations show reasonable qualitative agreement in wave structure, speed, and conditional statistics.

42 ENGINEERING↗
DOE OSTI2022

Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Abstract A new adaptive clipping‐and‐redistribution method is presented which provides bounds‐preservation for multidimensional interpolation in the context of high‐order finite‐volume discretizations with adaptive mesh refinement (AMR). The underlying finite‐volume method (FVM) for the computational fluid dynamics applications is fourth‐order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High‐order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high‐order interpolation method. First, the method needs to be bound‐preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth‐order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock‐induced ‐ combustion and a ‐air flame in a practical bluff‐body combustor. Results show the method prevents new extrema near discontinuities while maintaining high‐order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Asynchronous-many-task systems: Challenges and opportunities - Scaling an AMR astrophysics code on exascale machines using Kokkos and HPX

Dynamic and adaptive mesh refinement is pivotal in high-resolution, multi-physics, multi-model simulations, necessitating precise physics resolution in localized areas across expansive domains. Today’s supercomputers’ extreme heterogeneity presents a significant challenge for dynamically adaptive codes, highlighting the importance of achieving performance portability at scale. Our research focuses on astrophysical simulations, particularly stellar mergers, to elucidate early universe dynamics. Here, we present Octo-Tiger, leveraging Kokkos, HPX, and SIMD for portable performance at scale in complex, massively parallel adaptive multi-physics simulations. Octo-Tiger supports diverse processors, accelerators, and network backends. Experiments demonstrate exceptional scalability across several heterogeneous supercomputers including Perlmutter, Frontier, and Fugaku, encompassing major GPU architectures and x86, ARM, and RISC-V CPUs. Parallel efficiency of 47.59% (110,080 cores and 6880 hybrid A100 GPUs) on a full-system run on Perlmutter (26% HPCG peak performance) and 51.37% (using 32,768 cores and 2048 MI250X) on Frontier are achieved.

97 MATHEMATICS AND COMPUTING↗
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↗
DOE OSTI2025

E3SM‐Arctic: Regionally Refined Coupled Model for Advanced Understanding of Arctic Systems Interactions

Earth system models are essential tools for climate projections, but coarse resolutions limit regional accuracy, especially in the Arctic. Regionally refined meshes (RRMs) enhance resolution in key areas while maintaining computational efficiency. This paper provides an overview of the United States (U.S.) Department of Energy's (DOE's) Energy Exascale Earth System Model version 2.1 with an Arctic RRM, hereafter referred to as E3SMv2.1-Arctic, for the atmosphere (25 km), land (25 km), and ocean/ice (10 km) components. We evaluate the atmospheric component and its interactions with land, ocean, and cryosphere by comparing the RRM (E3SM2.1-Arctic) historical simulations (1950–2014) with the uniform low-resolution (LR) counterpart, reanalysis products, and observational data sets. The RRM generally reduces biases in the LR model, improving simulations of Arctic large-scale mean fields, such as precipitation, atmospheric circulation, clouds, atmospheric river frequency, and sea ice thickness. However, it introduces a seasonally dependent surface air temperature bias, reducing the LR cold bias in summer but enhancing the LR warm bias in winter, which contributes to the underestimated winter sea ice area and volume. Radiative feedback analysis shows similar climate feedback strengths in both model configurations, with the RRM exhibiting a more positive surface albedo feedback and contributing to a stronger surface warming than LR. These findings underscore the importance of high-resolution modeling for advancing our understanding of Arctic climate changes and their broader global impacts, although some persistent biases appear to be independent of model resolution at 10–100 km scales.

Energy Exascale Earth System Model (E3SM)↗
DOE OSTI2021

Energy Exascale Earth System Model v2.0

First release of version 2 of the Energy Exascale Earth System Model. The atmosphere component remains EAM. Major changes since version 1 include: all column-physics parameterizations are computed on a separate grid that has approximately half the number of points of the dynamics grid, a new nonhydrostatic dynamical core (running in hydrostatic mode) with semi-Lagrangian tracer transport, CLUBB updated from v1 to v2, a new convective trigger (dCAPE/ULL) based on the dynamic Convective Available Potential Energy (CAPE) (dCAPE) and the Unrestricted Launch Level (ULL) concepts is used in ZM. minimum cloud droplet number changed, gravity wave drag energy conservation fixed and new tunings used, dust emission size distribution changed to emit more coarse dust particles The land component is still ELM. Major changes since version 1 include: using SNICAR-AD for radiation in snow to match the sea-ice model and fixing bugs in snow compaction and water state calculation. The ocean component remains MPAS-ocean. Major change since version 1 include: Redi isopycnal mixing has been updated, tested, and tuned in combination with the Gent-McWilliams parameterization, a sign error was fixed in the 3rd-order flux routines, the mesh used in low-resolution coupled cases was modified and the time steps adjusted, new regionally refined meshes were created, one focused on North America and another on the Southern Ocean, including ice shelf cavities. The sea-ice component remains MPAS-seaice. Major changes since version 1 include: A new heat- and freshwater-conserving coupling of frazil ice, turning off of SSH filtering, addition of SNICAR-AD and snow grain aging. The land-ice component remains MPAS-Albany-landIce (MALI) and is a static ice sheet. There is more out-of-the-box support for cryosphere configurations including the new regionally refined configuration around Antarctica with ice shelf cavities. The river model is MOSART. The half-degree river mesh was redone so it no longer treats Black and Caspian seas as ocean. The coupler remains cpl7/MCT. Major changes since version 1 include handling of ice shelf melt fluxes (heat / freshwater exchange with the ocean), and data icebergs. All components allow regional refinement of their meshes and two separate example of refinement, one in and around North America and one around Antarctica and the Southern Ocean, are provided.

E3SM Project, DOE↗
DOE OSTI2024

Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagrangian–Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. Here, the efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Overview of Gemma FY20 Verification Activities

Gemma verification activities for FY20 can be divided into three categories: the development of specialized quadrature rules, initial progress towards the development of manufactured solutions for code verification, and automated code-verification testing. In the method-of-moments implementation of the electric-field integral equation, the presence of a Green’s function in the four-dimensional integrals yields singularities in the integrand when two elements are nearby. To address these challenges, we have developed quadrature rules to integrate the functions through which the singularities can be characterized. Code verification is necessary to develop confidence in the implementation of the numerical methods in Gemma. Therefore, we have begun investigating the use of manufactured solutions to more thoroughly verify Gemma. Manufactured solutions provide greater flexibility for testing aspects of the code; however, the aforementioned singularities provide challenges, and existing work is limited in rigor and quantity. Finally, we have implemented automated code-verification testing using the VVTest framework to automate the mesh refinement and execution of a Gemma simulation to generate mesh convergence data. This infrastructure computes the observed order of accuracy from these data and compares it with the theoretical order of accuracy to either develop confidence in the implementation of the numerical methods or detect coding errors.

97 MATHEMATICS AND COMPUTING↗