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All sources NASA NTRS DOE OSTI

DOE OSTI2022

Accelerated Deterministic Phonon Transport With Consistent Material Temperature and Intensities

Abstract We present a method for deterministically solving the frequency and temperature dependent phonon radiative transport (PRT) equation in the single-mode relaxation time (SMRT) approximation in the self-adjoint angular flux (SAAF) form. To handle the nonlinear coupling between the phonon intensities and the material temperature, we apply a linearization approach that is similar to one in thermal radiative transport. This procedure leads to the PRT equation with pseudo-scattering. The method presented includes acceleration of both the inner pseudo-scattering source iterations and outer temperature iteration with a gray diffusion synthetic acceleration (DSA) and Anderson acceleration, respectively. We use the finite-element method to discretize the PRT equation in space and the method of discrete ordinates (SN) for angular discretization. The proposed method is verified by a gray method of manufactured solutions problem and demonstrated on a problem using temperature and direction dependent multigroup data from lithium aluminate (LiAlO2). The iterative performance of the acceleration method in each test is then compared to the unaccelerated method.

Engineering↗

NASA NTRS2017

Stabilized Finite Elements in FUN3D

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Anderson, W. Kyle↗

DOE OSTI2023

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

Code verification plays an important role in establishing the credibility of computational simulations by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, the numerical solution to integral equations incurs multiple interacting sources of numerical error, as well as other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the combined-field integral equation. Here, we demonstrate the effectiveness of these approaches for cases with and without coding errors.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Economical Third-Order Methods for Accurate Surface Heating Predictions on Simplex Element Meshes

A node-centered edge-based finite volume discretization of the compressible Navier-Stokes equations is presented with the heat flux reformulated as a first order system. A dissipation vector is derived for the reformulated system, such that the heat flux can be upgraded to O(h^3) on simplex element meshes in the same fashion as the inviscid fluxes. The method of manufactured solutions is used to demonstrate this uniform order property in heat flux. This new system is shown to efficiently produce accurate surface heating predictions on hypersonic hemisphere flow using an anisotropic simplex element mesh, achieving O(h^3) accuracy at relatively low computational cost compared to similar methods.

Computational Fluid Dynamics↗

DOE OSTI2021

Solution Irregularity Remediation for Spatial Discretization Error Estimation for S N Transport Solutions

The discrete ordinates linear Boltzmann transport equation is typically solved in its spatially discretized form, incurring spatial discretization error. Quantification of this error for purposes such as adaptive mesh refinement or error analysis requires an a posteriori estimator, which utilizes the numerical solution to the spatially discretized equation to compute an estimate. Because the quality of the numerical solution informs the error estimate, irregularities, present in the true solution for any realistic problem configuration, tend to cause the largest deviation in the error estimate vis-a-vis the true error. In this paper, an analytical partial singular characteristic tracking (pSCT) procedure for reducing the estimator’s error is implemented within our novel residual source estimator for a zeroth-order discontinuous Galerkin scheme, at the additional cost of a single inner iteration. Here, a metric-based evaluation of the pSCT scheme versus the standard residual source estimator is performed over the parameter range of a Method of Manufactured Solutions test suite. The pSCT scheme generates near-ideal accuracy in the estimate in problems where the dominant source of the estimator’s error is the solution irregularity, namely, problems where the true solution is discontinuous and problems where the true solution’s first derivative is discontinuous and the scattering ratio is low. In problems where the scattering ratio is high and the true solution is discontinuous in the first derivative, the error in the scattering source, which is not converged by the pSCT scheme, is greater than the error incurred due to the irregularity. Ultimately, a pSCT scheme is judged to be useful for error estimation in problems where the computational cost of the scheme is justified. In the presence of many irregularities, such a scheme may be intractable for general use, but in benchmarks, as an analytical tool, or in problems that have nondissipative discontinuities, the scheme may prove invaluable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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 OSTI2021

Computational Evaluation of Thermal Response of Open-Cell Foam With Circular Pore (Computional Evaluation of Thermal Response of Open-Cell Foam with Circular Pore)

The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) critically relevant to a wide spectrum of applications, including nuclear power, electronic packaging, flame retardants, hypersonics, and gas turbine power. The work described in this paper is centered around the numerical assessment of the thermal behavior of porous materials obtained from finite element thermal modeling and simulation. Here, two-dimensional, steady state analyses were performed on unit cells with centered, circular pores using a second order accurate Galerkin finite element method (FEM). The effective thermal conductivities of the porous systems were examined, encompassing a range of porosities from 4.9% to 60.1%. The geometries of the models were generated based on ordered circular pores for each modeled porosity level. The system response quantity (SRQ) under investigation was the dimensionless effective thermal conductivity across the unit cell. The dimensionless effective thermal conductivity was compared across all simulated cases, producing a trend between porosity and effective thermal conductivity. In the presented investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) was employed to estimate discretization uncertainty as solution verification. Code verification concluded an approximately second order accurate Galerkin FEM solver. It was found that the introduction of porosity to the unit cell material structure reduces effective thermal conductivity, as anticipated. Numerical results obtained in this study are compared to an analytical solution and to a sample of empirical data.

36 MATERIALS SCIENCE↗

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↗