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All sources NASA NTRS DOE OSTI

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

Adopting Code Verification Methodology Based on Model Form

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

Overview of Code Verification

The verified code for the SIFT Executive is not the code that executes on the SIFT system as delivered. The running versions of the SIFT Executive contain optimizations and special code relating to the messy interface to the hardware broadcast interface and to packing of data to conserve space in the store of the BDX930 processors. The running code was in fact developed prior to and without consideration of any mechanical verification. This was regarded as necessary experimentation with the SIFT hardware and special purpose Pascal compiler. The Pascal code sections cover: the selection of a schedule from the global executive broadcast, scheduling, dispatching, three way voting, and error reporting actions of the SIFT Executive. Not included in these sections of Pascal code are: the global executive, five way voting, clock synchronization, interactive consistency, low level broadcasting, and program loading, initialization, and schedule construction.

Source record↗

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↗

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 OSTI2024

Level 2 Milestone: Develop and Incorporate Novel Code Verification of Fundamental Equations in Gemma and Set Up Appropriate Tests

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 implementations of the electric-, magnetic-, and combinedfield integral equations, 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 report, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches in Gemma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1986

Measurements for liquid rocket engine performance code verification

The goal of the rocket engine performance code verification tests is to obtain the I sub sp with an accuracy of 0.25% or less. This needs to be done during the sequence of four related tests (two reactive and two hot gas simulation) to best utilize the loss separation technique recommended in this study. In addition to I sub sp, the measurements of the input and output parameters for the codes are needed. This study has shown two things in regard to obtaining the I sub sp uncertainty within the 0.25% target. First, this target is generally not being realized at the present time, and second, the instrumentation and testing technology does exist to obtain this 0.25% uncertainty goal. However, to achieve this goal will require carefully planned, designed, and conducted testing. In addition, the test-stand (or system) dynamics must be evaluated in the pre-test and post-test phases of the design of the experiment and data analysis, respectively always keeping in mind that a .25% overall uncertainty in I sub sp is targeted. A table gives the maximum allowable uncertainty required for obtaining I sub sp with 0.25% uncertainty, the currently-quoted instrument specification, and present test uncertainty for the parameters. In general, it appears that measurement of the mass flow parameter within the required uncertainty may be the most difficult.

Praharaj, Sarat C.↗

NASA NTRS2004

Investigation of Navier-Stokes Code Verification and Design Optimization

With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization study is carried out using a geometric mean approach. Following this, sensitivity analyses with the aid of variance-based non-parametric approach and partial correlation coefficients are conducted using data available from surrogate models of the objectives and the multi-objective optima to identify the contribution of the design variables to the objective variability and to analyze the variability of the design variables and the objectives. In summary the present dissertation offers insight into an improved coarse to fine grid extrapolation technique for Navier-Stokes computations and also suggests tools for a designer to conduct design optimization study and related sensitivity analyses for a given design problem.

Vaidyanathan, Rajkumar↗

DOE OSTI2022

Code verification for practically singular equations

We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Beyond Guesswork: Code Verification for Acoustic Duct Mode Prediction

The code used in the work (Swirl) is a frequency-domain linearized Euler equation solver that is designed to predict the effect of acoustic liners on acoustic modes propagating in realistic sheared and swirling mean flows, guiding the design of more efficient liner configurations. The purpose of this study is to validate Swirl using the Method Of Manufactured Solutions (MMS). This study also investigated the effect of the integration and spatial differencing methods on the convergence for a given Manufactured Solution. In addition, the effect of boundary condition implementation was tested. Through rigorous validation of the Swirl code using the MMS, this research underscores the significance of integration and spatial differencing methods on convergence, evaluates boundary condition implementations, and systematically assesses the impact of various filters.

Code Verification↗

NASA NTRS1987

Wind tunnel requirements for computational fluid dynamics code verification

The role of experiment in the development of Computational Fluid Dynamics (CFD) for aerodynamic flow field prediction is discussed. Requirements for code verification from two sources that pace the development of CFD are described for: (1) development of adequate flow modeling, and (2) establishment of confidence in the use of CFD to predict complex flows. The types of data needed and their accuracy differs in detail and scope and leads to definite wind tunnel requirements. Examples of testing to assess and develop turbulence models, and to verify code development, are used to establish future wind tunnel testing requirements. Versatility, appropriate scale and speed range, accessibility for nonintrusive instrumentation, computerized data systems, and dedicated use for verification were among the more important requirements identified.

Marvin, Joseph G.↗

NASA NTRS1988

Wind tunnel requirements for computational fluid dynamics code verification

The role of experiment in the development of computational fluid dynamics (CFD) for aerodynamic flow field prediction is discussed. Requirements for code verification from two sources that pace the development of CFD are described for: (1) development of adequate flow modeling, and (2) establishment of confidence in the use of CFD to predict complex flows. The types of data needed and their accuracy differs in detail and scope and leads to definite wind tunnel requirements. Examples of testing to assess and develop turbulence models, and to verify code development, are used to establish future wind tunnel testing requirements. Versatility, appropriate scale and speed range, accessibility for nonintrusive instrumentation, computerized data systems, and dedicated use for verification were among the more important requirements identified.

Marvin, Joseph G.↗

NASA NTRS1986

Future requirements of wind tunnels for Computational Fluid Dynamics code verification

The role of experiment in the development of Computational Fluid Dynamics (CFD) for external aerodynamic flow-field prediction is discussed. Requirements for code verification from two sources pacing the development of CFD are described: (1) the need for developing adequate flow modeling, and (2) the need for establishing confidence in the use of CFD for predicting complex flows. The type of data needed to meet these needs differs in detail and scope and leads to definite wind tunnel requirements. Recent examples of testing to assess and develop turbulence models, and to verify code development are used to establish future requirements of wind tunnel testing for CFD verification.

Marvin, J. G.↗

DOE OSTI2023

Fuel cycle depletion validation and code-to-code verification studies for High Flux Isotope Reactor highly and low-enriched uranium fuel designs

Here, this paper documents fuel cycle depletion validation and code-to-code verification studies for the High Flux Isotope Reactor (HFIR) highly enriched uranium (HEU) and proposed low-enriched uranium (LEU) fuel designs. In support of HFIR’s world-leading performance, transport and depletion simulations are performed to ensure safe operations, design and qualify irradiation experiments, enhance core components and irradiation facilities, and design and characterize LEU fuel designs. Identifying well-validated, computationally efficient codes is required for the success of these efforts. The HFIR Controller, Shift, and VESTA codes were deployed to simulate HEU uranium–oxide dispersion fuel cycles at 85, 95, and 100 MW operations, as well as LEU fuel cycles operating at 95 MW with uranium–silicide dispersion and uranium–molybdenum monolithic alloy fuel forms. Excellent agreement between the codes and with experimentally obtained 235 U enrichment distributions provides increased confidence in the ability of these codes to model and simulate HFIR’s unique core design.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Code Verification of Multiple Physics-Fidelity Models in Hypersonic Aerodynamics

Hypersonic aerodynamics models exist across a range of physics fidelities with associated computational expenses. These models may be run independently or in a multifidelity framework that leverages their complementary strengths of speed for lower-fidelity and accuracy for higher-fidelity models. This work presents applied code verification of two lower-fidelity models contained within the Sandia hypersonic aerodynamics code. Each model has a different form that requires individualized verification approaches, including comparison to analytical solutions as well as manufactured solutions with order-of-accuracy testing. In conclusion, results of this effort include the identification and resolution of code errors and shortcomings, as well as the demonstration of code correctness and consistency for both models.

Aerodynamics↗

NASA NTRS2016

Deductive Evaluation: Implicit Code Verification With Low User Burden

We describe a framework for symbolically evaluating C code using a deductive approach that discovers and proves program properties. The framework applies Floyd-Hoare verification principles in its treatment of loops, with a library of iteration schemes serving to derive loop invariants. During evaluation, theorem proving is performed on-the-fly, obviating the generation of verification conditions normally needed to establish loop properties. A PVS-based prototype is presented along with results for sample C functions.

Di Vito, Ben L.↗

NASA NTRS1991

Testing, analysis, and code verification of aerodynamics and heat transfer related to turbomachinery

Discussed here are the writing of a data acquisition code and the installation and testing of new pressure and temperature instrumentation to be used in the testing and evaluation of miniature heat flux sensors. A brief summary of the problem which led to the need for these tests is presented as well as a proposed data acquisition program and the results of investigations of two measurement systems, the Omega OM-900 temperature sensing system and the Scani-Valve Hyscan pressure measurement system.

King, Paul I.↗

NASA NTRS1991

Pressure measurements in a low-density nozzle plume for code verification

Measurements of Pitot pressure were made in the exit plane and plume of a low-density, nitrogen nozzle flow. Two numerical computer codes were used to analyze the flow, including one based on continuum theory using the explicit MacCormack method, and the other on kinetic theory using the method of direct-simulation Monte Carlo (DSMC). The continuum analysis was carried to the nozzle exit plane and the results were compared to the measurements. The DSMC analysis was extended into the plume of the nozzle flow and the results were compared with measurements at the exit plane and axial stations 12, 24 and 36 mm into the near-field plume. Two experimental apparatus were used that differed in design and gave slightly different profiles of pressure measurements. The DSMC method compared well with the measurements from each apparatus at all axial stations and provided a more accurate prediction of the flow than the continuum method, verifying the validity of DSMC for such calculations.

Penko, Paul F.↗