Numerical and Parameter Uncertainties: Are They Independent?

Quantifying Uncertainty in CFD

Abstract. The work package “Uncertainty Management multi-Actor Network”, UMAN, within EURAD, the European Joint Programme on Radioactive Waste Management, was dedicated to the management of uncertainties potentially relevant to the safety of different radioactive waste management stages and programmes. One important goal there was to compile, review, compare and refine strategies, approaches and tools for the management of uncertainties in the safety assessment that are being used, planned to be used or being developed in different countries. This paper presents major findings from the UMAN Deliverable 10.3 “Uncertainty identification, classification and quantification” (Brendler and Pospiech, 2024) and reflects on the outcome of that work. It addresses approaches to identify and categorize uncertainties that might be of relevance in the various stages of radioactive waste management as well as in the quantification of numerical uncertainties. After an introduction, bottom-up and top-down strategies are compared. Sources used for the paper as input were expert elicitation (here primarily based on a respective questionnaire send out to UMAN participants) and literature surveys. This paper then advises on how uncertainties can be structured, rendering it suitable for a comprehensive assessment of numerical uncertainties: fishbone diagrams and tables for uncertainty characteristics. Results support the identification of uncertainties with high relevance for radioactive waste management. Nine potentially useful categories are identified; the uncertainties are then grouped (including representative examples utilizing fishbone diagrams and tables) according to the occurrence by system phenomena, following the Themes and Sub-themes of the EURAD Roadmap. The last part deals with the evaluation as well as quantification of uncertainties. The paper closes with recommendations aimed at future research directions for parameter uncertainties. Finally, a glossary provides definitions for some terms frequently used (uncertainty in general, parameter uncertainty, uncertainty models and aleatory vs. epistemic uncertainties).

We develop a parsimonious SEIRV–SIRS framework with leaky vaccination, distinct waning of infection- and vaccine-acquired immunity, and demographic turnover, implemented in toolbox-free, fully reproducible MATLAB/Octave code. We address three questions: (i) when elimination by vaccination alone is mathematically impossible; (ii) which epidemiological and immunological parameters most strongly control endemic prevalence; and (iii) how robust these insights are to parameter and numerical uncertainty. Using next-generation matrix methods we derive an explicit feasibility boundary for vaccination-only control, showing that sufficiently leaky vaccines (η ≥ 1/R₀) cannot achieve elimination regardless of coverage. Monte Carlo experiments and global sensitivity analysis consistently identify the infectious period and waning of infection-acquired immunity as dominant levers, with coverage and transmission playing secondary roles under our baseline. Across multiple perturbation schemes and solver checks, these qualitative rankings and feasibility conclusions remain stable. The framework functions as an auditable decision-support component that links mechanistic vaccination and waning assumptions to transparent threshold maps and risk summaries and can be readily adapted to other endemic pathogens.

Integration of Design and Control Using Efficient PSE Approximations

Entropy generation in bypass transitional boundary layer flows

Methods for the quantification of numerical uncertainty have been a subject of interest to the American Society of Mechanical Engineers (ASME) and the mechanical engineering community as a whole for over a decade. During this time period, ASME has promulgated three statements of standards for the reporting of numerical uncertainty in archival publications (Journal of Fluids Engineering). This paper summarizes the work that has gone into the specification of these standards and the continuing effort in formulation of methods and procedures for quantifying numerical uncertainty. Specifically, this paper discusses the efforts of the ASME V&V 20 Committee (Verification and Validation in Computational Fluid Dynamics and Heat Transfer) to lay a foundation and structure to verification and validation for fluid flow and heat transfer simulations. Issues and methods related to code verification and in particular solution verification are presented and discussed in the context of the recently released V&V20 Standard.

Eigenvalue sensitivity and uncertainty analysis based on a 2-D/1-D whole-core transport code KYADJ

Tidal turbines are a renewable energy source on the rise. The exceptional predictability of tidal currents contributes to a high reliability of this technology, which represents a key advantage in the endeavor to become a major contributor to the energy mix. To foster the development and to support the design process of tidal turbines, reliable numerical modeling techniques are required. This paper presents verification and validation work performed within the framework of the Supergen ORE Tidal Turbine Benchmarking Study. Viscous-flow CFD code ReFRESCO is used to conduct blade-resolved simulations of the towing tank experiments. In a first approximation, a steady-state frozen-rotor approach is chosen. A transition model, Gamma-ReTheta, is employed to predict the flow state transition on the turbine blades. In the process, the sensitivity to input turbulence quantities is highlighted. The numerical uncertainty is estimated based on mesh refinements. Finally, a conclusion is drawn to which accuracy the presented numerical models can predict the outcome of the experiments.

An efficient procedure for the determination of the error bounds (95% confidence intervals) of forecasted horizontal well production rates is presented. In particular, we advocate the use of automatic history matching (based on non-linear regression) to arrive at the best reservoir parameter values (typically porosities and permeabilities) for a given reservoir structure (i.e., for a given grid block representation). If the Gauss-Newton-method is used for the parameter search, the sensitivity coefficients required for the estimation of the standard error of the parameters and the well production rates are computed as part of the parameter search algorithm. Using typical techniques from statistical analysis (and the statistical properties of multivariable non-linear regression estimates), one can readily compute the confidence intervals of the predicted production rates. These confidence intervals around the expected reservoir behaviour incorporate the uncertainty in all reservoir parameters. As a result, a realistic measure of the uncertainty in the model predictions of future reservoir performance is obtained. The proposed procedure is illustrated with a case study. Introduction The final task of a reservoir simulation study is often the computation of future production levels of the history matched reservoir under alternative depletion plans. Moreover, the reservoir engineer often examines the sensitivity of the forecasted performance to different reservoir descriptions in an effort to establish the risks associated with a particular depletion plan. Typically, this is accomplished by varying key reservoir parameters such as porosities and permeabilities and determining how much the performance of a particular well or of the whole reservoir is affected. With the continuous development of powerful workstations and desktop personal computers, a renewed interest in automatic history marching procedures can be observed in the past few years. For the minimization of the resulting least squares (LS) objective function, two different approaches have been widely used: nonlinear regression(1–6) and optimal control methods(7–11). Recently, the simulated annealing(12) method has also proven to be a reliable procedure. In practical applications some form of reguralization(13,14) is always required to overcome the very serious problem of ill-conditioning, particularly as the number of parameters increases to more than ten or so. In our approach to automatic history matching, we minimize the resulting nonlinear LS objective function using an efficient implementation of the Gauss-Newton method(1). The necessary computation of the sensitivity coefficients when he Gauss-Newton method is used enables us to readily determine the uncertainty in the estimated parameter values(2). Furthermore, if we compute the sensitivity coefficients at future times where the performance of the reservoir is forecasted, we can generate 95% confidence intervals of the model predictions. The confidence intervals around the expected reservoir behaviour incorporate the uncertainty in all reservoir parameters and hence this approach provides a more realistic measure of the uncertainty in the model predictions of future reservoir behaviour(15). When several different grid representations of the reservoir are available with a known probability of being correct, the above described approach yields conditional expectations of future production rates which can subsequently be combined to arrive at an overall probability distribution of key variables, like cumulative oil production, WOR, GOR, etc.

Development of a computational fluid dynamics compatible mathematical model for boundary layer transitional flows in low-disturbance environment

The credibility of Computational Fluid Dynamics (CFD) has been a topic of debate due to the significant uncertainties inherent in its modeling processes and numerical implementations. Uncertainty Quantification (UQ) offers a scientific framework for quantitatively assessing and mitigating uncertainties in CFD simulations. However, this procedure typically requires numerous CFD simulations and considerable manual effort for both simulation management and data analysis. To overcome these challenges, this work develops a platform called UQ4CFD, a browser–server software that provides automated and customized uncertainty quantification capabilities for CFD studies. The UQ4CFD platform integrates different kinds of methodologies to perform comprehensive uncertainty analysis, including uncertainty propagation, sensitivity analysis, surrogate modeling, numerical discretization uncertainty analysis, model validation, model calibration, etc. A tightly coupled CFD-UQ workflow is built to automate the complete analytical process, encompassing parameter sampling, simulation execution, and results analysis, which significantly improves computational efficiency while reducing risks associated with data processing errors. Comprehensive validation employing both analytical benchmark functions and practical CFD cases has been conducted to demonstrate the platform’s effectiveness and adaptability in diverse UQ scenarios.

To estimate the uncertainty of the neutronic parameters it is required to calculate sensitivity coefficients to cross section changes. The sensitivity coefficients are usually calculated based on the diffusion theory. However, the accuracy of the sensitivity coefficients becomes doubtful because of the use of diffusion theory. The purpose of this paper is to derive the generalized perturbation theory using the transport theory, and to evaluate transport effect on the sensitivity coefficients. Sensitivity calculations were performed in 70 energy groups. The calculated sensitivity coefficients were compared with those obtained from direct transport calculations to check the accuracy of the present method, and those obtained from the generalized perturbation calculation based on the diffusion theory to investigate the transport effect on sensitivity coefficients. From the comparison, the difference was remarkably large for the neutronic parameters such as reaction rate distribution, reaction rate ratio, and reactivity worth. For example, the sensitivity coefficient of the 238U capture to 239Pu fission rate ratio in the lower core region of the under-moderated LWR core was large in the energy range 17.6–22.6 eV, and the sensitivity to 238U capture cross section calculated by the transport theory was 20% larger than that by the diffusion theory.

Simultaneous design and control under uncertainty: A back-off approach using power series expansions

Modeling and simulation have become an important aspect of the design and development process of aircraft systems. During the design of high lift actuation systems for example, the dynamic loads in the transmission are estimated by simulation. Nevertheless huge development efforts and financial resources are still invested in physical testing. These integration and testing phases take place at a late stage in the design process. Therefore, identified malfunctions and development errors lead to undesired iterations and thus to high costs as well as to an increased development time. This issue is emphasized as system complexity is rising continuously in conjunction with an increase in the number of interconnections and functionality. Hence, early and continuous virtual testing activities on the overall system level become increasingly important. In order to establish such a process, this paper analyzes the effects of modeling depth and parameter uncertainties on the overall system behavior considering nominal operation as well as failure cases. It identifies which test cases can be performed in which development phase depending on the information required. The modeling and simulation is implemented in the multiphysics and object-oriented simulation environment Matlab/Simulink/Simscape using an example of a multifunctional high lift actuation system.

An analysis framework for quantitative evaluation of parametric uncertainty in a cooperated energy storage system with multiple energy carriers