Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...最新文献

{"title":"Bootstrapping and Jackknife Resampling to Improve Sparse-Sample UQ Methods for Tail Probability Estimation","authors":"C. Jekel, V. Romero","doi":"10.1115/vvs2019-5127","DOIUrl":"https://doi.org/10.1115/vvs2019-5127","url":null,"abstract":"Tolerance Interval Equivalent Normal (TI-EN) and Superdistribution (SD) sparse-sample uncertainty quantification (UQ) methods are used for conservative estimation of small tail probabilities. These methods are used to estimate the probability of a response laying beyond a specified threshold with limited data. The study focused on sparse-sample regimes ranging from N = 2 to 20 samples, because this is reflective of most experimental and some expensive computational situations. A tail probability magnitude of 10−4 was examined on four different distribution shapes, in order to be relevant for quantification of margins and uncertainty (QMU) problems that arise in risk and reliability analyses. In most cases the UQ methods were found to have optimal performance with a small number of samples, beyond which the performance deteriorated as samples were added. Using this observation, a generalized Jackknife resampling technique was developed to average many smaller subsamples. This improved the performance of the SD and TI-EN methods, specifically when a larger than optimal number of samples were available. A Complete Jackknifing technique, which considered all possible sub-sample combinations, was shown to perform better in most cases than an alternative Bootstrap resampling technique.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74734737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sequential Bayesian History Matching for Model Calibration","authors":"P. Gardner, C. Lord, R. Barthorpe","doi":"10.1115/vvs2019-5149","DOIUrl":"https://doi.org/10.1115/vvs2019-5149","url":null,"abstract":"\u0000 Computer models, whilst frequently utilised for many complex engineering tasks, suffer from model form errors due to some level of simplification and/or absence of certain physics. These model form errors lead to a mismatch between model outputs and observational data when the ‘true’ parameters are known; a phenomenon known as model discrepancy. Calibration of a computer model without consideration of this type of uncertainty therefore leads to biased estimates of system parameters. Bayesian history matching (BHM) is one such method of calibrating a computer model whilst accounting for uncertainties associated with model discrepancy. The ‘likelihood-free’ technique assesses the system parameter domain using an emulator of the complex computer model in order to discard parameter combinations based on how unlikely they were to have produced a known observation response. BHM can be approached in an iterative manner, allowing sequential-based approaches to be used in selecting new computer model evaluations that will maximise the improvement in emulator performance. This paper develops techniques for sequentially selecting new computer model evaluations, reducing the total number of evaluations and increasing improvements in the emulator. The developed metrics and criteria are outlined with a demonstration on a numerical case study in order to visually demonstrate their applicability and increase in computational efficiency.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82041060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Numerical Study of Laminar and Intermittently Turbulent Flow Over a Flat Plate Using Pseudo-Compressibility Model","authors":"S. Srivastava, J. Eastridge, B. Taravella, K. Akyuzlu","doi":"10.1115/vvs2019-5157","DOIUrl":"https://doi.org/10.1115/vvs2019-5157","url":null,"abstract":"\u0000 A study was conducted to investigate the characteristics of incompressible unsteady boundary layer flows (laminar and intermittently turbulent), numerically and experimentally. The main objective of the study is to validate and verify (V&V) the accuracy of the proposed pseudo-compressibility model in solving the incompressible Navier-Stokes (NS) equations. This approach will enable one to use a second order accurate (temporally and spatially) implicit finite-difference (FD) technique to solve NS equations (including RANS equations).\u0000 Here, the proposed pseudo-compressibility model is used for laminar and intermittent turbulent flow simulations. Flow over a flat plate is chosen as the benchmark case for the validation of the proposed pseudo-compressibility model. An in-house code is developed to solve the boundary layer equations using an Alternating-Direction Explicit (ADE) FD technique. The boundary layer equations are discretized using explicit FD techniques which are second order accurate. The velocity field predicted by this code is compared to the one given by Blasius’ analytical solution. A second in-house code is also developed which adopts the proposed model of pseudo-compressibility to solve the incompressible NS equations. The two dimensional, unsteady conservation of mass and momentum equations are discretized using explicit finite-difference techniques. A standard K-ε closure model is used along with RANS equation to simulate turbulent flows. The primitive variables (velocity and pressure) predicted by this code are compared to the ones predicted by a commercial CFD package (Fluent). Once the method of pseudo-compressibility is validated, it is then implemented into another in-house computer code which employs implicit FD technique and Coupled Modified Strongly Implicit Procedure (CMSIP) to solve for the unknowns of the problem under study.\u0000 The predictions based on the pseudo-compressibility model for laminar flow are validated using the results of the experiments in which Particle Image Velocimetry (PIV) technique was employed. The verification; that is, the numerical uncertainty estimation of the pseudo-compressible code was accomplished by using the Grid Convergence Index (GCI) method. The results of the present study indicate that the proposed pseudo-compressibility model is capable of predicting experimentally observed characteristics of the external flows successfully, and deviations between the predicted velocity magnitudes and experimentally measured velocities are within an acceptable range for laminar and intermittently turbulent flows conditions.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83833303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Verifying Spatiotemporal Systems via Robustness Bounds: An Application to Unmanned Underwater Vehicles","authors":"Tiancheng Liu, Xiangxue Zhao, K. Quigley, S. Azarm, S. Gabriel, D. Lordan","doi":"10.1115/vvs2019-5155","DOIUrl":"https://doi.org/10.1115/vvs2019-5155","url":null,"abstract":"\u0000 The authors present an approach for verifying computer simulations for spatiotemporal systems. Specifically, the goal is to confirm that the computer simulation for a linear controller of an Unmanned Underwater Vehicle (UUV) correctly captures key elements of a conceptual model for the UUV controller. The key elements considered are stability and robustness of the UUV’s control system model. Here, stability refers to asymptotic stability of the model’s state variables, assuming bounded input parameters. Robustness refers to the model’s ability to handle uncertainty in these parameters. The verification is performed in two steps. First, for a fixed UUV controller, a maximum range of uncertain parameters is found and for that entire range confirmed that the computer simulation remains stable as required by the conceptual model. Next, a combination of control cost function and range of uncertain parameters is optimized while maintaining UUV stability, again, for the entire range of uncertainty and as required by the conceptual model. In both steps, independent Monte-Carlo simulations are performed to confirm the verification.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"89 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79907830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical and Parameter Uncertainties: Are They Independent?","authors":"L. Eça, Rui Lopes, F. Pereira, G. Vaz","doi":"10.1115/vvs2019-5125","DOIUrl":"https://doi.org/10.1115/vvs2019-5125","url":null,"abstract":"\u0000 In the Validation procedure proposed by the ASME V&V 20 Standard, the quantification of the modeling error of mathematical models solved by Computational Fluid Dynamics (CFD) requires the estimation of the experimental, numerical and parameter uncertainties. In its simplest form, these uncertainties are assumed independent. Parameter uncertainty is typically a consequence of lack of exact values for the boundary conditions and/or fluid properties. Its evaluation is handled by the broad field of uncertainty quantification. However, this evaluation requires simulations that are unavoidably affected by numerical errors. Therefore, it may be questionable if parameter and numerical uncertainties are really independent or, alternatively, how small must be the numerical uncertainty to estimate parameter uncertainties without its influence. In this paper we address the relation between parameter and numerical uncertainties using two test cases: the transition from laminar to turbulent flow on a flat plate at a Reynolds number of 107; the flow around the Eppler 387 airfoil at an angle of attack of 1o and Re = 3 × 105. The mathematical model for the three cases is the Reynolds-Averaged Navier-Stokes equations supplemented by the k–ω SST eddy-viscosity turbulence model and the one-equation γ transition model. Sensitivity coefficients are determined for the selected quantities of interest using the local sensitivity method and finite-differences. These estimates are performed for different levels of grid refinement to check its dependency on the estimated numerical error obtained from power series expansions. Results obtained in this study suggest that the evaluation of the parameter uncertainty only becomes independent of the numerical error when the simulation results are in the asymptotic range.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81346722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nuclear Dry Cask Storage Container CFD Model Experimental Validation and Uncertainty Quantification","authors":"Kimbal Hall, A. Zigh, J. Solı́s","doi":"10.1115/vvs2019-5142","DOIUrl":"https://doi.org/10.1115/vvs2019-5142","url":null,"abstract":"\u0000 CFD is a valuable tool for showing compliance with peak temperatures in dry cask storage systems (DCSS). When demonstrating compliance, it is valuable to quantify the uncertainty in the simulation result as a function of the computational mesh and simulation inputs. USNRC was a participant in a CFD validation test using the TN-32B cask, with extensive temperature measurements throughout the DCSS, including measurements on the cask surface and in fuel bundles.\u0000 This paper discusses validation and uncertainty quantification of a CFD model using experimental data. Uncertainty quantification follows the procedures outlined in ASME V&V20-2009 [1]. Sources of uncertainty that were examined in the analysis include iterative uncertainty, spacial discretization, and uncertainty due to approximately twenty input parameters. Input parameters investigated include environmental conditions, material properties, decay heat, and the spacing of the many small gaps in the installation. The uncertainty in gap size was found to be a particularly large source of uncertainty in this particular installation.\u0000 Results of a “base case” using the conservative estimates outlined in the updated final safety analysis report (UFSAR) [2] are presented, as well as a “best estimate case” that uses more realistic values. These results are compared to experimentally measured values, which fall within the uncertainty band of the analysis. This work is also the subject of an upcoming NUREG/CR.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84032822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bayesian Approach to Estimating Fireball Parameters From Remote Sensing Data","authors":"Derek E. Armstrong","doi":"10.1115/vvs2019-5112","DOIUrl":"https://doi.org/10.1115/vvs2019-5112","url":null,"abstract":"\u0000 Remote sensors in the infrared region can be used to study the progression of fireballs generated from experiments involving high explosives (HE). Developing an improved understanding of HE fireballs can be used to validate and improve computational physics codes that simulate such events. In this paper, Bayesian approaches are studied to estimate time-dependent optimal fireball parameters and their uncertainties using Fourier transform infrared (FTIR) spectroscopy. The optical signal measured by an FTIR sensor provides information on the fireball due to thermal emission, particulate emission/absorption, and HE gas product emission/absorption from the fireball. FTIR sensors have the advantage of being able to capture and measure the radiance in a large part of the infrared spectrum. The parameters to be estimated from the fireball include temperature and size, soot quantity, gas species concentrations (e.g., H2O, CO2, CO), and information on the presence of metals. In general, this inverse optimization problem is difficult due to the estimated quantities being correlated, the low spectral resolution of the FTIR sensor, and the intervening atmosphere absorbing the radiation emitted from the fireball. Bayesian calibration and Bayesian model averaging are applied to address these difficulties and to quantify the uncertainty in the estimated optimal parameter values. The fireball parameter settings are evaluated by the fit of a simplified spectral model to FTIR data. The overall problem will be presented together with a description of the Bayesian approaches. In this paper, the Bayesian approaches are applied to artificially generated FTIR data to illustrate the approach.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"153 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78062754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Risk Assessment for Model and Simulation Credibility Characteristics","authors":"J. G. Madry, James N. Elele, David H. Hall, D. J. Turner","doi":"10.1115/vvs2019-5152","DOIUrl":"https://doi.org/10.1115/vvs2019-5152","url":null,"abstract":"\u0000 The Department of Defense (DoD) uses the principles of risk assessment extensively throughout the acquisition process to identify, manage, and mitigate risk in many areas including software (both simulation software and software embedded in materiel systems). The approach to assessing the risks associated with using results from Models and Simulations (M&S) to influence decision-making that is described here is used by the Naval Air Systems Command (NAVAIR) 5.4H Verification, Validation, and Accreditation office.\u0000 The focus of the risk assessment is on ten specific characteristics of M&S Capability, Accuracy, and Usability that have the most potential impact on the intended uses. In this method, the characteristics of the M&S are evaluated against standard criteria, and then assigned a color-rating of Green, Yellow, or Red based on the actual data obtained from the M&S itself. A simple computation is then used to weigh the ratings of the characteristics into the likelihood of error aspect of the risk of using the M&S. A thorough understanding of the M&S and its application is a prerequisite to using this approach since the analyst is required to provide a technical justification for the rating assigned to a characteristic. Should the assigned rating for a characteristic of the M&S not be green, the analyst is required to recommend actions and/or mitigations for the M&S developer to take that would improve the rating to green.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85521565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Validation of a Surrogate Model for Marine Mammal Lung Dynamics Under Underwater Explosive Impulse","authors":"E. Guzas, S. Turner, M. Babina, B. Casper, Thomas Fetherston, J. M. Ambrico","doi":"10.1115/vvs2019-5143","DOIUrl":"https://doi.org/10.1115/vvs2019-5143","url":null,"abstract":"\u0000 Primary blast injury (PBI), which relates gross blast-related trauma or traces of injury in air-filled tissues or those tissues adjacent to air-filled regions (rupture/lesions, contusions, hemorrhaging), has been documented in a number of marine mammal species after blast exposure [1, 2, 3]. However, very little is known about marine mammal susceptibility to PBI except in rare cases of opportunistic studies. As a result, traditional techniques rely on analyses using small-scale terrestrial mammals as surrogates for large-scale marine mammals. For an In-house Laboratory Independent Research (ILIR) project sponsored by the Office of Naval Research (ONR), researchers at the Naval Undersea Warfare Center, Division Newport (NUWCDIVNPT), have undertaken a broad 3-year effort to integrate computational fluid-structure interaction techniques with marine mammal anatomical structure. The intent is to numerically simulate the dynamic response of a marine mammal thoracic cavity and air-filled lungs to shock loading, to enhance understanding of marine mammal lungs to shock loading in the underwater environment.\u0000 In the absence of appropriate test data from live marine mammals, a crucial part of this work involves code validation to test data for a suitable surrogate test problem. This research employs a surrogate of an air-filled spherical membrane structure subjected to shock loading as a first order approximation to understanding marine mammal lung response to underwater explosions (UNDEX). This approach incrementally improves upon the currently used one-dimensional spherical air bubble approximation to marine mammal lung response by providing an encapsulating boundary for the air. The encapsulating structure is membranous, with minimal simplified representation not accounting for marine mammal species-specific and individual animal differences in tissue composition, rib mechanics, and mechanical properties of interior lung tissue.\u0000 NUWCDIVNPT partnered with the Naval Submarine Medical Research Laboratory (NSMRL) to design and execute a set of experiments to investigate the shock response of an air-filled rubber dodgeball in a shallow underwater environment. These tests took place in the 2.13 m (7-ft) diameter pressure tank at the University of Rhode Island, with test measurements including pressure data and digital image correlation (DIC) data captured with high-speed cameras in a stereo setup. The authors developed 3-dimensional computational models of the dodgeball experiments using Dynamic System Mechanics Advanced Simulation (DYSMAS), a Navy fluid-structure interaction code. DYSMAS models of a variety of different problems involving submerged pressure vessel structures responding to hydrostatic and/or UNDEX loading have been validated against test data [4].\u0000 Proper validation of fluid structure interaction simulations is quite challenging, requiring measurements in both the fluid and structure domains. This paper details the development of metrics fo","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"128 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81819585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rigorous Code Verification: An Additional Tool to Use With the Method of Manufactured Solutions","authors":"A. Krueger, V. Mousseau, Y. Hassan","doi":"10.1115/vvs2019-5166","DOIUrl":"https://doi.org/10.1115/vvs2019-5166","url":null,"abstract":"\u0000 The Method of Manufactured Solutions (MMS) has proven to be useful for completing code verification studies. MMS allows the code developer to verify that the observed order-of-accuracy matches the theoretical order-of accuracy. Even though the solution to the partial differential equation is not intuitive, it provides an exact solution to a problem that most likely could not be solved analytically. The code developer can then use the exact solution as a debugging tool. While the order-of-accuracy test has been historically treated as the most rigorous of all code verification methods, it fails to indicate code “bugs” that are of the same order as the theoretical order-of-accuracy. The only way to test for these types of code bugs is to verify that the theoretical local truncation error for a particular grid matches the difference between the manufactured solution (MS) and the solution on that grid. The theoretical local truncation error can be computed by using the modified equation analysis (MEA) with the MS and its analytic derivatives, which we call modified equation analysis method of manufactured solutions (MEAMMS). In addition to describing the MEAMMS process, this study shows the results of completing a code verification study on a conservation of mass code. The code was able to compute the leading truncation error term as well as additional higher-order terms. When the code verification process was complete, not only did the observed order-of-accuracy match the theoretical order-of-accuracy for all numerical schemes implemented in the code, but it was also able to cancel the discretization error to within roundoff error for a 64-bit system.","PeriodicalId":87343,"journal":{"name":"Proceedings of the ASME Verification and Validation Symposium -2019- : VVS2019 : presented at ASME 2019 Verification and Validation Symposium, May 15-17, 2019, Las Vegas, Nevada, USA. ASME Verification and Validation Symposium (2019 : L...","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90745048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}