6.5 Verification and validation

Verification and validation are crucial for ensuring accuracy in multiphase flow modeling. These processes assess model correctness, implementation, and agreement with real-world data. They build confidence in a model's ability to represent complex phenomena and support decision-making.

Verification checks mathematical model accuracy and code implementation. Validation compares model predictions to experimental data. Together, they form a systematic approach to developing reliable computational models for multiphase flows, guiding improvements and establishing credibility.

Verification vs validation

• Verification and validation are critical components of ensuring the accuracy and reliability of computational models in multiphase flow modeling
• Verification focuses on assessing the correctness of the mathematical model and its implementation, while validation evaluates the agreement between the model predictions and experimental data
• Proper verification and validation practices help build confidence in the model's ability to represent real-world phenomena and support decision-making processes

Verification

• Verification is the process of determining whether a computational model accurately represents the underlying mathematical model and its solution
• It involves assessing the correctness of the code implementation and the numerical accuracy of the solution
• Verification is an essential step in ensuring that the model is free from errors and inconsistencies

Code verification

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• Code verification assesses the correctness of the software implementation of the mathematical model
• Involves checking for programming errors, inconsistencies, and compliance with coding standards
• Techniques include code reviews, static analysis, and unit testing
  • Code reviews involve manual inspection of the source code by peers to identify potential issues
  • Static analysis tools automatically examine the code for common programming errors and style violations
  • Unit testing verifies individual components of the code by comparing their output with known solutions

Solution verification

• Solution verification evaluates the numerical accuracy of the computational solution
• Assesses the discretization error, which arises from the approximation of continuous equations on a discrete grid
• Techniques include grid convergence studies and comparison with analytical solutions
  • Grid convergence studies involve systematically refining the computational mesh and examining the convergence of the solution
  • Comparison with analytical solutions, when available, provides a direct measure of the numerical accuracy

Verification procedures

• Verification procedures should be systematic, well-documented, and integrated into the development process
• Includes establishing verification test cases, such as manufactured solutions and benchmark problems
• Verification should be performed regularly, especially after major code modifications
• Results of verification tests should be carefully analyzed and documented
• Verification procedures help maintain code quality and reliability throughout the development cycle

Validation

• Validation assesses the agreement between the computational model predictions and experimental data
• It evaluates the extent to which the model accurately represents the real-world phenomena of interest
• Validation is crucial for establishing the credibility and predictive capability of the model

Validation process

• The validation process involves comparing model predictions with high-quality experimental data
• Includes selecting appropriate validation experiments, defining validation metrics, and assessing model performance
• Validation experiments should cover a range of relevant operating conditions and physical parameters
• The validation process should be iterative, with model improvements based on the identified discrepancies
• Collaboration between modelers and experimentalists is essential for effective validation

Validation hierarchy

• The validation hierarchy organizes validation activities based on the level of complexity and specificity
• Starts with basic validation at the component level and progresses to subsystem and system-level validation
• Component-level validation focuses on individual physical models and constitutive relations
• Subsystem-level validation considers the interaction between multiple components
• System-level validation assesses the overall performance of the integrated model
• The validation hierarchy helps prioritize validation efforts and systematically build confidence in the model

Validation metrics

• Validation metrics quantify the agreement between model predictions and experimental data
• Common metrics include mean absolute error, root mean square error, and normalized errors
• Validation metrics should be carefully selected based on the quantity of interest and the intended use of the model
• Statistical techniques, such as hypothesis testing and confidence intervals, can be used to assess the significance of the validation results
• Validation metrics provide a quantitative basis for evaluating model performance and guiding model improvements

Uncertainty quantification

• Uncertainty quantification (UQ) is the process of characterizing and propagating uncertainties in computational models
• It aims to assess the impact of input uncertainties on the model predictions and quantify the associated confidence intervals
• UQ is essential for informed decision-making and risk assessment in multiphase flow modeling

Types of uncertainty

• Uncertainties can be classified into two main categories: aleatory and epistemic
• Aleatory uncertainty arises from inherent randomness in the system, such as material properties or operating conditions
• Epistemic uncertainty stems from incomplete knowledge or lack of understanding of the system
• Distinguishing between aleatory and epistemic uncertainties is important for appropriate treatment in UQ
• Aleatory uncertainties are typically represented using probability distributions, while epistemic uncertainties may require alternative approaches (interval analysis, fuzzy sets)

Uncertainty propagation

• Uncertainty propagation involves evaluating the effect of input uncertainties on the model outputs
• Techniques include Monte Carlo simulation, polynomial chaos expansion, and stochastic collocation
• Monte Carlo simulation involves randomly sampling input parameters and running multiple model realizations
• Polynomial chaos expansion represents the model output as a series expansion of orthogonal polynomials
• Stochastic collocation constructs a polynomial approximation of the model output using a set of collocation points
• The choice of uncertainty propagation method depends on the complexity of the model and the desired accuracy

Sensitivity analysis

• Sensitivity analysis assesses the relative importance of input parameters on the model output
• Helps identify the most influential parameters and prioritize data collection and model refinement efforts
• Techniques include local sensitivity analysis (one-at-a-time variation) and global sensitivity analysis (variance-based methods)
• Local sensitivity analysis examines the impact of small perturbations around nominal parameter values
• Global sensitivity analysis considers the entire range of parameter variations and their interactions
• Sensitivity analysis provides insights into the model behavior and guides uncertainty reduction strategies

Verification and validation examples

• Verification and validation examples demonstrate the application of V&V techniques to specific multiphase flow problems
• Examples cover a range of flow regimes, physical phenomena, and modeling approaches
• Serve as case studies to illustrate best practices and challenges in V&V of multiphase flow models

Single-phase flow

• Verification of a single-phase flow solver using the method of manufactured solutions
• Validation of a turbulence model for predicting flow separation over an airfoil
• Grid convergence study for a pipe flow simulation to assess numerical accuracy
• Comparison of CFD predictions with experimental data for flow through a sudden expansion

Multiphase flow

• Verification of a two-fluid model implementation using analytical solutions for simplified cases
• Validation of a bubble column simulation against experimental data on gas holdup and bubble size distribution
• Uncertainty quantification of input parameters in a fluidized bed reactor model
• Sensitivity analysis of interphase momentum transfer coefficients in a gas-liquid flow simulation

Turbulent flows

• Verification of a large eddy simulation (LES) code using decaying isotropic turbulence
• Validation of a Reynolds-averaged Navier-Stokes (RANS) model for predicting turbulent jet flow
• Comparison of different subgrid-scale models in LES of a turbulent channel flow
• Uncertainty propagation in a turbulent mixing layer simulation due to inlet boundary conditions

Best practices

• Best practices in verification and validation ensure the quality, reproducibility, and credibility of computational models
• They provide guidelines for effective V&V planning, execution, and documentation
• Adherence to best practices promotes transparency, collaboration, and continuous improvement in multiphase flow modeling

Documentation

• Comprehensive documentation is essential for effective V&V
• Includes detailed description of the mathematical model, numerical methods, and assumptions
• Verification and validation procedures, test cases, and results should be thoroughly documented
• Documentation should be version-controlled and accessible to all stakeholders
• Well-documented models facilitate reproducibility, knowledge transfer, and regulatory compliance

Code management

• Robust code management practices are crucial for maintaining code quality and reproducibility
• Includes version control systems (Git), code review processes, and automated testing frameworks
• Version control enables tracking of code changes, collaborative development, and reproducibility of results
• Regular code reviews catch potential issues early and promote knowledge sharing among team members
• Automated testing ensures code correctness and prevents regressions during development
• Proper code management streamlines the V&V process and enhances the reliability of the computational model

Collaboration

• Collaboration between modelers, experimentalists, and domain experts is vital for successful V&V
• Promotes exchange of knowledge, identification of validation priorities, and interpretation of results
• Collaborative design of validation experiments ensures alignment with modeling needs and objectives
• Regular communication and feedback loops facilitate continuous improvement of the model and validation process
• Collaboration across disciplines and institutions leverages diverse expertise and resources
• Effective collaboration accelerates the development of high-quality, validated models for multiphase flow applications