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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Robust Solution Verification Experiments on Nonuniform Meshes

The activities of verification, validation, and uncertainty quantification (VVUQ) provide a comprehensive means to assess the credibility of computational models. Within VVUQ, solution verification assesses numerical errors and evaluates whether the simulation is sufficiently accurate for its intended applications. As computational modeling gains traction in the development of complex, high-consequence systems, the need for robust solution verification intensifies, particularly because experimental data for these systems are often limited. This work examines improvements in the robustness of Richardson extrapolation (RE), a method commonly used in solution verification to study the discretization error of computational models using a power law. Nonuniform mesh refinement is discussed alongside other pollutants that affect the robustness of the power law model. Maximum likelihood estimation (MLE) is proposed as a robust strategy to address the uncertainty generated by nonuniform mesh refinement. An exploratory computational fluid dynamics (CFD) study of a 2D planar Poiseuille flow is conducted to determine if nonuniform mesh noise can be modeled with this MLE approach for more robust RE.

Weinmeister, Justin [ORNL] (ORCID:0000000160090237↗
DOE OSTI2025

An Open-Source Python Package for CFD Solution Verification

Informed decision-making using computational fluid dynamics (CFD) results requires quantifying the errors and uncertainties of a simulation. Verification, validation, and uncertainty quantification (VVUQ) methods were developed to address this need and have matured. However, these VVUQ analyses are often non-trivial and require CFD analysts and practitioners to have specific skill sets. This has led to the uneven adoption of VVUQ analyses, in part, based on the availability of software tools to aid CFD analysts and practitioners. Solution verification, a procedure to evaluate the accuracy of a simulation by estimating potential errors arising from the computational model and computing the uncertainties without comparing to results from a physical system, is one of the lagging VVUQ analyses as the absence of software has forced CFD analysts and practitioners to develop their own codes or piece together incomplete software from across the internet. This work presents an opensource Python package, CFDverify, to lower the barrier of entry and fill in the technological gap in solution verification. CFDverify also provides a streamlined framework to remove some potential errors in post-processing CFD results. The hope is that CFDverify can improve the quality and quantity of CFD solution verification in scientific and research studies and attract interest in developing a communal tool. This paper describes the design, features, and an example use of CFDverify.

Weinmeister, Justin [ORNL] (ORCID:0000000160090237↗
NASA NTRSDate not supplied

Modeling and Simulation Credibility Assessment of Finite Element Models for Fall From Heights Injury Scenarios

Finite element (FE) computational models of the whole human body are being used to investigate the injury modalities and mechanisms arising from suited astronauts’ ExtraVehicular Activities (EVAs). These FE whole body models – simplified Elemance and THUMS pedestrian versions – have undergone a series of verification and validation (V&V) assessments for applications in automotive, domestic, and contact sports arenas. However, the FE models’ Modeling and Simulation (M&S) credibility assessments for simulating suited astronaut injuries due to fall from heights in altered gravity environments are limited. The current study evaluates the M&S credibility of simplified Elemance and THUMS pedestrian FE models based on eight credibility factors – data pedigree, input pedigree, code verification, solution verification, conceptual validation, referent validation, results uncertainty, and results robustness – as per NASA-STD-7009A [1]. These credibility factors were assigned ordinal scores ranging between 0 to 4, with a score of 0 in the case of insufficient evidence and 4 when all data for the model is known, used appropriately, and traceable to the Real-World System (RWS) with acceptable accuracy, precision, and uncertainty. The credibility factor sufficiency thresholds were assigned upon guidance from NASA EVA subject matter experts. The factor scores were ascertained through the evaluation of M&S credibility assessment procedures described in the published literature and FE model reports. The M&S credibility scores for the Elemance and THUMS FE models vary between 1 and 3 for data pedigree, input pedigree, and referent validation credibility factors, and between 0 and 1 for code verification, solution verification, conceptual validation, results uncertainty and results robustness. The results show that these FE models are credible for simulating fall from heights injury scenarios in specific kinematic and kinetic ranges that correlate with highway and contact sports-related external conditions. Multiple credibility elevation strategies are prescribed to improve the Elemance and THUMS models’ credibility for use in the EVA fall from height injury scenarios.

R A Perkins↗
NASA NTRS2025

Modeling and Simulation Credibility Assessments of Musculoskeletal Computational Models for Simulating Astronaut Injuries Due to a Poor Spacesuit Fit

The musculoskeletal (MS) system of astronauts is subject to physiological changes, potentially leading to injuries due to the exposure to different gravitational environments experienced during spaceflight. These injuries can occur while an astronaut is performing an Extravehicular Activity (EVA) in space, on lunar or planetary surfaces or while wearing a spacesuit during terrestrial training for an EVA. The OpenSim MS modeling software can assess EVA induced MS injury mechanisms such as muscle strains, ligament injuries and joint injuries. One area of concern, since there are only a few different spacesuit sizes with limited adjustability, is the possibility of a poorly fitting spacesuit. This can cause unnatural joint motions and torques resulting in various MS injuries. A credibility assessment of the OpenSim modeling and simulation procedures is performed per NASA-STD-7009A to provide information on the credibility of the model’s use in simulating EVA related injury mechanisms. The credibility assessment evaluated various OpenSim models against the following eight credibility factors: data pedigree, input pedigree, code verification, solution verification, conceptual validation, referent validation, results uncertainty and results robustness (sensitivity). The models evaluated for EVA injuries will require additional credibility factor analysis and upgrades to the model features, such as adding ligaments to a whole-body model, to reliably predict and analyze the EVA injuries expected to occur due to a poor spacesuit fit. The degree of elevation strategy required to increase the credibility assessment scores will depend on the model complexity and the injury mechanism.

Christopher A. Gallo↗
NASA NTRS2024

Modeling and Simulation Credibility Assessments of Musculoskeletal Computational Models for Simulating Astronaut Injuries Due to a Poor Spacesuit Fit

The musculoskeletal (MS) system of astronauts is subject to physiological changes, potentially leading to injuries due to the exposure to different gravitational environments experienced during spaceflight. These injuries can occur while an astronaut is performing an Extravehicular Activity (EVA) in space, on lunar or planetary surfaces or while wearing a spacesuit during terrestrial training for an EVA. The OpenSim MS modeling software can assess EVA induced MS injury mechanisms such as muscle strains, ligament injuries and joint injuries. One area of concern, since there are only a few different spacesuit sizes with limited adjustability, is the possibility of a poorly fitting spacesuit. This can cause unnatural joint motions and torques resulting in various MS injuries. A credibility assessment of the OpenSim modeling and simulation procedures is performed per NASA-STD-7009A to provide information on the credibility of the model’s use in simulating EVA related injury mechanisms. The credibility assessment evaluated various OpenSim models against the following eight credibility factors: data pedigree, input pedigree, code verification, solution verification, conceptual validation, referent validation, results uncertainty and results robustness (sensitivity). The models evaluated for EVA injuries will require additional credibility factor analysis and upgrades to the model features, such as adding ligaments to a whole-body model, to reliably predict and analyze the EVA injuries expected to occur due to a poor spacesuit fit. The degree of elevation strategy required to increase the credibility assessment scores will depend on the model complexity and the injury mechanism.

Christopher A Gallo↗
NASA NTRS2007

The Roles of Verification, Validation and Uncertainty Quantification in the NASA Standard for Models and Simulations

The National Aeronautics and Space Administration (NASA) recently issued an interim version of the Standard for Models and Simulations (M&S Standard) [1]. The action to develop the M&S Standard was identified in an internal assessment [2] of agency-wide changes needed in the wake of the Columbia Accident [3]. The primary goal of this standard is to ensure that the credibility of M&S results is properly conveyed to those making decisions affecting human safety or mission success criteria. The secondary goal is to assure that the credibility of the results from models and simulations meets the project requirements (for credibility). This presentation explains the motivation and key aspects of the M&S Standard, with a special focus on the requirements for verification, validation and uncertainty quantification. Some pilot applications of this standard to computational fluid dynamics applications will be provided as illustrations. The authors of this paper are the members of the team that developed the initial three drafts of the standard, the last of which benefited from extensive comments from most of the NASA Centers. The current version (number 4) incorporates modifications made by a team representing 9 of the 10 NASA Centers. A permanent version of the M&S Standard is expected by December 2007. The scope of the M&S Standard is confined to those uses of M&S that support program and project decisions that may affect human safety or mission success criteria. Such decisions occur, in decreasing order of importance, in the operations, the test & evaluation, and the design & analysis phases. Requirements are placed on (1) program and project management, (2) models, (3) simulations and analyses, (4) verification, validation and uncertainty quantification (VV&UQ), (5) recommended practices, (6) training, (7) credibility assessment, and (8) reporting results to decision makers. A key component of (7) and (8) is the use of a Credibility Assessment Scale, some of the details of which were developed in consultation with William Oberkampf, David Peercy and Timothy Trocano of Sandia National Laboratories. The focus of most of the requirements, including those for VV&UQ, is on the documentation of what was done and the reporting, using the Credibility Assessment Scale, of the level of rigor that was followed. The aspects of one option for the Credibilty Assessment Scale are (1) code verification, (2) solution verification, (3) validation, (4) predictive capability, (5) technical review, (6) process control, and (7) operator and analyst qualification.

Zang, Thomas A.↗
DOE OSTI2025

Single Grid Error Estimation for Neutron Transport Solvers

The method of nearby problems (MNP) is a solution verification technique that does not require the use of multiple spatial grids. To estimate spatial discretization error without requiring a high-fidelity spatial grid, an analytical curve fit is interpolated from the numerical solution. The residual between the curve fit solution and numerical solution is calculated and added as an additional source term to the governing equation. The nearby solution is estimated using the updated source term and boundary conditions to remain consistent with the curve fit interpolation. The nearby solution can be compared to the curve fit solution as a discretization error estimation while using a single spatial grid. Without the use of higher fidelity spatial grids, the MNP is able to approximate the spatial discretization error, a facet of solution verification. The application of the method of nearby problems is presented for one- and two-dimensional neutron transport problems for both fixed source and criticality problems on the spatial variable. The fixed source results demonstrate the effectiveness of nearby problems for spatial error identification using the discrete ordinates method. Criticality results are shown to identify area of high spatial error for the C5G7 problem as well as for the discrete ordinates solver. A novel approach of combining the capabilities of Monte Carlo with the discrete ordinates nearby problems is presented for one- and two-dimensional fixed source problems. In conclusion, the MNP demonstrates its effectiveness at identifying spatial error on a single structured grid with a wide variety of neutron transport problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRSDate not supplied

HLPW-4/GMGW-3: Mesh Adaptation for RANS Technology Focus Group Workshop Summary

The AIAA workshop series helps guide the Computational Fluid Dynamics (CFD) community through publicly available test cases and impartial evaluation to establish the state-of-the-art in applied CFD. A summary of the Mesh Adaptation Technical Focus Group submissions for the joint Fourth CFD High Lift Prediction and Third Geometry & Mesh Generation Workshop is provided. The Common Research Model High-Lift variant (CRM-HL) is the target of this investigation. A 2D high-lift airfoil solution verification case was extracted from the 3D CRM-HL. Low variation is shown between 2D solutions with mesh adaptation to control estimated solution interpolation and output errors. As expected, variation for these mesh adaptation techniques is larger for the 3D CRM-HL than the 2D airfoil. More importantly, the 3D mesh adapted results have a lower variation than expert-crafted meshes of equal or larger size. Suspected multiple solutions to Reynolds-averaged Navier-Stokes with the Spalart-Allmaras turbulence model appear to resolve into a common solution with mesh resolution.

HLPW-4↗
NASA NTRSDate not supplied

Recent Advances in Discrete Crack Modeling Applied to Laminated Composites with Emphasis on: Floating Node Method, VCCT and Cohesive Zone Modeling

The present talk will provide an overview of the work performed during the Advanced Composites Project (ACP) on the development, and verification and validation of the Floating Node Method (FNM) as well as the Virtual Crack Closure Technique (VCCT) and cohesive zone modeling (CZM). The FNM is a finite element-based technique to represent crack networks. The complex nature of matrix crack-delamination interactions observed in unidirectional (UD) tape laminates suggests that a methodology such as the FNM method may be required to be able to accurately simulate damage progression in these laminates. Simulating crack onset and growth within the context of the FNM relies on techniques such as VCCT and CZM. The talk is organized to provide, via select examples, an overview of the breadth of the Verification & Validation (V&V) exercises performed during the ACP, and how these challenged the state-of-the art and guided further developments in discrete crack modeling, while helping to establish confidence in the progress made and map the challenges ahead. The performance of the VCCT and CZM individually, and in combination with the FNM can be assessed through verification exercises. These exercises typically consist of a comparison of simulation results to known numerical or analytical solutions. Verification is key to identify implementation issues and limitations that, otherwise, may remain undetected and cloud any subsequent validation efforts. Indeed, a subset of these numerical exercises led to further developments of the VCCT and the FNM method as will be illustrated. Before embarking on the subsequent validation of the framework, it is critical to have adequate characterization data. However, the testing campaign conducted revealed material responses that challenged the state-of-the-art and required further developments. The developments in CZM technology associated with the modeling of the responses of hybrid interfaces (fabric/UD) will be given as an example. Finally, the talk will conclude with a summary of the validation exercises performed under quasi-static and fatigue loadings, highlighting some of the key achievements, outstanding challenges and lessons learned.

finite elements↗
NASA NTRS2014

Numerical Simulations For the F-16XL Aircraft Configuration

Numerical simulations of flow around the F-16XL are presented as a contribution to the Cranked Arrow Wing Aerodynamic Project International II (CAWAPI-II). The NASA Tetrahedral Unstructured Software System (TetrUSS) is used to perform numerical simulations. This CFD suite, developed and maintained by NASA Langley Research Center, includes an unstructured grid generation program called VGRID, a postprocessor named POSTGRID, and the flow solver USM3D. The CRISP CFD package is utilized to provide error estimates and grid adaption for verification of USM3D results. A subsonic high angle-of-attack case flight condition (FC) 25 is computed and analyzed. Three turbulence models are used in the calculations: the one-equation Spalart-Allmaras (SA), the two-equation shear stress transport (SST) and the kε turbulence models. Computational results, and surface static pressure profiles are presented and compared with flight data. Solution verification is performed using formal grid refinement studies, the solution of Error Transport Equations, and adaptive mesh refinement. The current study shows that the USM3D solver coupled with CRISP CFD can be used in an engineering environment in predicting vortex-flow physics on a complex configuration at flight Reynolds numbers.

Elmiligui, Alaa A.↗
DOE OSTI2025

Adopting Code Verification Methodology Based on Model Form

Code verification is an essential part of credibility analysis for computational models. It assesses whether the mathematical model is implemented correctly into the code and whether the numerical methods behave consistently, and is done before solution verification and validation. Robust guidance for code verification exists in the literature. However, there is no known, concise guide for selecting the approach based on the model form that also presents an overview of the common elements. This document was written to address this gap as an accessible reference for beginning a code-verification effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Adapting Code Verification Methodology to Model Form

Code verification is an essential part of credibility analysis for computational models. It assesses whether the mathematical model is implemented correctly into the code and whether the numerical methods behave consistently, and is done before solution verification and validation. Robust guidance for code verification exists in the literature. However, there is no known, concise guide for selecting the approach based on the model form that also presents an overview of the common elements. This document was written to address this gap as an accessible reference for beginning a code-verification effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

CFDverify

Estimating the discretization error of computational fluid dynamics (CFD) or other scientific codes as part of solution verification is often a non-trivial part of the analysis process. Methods can be complicated and may include assumptions/qualifications that need to be checked during analysis. CFD analysts, therefore, are likely to make errors when trying to conduct this necessary analysis on their own in not knowing about the best method for their problem, not correctly implementing a method, or in not have diagnostic tools to determine if the method was correctly applied.

Weinmeister, Justin [Oak Ridge National Laboratory↗
DOE OSTI2025

The Fluid Dynamics Uncertainty Quantification Challenge Problem: XFOIL vs. MFOIL

Uncertainty quantification (UQ) has become more critical in aerospace engineering due to the growing dependence on computational tools for design optimization and performance analyses of aerospace vehicles. Even though the significance of UQ in assessing the credibility of computational analyses is well recognized, its costs and complexity impede its integration into standard practices, particularly in computational fluid dynamics (CFD) and other fluid analyses. This paper presents a UQ study for low-fidelity computational aerodynamics analyses with XFOIL and mfoil (i.e., the MATLAB version of XFOIL with several implementation modifications); these tools are utilized widely in both research and education. The main contributions of this paper are as follows: 1) improved precision in quantifying the uncertainty of the baseline Monte Carlo results used to benchmark surrogate modeling techniques for UQ, 2) quantification of the effect of the implementation differences between XFOIL and mfoil on solution quantities of interest (QoIs), such as lift and pitching moment coefficients, and 3) development of an open-source UQ library for use with XFOIL and mfoil, which has educational values and helps promote UQ for fluid analyses with aerospace applications. Results and discussions revolve around cases 1-4 of the challenge problem posed by the AIAA Fluid Dynamics Technical Committee’s Uncertainty Quantification Discussion Group (UQDG). In case 3, this work employs CFDverify, an open-source solution verification software, to quantify the discretization error and evaluate the extrapolated QoIs based on the grid convergence index (GCI). This UQ study differentiates itself from previous studies in the rigor of handling baseline Monte Carlo uncertainty and in including mfoil, which is a more accessible alternative to XFOIL. Finally, despite the growing computing power, low-fidelity computational tools remain valuable, such as for aerodynamic shape optimization at Mach numbers below 0.65 and low-to-mid Reynolds numbers.

Lay, Aidan S [University of Tennessee, Knoxville (↗
NASA NTRSDate not supplied

Overview of Predictive Simulation Capability Development for Crater Evolution and Ejecta in Continuum/Rarefied Flows

As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The Predictive Simulation Capability (PSC) Element is focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the predictive simulation capability, the GCD Program also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. The focus of this paper is to provide an overview and a brief status on one area of capability development through this GCD PSI project - capturing the effects of mixed continuum/rarefied flow on crater development and ejecta sheets. This includes both capability enhancements and maturation of the predictive tool, Loci/GGFS, into a production capable tool as well as validation of the tool against PSI data in Martian and Lunar environments. There are six newly developed capabilities that will be production ready by the end of the fiscal year. Newly developed capabilities must first be verified prior to being production ready, and this process includes capability demonstration, solution verification, and performance evaluation. An overview of the newly developed capabilities with respect to several test cases, including cratering simulations of the Apollo Lunar Module, will be presented. Several validation analyses have been performed to validate in Martian and more Lunar-like environments, including simulations of cratering from a subsonic flow test at Planetary Aeolian Lab (PAL) conducted in a Martian-like environment and pre-test cratering predictions of Physics Focused Ground Test (PFGT) tests planned to be performed in Martian-like and more Lunar-like environments. An overview of these validation analyses as it pertains to the capability development will be presented.

Andrew Weaver↗
NASA NTRS2020

Formal Verification of a Solution to the n-Queens Problem

This report describes a formal verification of a concise algorithm that computes a solution to the n-Queens problem for all natural numbers n, such that n > 3. The formal proof of the algorithm is completed in the Prototype Verification System (PVS) theorem prover. This verification effort serves two purposes. First, it is presented as a pedagogical example for learning a theorem prover, such as PVS, and second, as a candidate benchmark for comparing other formal methods tools to PVS.

Mahyar R Malekpour↗
NASA NTRS1990

Spacecraft command verification: The AI solution

Recently, a knowledge-based approach was used to develop a system called the Command Constraint Checker (CCC) for TRW. CCC was created to automate the process of verifying spacecraft command sequences. To check command files by hand for timing and sequencing errors is a time-consuming and error-prone task. Conventional software solutions were rejected when it was estimated that it would require 36 man-months to build an automated tool to check constraints by conventional methods. Using rule-based representation to model the various timing and sequencing constraints of the spacecraft, CCC was developed and tested in only three months. By applying artificial intelligence techniques, CCC designers were able to demonstrate the viability of AI as a tool to transform difficult problems into easily managed tasks. The design considerations used in developing CCC are discussed and the potential impact of this system on future satellite programs is examined.

Fesq, Lorraine M.↗