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DOE OSTI2023

Code-verification techniques for the method-of-moments implementation of the magnetic-field integral equation

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementation of the magnetic-field integral equation, are frequently used to solve Maxwell's equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches for cases with and without coding errors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Spectrally accelerated edge and scrape-off layer gyrokinetic turbulence simulations

This paper presents the first gyrokinetic (GK) simulations of edge and scrape-off layer (SOL) turbulence accelerated by a velocity-space spectral approach in the full-f GK code GENE-X. Building upon the original grid velocity-space discretization, we derive and implement a new spectral formulation and verify the numerical implementation using the method of manufactured solution. We conduct a series of spectral turbulence simulations focusing on the TCV-X21 reference case (Oliveira et al., 2022 [26]) and compare these results with previously validated grid simulations (Ulbl et al., 2023 [25]). The spectral approach reproduces the outboard midplane (OMP) profiles (density, temperature, and radial electric field), dominated by trapped electron mode (TEM) turbulence, with excellent agreement and significantly lower velocity-space resolution. As a consequence, the spectral approach reduces the computational cost (CPUh) by at least an order of magnitude, of approximately 50 for the TCV-X21 case. This enables high-fidelity GK simulations to be performed within a few days on modern CPU-based supercomputers for medium-sized devices and establishes GENE-X as a powerful tool for studying edge and SOL turbulence, moving towards reactor-relevant devices like ITER.

Gyrokinetic↗

DOE OSTI2026

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Multiphase Species Transport Modeling for Molten Salt Reactors in the System Analysis Module: Generation, Decay, Deposition, and Extraction of Insoluble Fission Products

With the increase of interests in the design and deployment of advanced reactor systems, a desire for simulation tools supporting system analysis of reactor operation and safety is rising. Molten salt reactors (MSRs), one of the advanced reactor systems, utilize liquid fused salt fuel as both coolant and fuel. During operation, MSR generates insoluble fission products, including noble metals and gases. The buildup of these species in fuel salt presents safety concerns as they may deposit on surfaces of critical components and produce excessive decay heat, causing the failure of system components. Timely removal of these noble metals and gases would ensure the safe operation of the reactor system. The dynamic nature of salt fuel system, involving the generation, decay, deposition, and extraction of noble metals and gases, calls for robust species transport models to facilitate system analysis and monitoring, and design of efficient species removal components. This paper concentrates on the development of a computational framework for species transport, consisting of multiphase transport model formulation, mass transfer between phases, numerical implementation in MOOSE environment, verification through Method of Manufacture Solutions (MMS) and validation against experimental data from the Molten Salt Reactor Experiment (MSRE). Integrating this framework into the System Analysis Module (SAM) code further enhances SAM’s capabilities for advanced reactor analysis in the future.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Vidyut3d: A Gpu Accelerated Fluid Solver for Non-Equilibrium Plasmas on Adaptive Grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure twin electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate approximately 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

Sitaraman, Hariswaran↗

DOE OSTI2022

EEL: A MOOSE-based Application for 3D Electro-Chemo-Thermo-Mechanical Modeling of Solid-State Batteries

This report describes a tool for three dimensional, high fidelity, coupled electro-chemo-thermo-mechanical modeling of solid-state batteries. A complete version of the tool is available as open source software at https://github.com/hugary1995/eel.git. The theoretical framework of the tool revolves around an inf-sup statement on a total potential, comprising the Helmholtz free energy, the electrical kinetic potential, the chemical potential, the Fourier potential, the chemical reaction potential, and the external power expenditure. The tool uses the finite element framework of Multiphysics Object-Oriented Simulation Environment (MOOSE) and a variational formulation to solve the boundary value problem for solid-state battery incorporating the full set of multiphysics couplings. The variational formulation also enables a modular software architecture for the tool so additional physics can be easily included by specifying the new contribution to the total potential. The report discusses several method of manufactured solutions that were used to verify the implementation of different physics and the Butler-Volmer reaction kinetics at the electrolyte-electrode interface. Finally, the report discusses results from complete charge/discharge simulations of a quasi-1D and a 3D solid-state battery.

25 ENERGY STORAGE↗

NASA NTRS2008

Application of FUN3D and CFL3D to the Third Workshop on CFD Uncertainty Analysis

Two Reynolds-averaged Navier-Stokes computer codes - one unstructured and one structured - are applied to two workshop cases (for the 3rd Workshop on CFD Uncertainty Analysis, held at Instituto Superior Tecnico, Lisbon, in October 2008) for the purpose of uncertainty analysis. The Spalart-Allmaras turbulence model is employed. The first case uses the method of manufactured solution and is intended as a verification case. In other words, the CFD solution is expected to approach the exact solution as the grid is refined. The second case is a validation case (comparison against experiment), for which modeling errors inherent in the turbulence model and errors/uncertainty in the experiment may prevent close agreement. The results from the two computer codes are also compared. This exercise verifies that the codes are consistent both with the exact manufactured solution and with each other. In terms of order property, both codes behave as expected for the manufactured solution. For the backward facing step, CFD uncertainty on the finest grid is computed and is generally very low for both codes (whose results are nearly identical). Agreement with experiment is good at some locations for particular variables, but there are also many areas where the CFD and experimental uncertainties do not overlap.

Rumsey, C. L.↗

NASA NTRS2014

Turbulence Modeling Verification and Validation

Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important steps in the process. Verification insures that the CFD code is solving the equations as intended (no errors in the implementation). This is typically done either through the method of manufactured solutions (MMS) or through careful step-by-step comparisons with other verified codes. After the verification step is concluded, validation is performed to document the ability of the turbulence model to represent different types of flow physics. Validation can involve a large number of test case comparisons with experiments, theory, or DNS. Organized workshops have proved to be valuable resources for the turbulence modeling community in its pursuit of turbulence modeling verification and validation. Workshop contributors using different CFD codes run the same cases, often according to strict guidelines, and compare results. Through these comparisons, it is often possible to (1) identify codes that have likely implementation errors, and (2) gain insight into the capabilities and shortcomings of different turbulence models to predict the flow physics associated with particular types of flows. These are valuable lessons because they help bring consistency to CFD codes by encouraging the correction of faulty programming and facilitating the adoption of better models. They also sometimes point to specific areas needed for improvement in the models. In this paper, several recent workshops are summarized primarily from the point of view of turbulence modeling verification and validation. Furthermore, the NASA Langley Turbulence Modeling Resource website is described. The purpose of this site is to provide a central location where RANS turbulence models are documented, and test cases, grids, and data are provided. The goal of this paper is to provide an abbreviated survey of turbulence modeling verification and validation efforts, summarize some of the outcomes, and give some ideas for future endeavors in this area.

Rumsey, Christopher L.↗

NASA NTRS2015

Verification of a Viscous Computational Aeroacoustics Code Using External Verification Analysis

The External Verification Analysis approach to code verification is extended to solve the three-dimensional Navier-Stokes equations with constant properties, and is used to verify a high-order computational aeroacoustics (CAA) code. After a brief review of the relevant literature, the details of the EVA approach are presented and compared to the similar Method of Manufactured Solutions (MMS). Pseudocode representations of EVA's algorithms are included, along with the recurrence relations needed to construct the EVA solution. The code verification results show that EVA was able to convincingly verify a high-order, viscous CAA code without the addition of MMS-style source terms, or any other modifications to the code.

Computational↗

NASA NTRS2015

Verification of a Viscous Computational Aeroacoustics Code using External Verification Analysis

Computational↗

DOE OSTI2022

Methods for producing and using perovskite materials and devices therefrom

The present disclosure describes solution methods for manufacturing perovskite halide films for use in solar cells. The methods include the use of additives that facilitate the formation of transitory, intermediate films that are later transformed into the final target perovskite halide films, such that the final films provide improved physical characteristics and operational performance.

Zhu, Kai↗

DOE OSTI2024

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units↗

DOE OSTI2025

Verification of a Fluid-Based Plasma-Edge Model Within the Multiphysics Object-Oriented Simulation Environment (MOOSE) Framework

As the goal of achieving fusion power on the grid comes closer to fruition, fully coupled multiphysics models of fusion devices will be crucial. These models must incorporate the interconnected phenomena of these devices, including plasma physics, neutronics, first wall interactions, and tritium transport. Currently, there are two main approaches to developing these platforms: (1) loosely coupled, where one couples existing codes and solvers together through input and output parameters and data, and (2) tightly coupled, where one develops the necessary models within a singular, integrated framework. This work focuses on the latter approach for magnetically confined fusion devices by developing a fluid-based plasma-edge model within the Multiphysics Object Oriented Simulation Environment (MOOSE) Framework. This effort is coordinated with other efforts to develop, test, demonstrate, and deploy fusion relevant multiphysics capabilities including electromagnetics, particle-in-cell plasma, tritium transport, and fusion blanket design. This new model is an expansion of the MOOSE-based plasma application, Zapdos, which was originally formulated to model low-temperature, non-magnetized plasma processes. Verification studies have been conducted using newly developed magnetic plasma capabilities. These involved convergence analyses utilizing the method of manufactured solutions to verify new operators and case studies. A modular approach was taken here to demonstrate increasingly complicated simulation scenarios, which included a singular fluid with uniform magnetic field case, a singular fluid with spatially varying magnetic field case, and a coupled multifluid case.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

The Verification and Validation of a Magnetic Plasma Fluid Model Utilizing the MOOSE (Multiphysics Object Oriented Simulation Environment) Framework

As the goal of achieving fusion power on the grid comes closer to fruition, fully coupled multiphysics models of fusion devices will be crucial. Currently, there are two main approaches to developing these platforms: (1) loosely coupled, where one couples existing codes and solvers together through input and output parameters and data, and (2) tightly coupled, where one develops the necessary models within a singular, integrated framework. This work focuses on the latter approach for magnetically confined fusion devices by developing a fluid-based plasma-edge model within the Multiphysics Object Oriented Simulation Environment (MOOSE) Framework. This effort is coordinated with other efforts to develop, test, demonstrate, and deploy fusion relevant multiphysics capabilities including electromagnetics, particle-in-cell plasma, tritium transport, and fusion blanket design. This new model is an expansion of the MOOSE-based plasma application, Zapdos, which was originally formulated to model low-temperature, non-magnetized plasma processes. Verification, benchmarking, and validation studies have been conducted. Verification studies involved utilizing the method of manufactured solutions and comparing the convergence slope of a known solution to the theoretical slope. Benchmarking consists of comparisons to existing edge codes, namely BOUT++ and SOLEDGE3X. Validation efforts focused on comparisons against open-source data from the TCV tokamak.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Micropolar Elastoplasticity Using a Fast Fourier Transform‐Based Solver

ABSTRACT This work presents a micromechanical spectral formulation for obtaining the full‐field and homogenized response of elastoplastic micropolar composites. A closed‐form radial‐return mapping is derived from thermodynamics‐based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size‐dependent material response and micro‐plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.

42 ENGINEERING↗

NASA NTRS1984

Solidification interface shape for continuous casting in an offset mold - Two analytical methods

A solution method for finding the unknown solidification interface in manufacturing slab ingots as a continuous casting is presented, which involves a product solution in the potential plane and the use of conjugate harmonic functions. It is argued that the method may be more direct for some geometries than the Cauchy boundary value method. Moreover, the usefulness of the Cauchy boundary value method is demonstrated through the example of a nonsymmetric horizontal mold where the walls are offset to support the lower ingot boundary.

Siegel, R.↗

DOE OSTI2022

Organic molecular dynamics and charge-carrier lifetime in lead iodide perovskite MAPbI 3

Significance Hybrid organic–inorganic perovskites (HOIPs) are among the most promising materials for next-generation solar cells that combine high efficiency and low cost. The record efficiency of HOIP-based solar cells has reached above 25%, and they can be manufactured using simple solution-processing methods that can be drastically cheaper than the current commercial solar cell technologies. Despite the progress so far, the microscopic mechanism for the high solar cell efficiency in HOIPs is yet to be understood. In this study, we show that the ability of organic molecules to rotate on an appropriate time scale in HOIPs can extend the lifetime of photoexcited charge carriers and lead to higher efficiency. This insight can guide the progress toward improved solar cell performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1982

Inexpensive Antireflection Coating for Solar Cells

Continuous method for applying antireflection coating to solar cells increases efficiency of devices by preventing energy from being reflected away, but adds little to manufacturing cost. Method consists of spraying solution on cells or glass collector plates, drying sprayed layer, and curing it. Solution is formulated to spread evenly over surfaces.

Tracy, C. E.↗