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Verification and Validation in Scientific Computing (Virtual Classroom)

Learn techniques and methods for verification of numerical simulations, validation of mathematical models, and quantify uncertainty in simulations.

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Register for this course and Probabilistic and Uncertainty Quantification Methods for Model Verification to save $495. Learn more.

this course commences at 10:30 AM and ends at 3:30 PM Eastern each day, with breaks scheduled throughout.

Scientific computing plays an increasingly important role in determining the expected behavior in engineered systems and manufacturing processes.  However, there is a frequent disconnect between simulations and what happens in reality. Without this awareness and understanding, decision makers could unknowingly put their customers, the public, the environment, or the system itself at risk.  This course presents modern terminology, techniques, and effective methods for verification of numerical simulations, validation of mathematical models, and uncertainty quantification of nondeterministic simulations.
Computational analysts, designers, and project managers who rely on simulation for decision making are shown practical techniques and methods for assessing simulation accuracy, credibility, and total uncertainty of the simulation. The techniques presented in this course are applicable to a wide range of engineering and science applications, including fluid dynamics, heat transfer, solid mechanics, and structural dynamics.  The mathematical models considered are given in terms of partial differential or integral equations, formulated as initial and boundary value problems. The computer codes that implement the mathematical models can use any type of numerical method (e.g., finite volume, finite element) and can be developed by commercial, corporate, government, or research organizations.
While the focus of the course is on modeling and simulation, experimentalists will benefit from a detailed discussion of techniques for designing and conducting high quality validation experiments. The course will also discuss the responsibilities of organizations and individuals serving in various positions where computational simulation software, mathematical models, and simulation results are produced.

By participating in this course, you will learn how to successfully:

  • Implement procedures for code verification and software quality assurance.
  • Implement procedures for solution verification, i.e., numerical error estimation. 
  • Plan and design validation experiments
  • Explain procedures for model accuracy assessment.
  • Explain the concepts and procedures for non-deterministic simulation.
  • Identify sources of uncertainty, such as aleatory and epistemic uncertainties.
  • Recognize the goals of model parameter calibration/updating.
  • Interpret local and global sensitivity analyses.
  • Recognize the practical difficulties in implementing VVUQ technologies.

Who Should Attend
This course benefits model developers, computational analysts, code developers, researchers, software engineers from physical and chemical sciences, and all regulatory bodies. Additionally, managers directing this work and project engineers relying on computational simulations for decision-making will also find this course to be beneficial. An undergraduate or advanced degree in engineering or the physical sciences is highly recommended. Training and experience in computational simulation of physical systems is also recommended.

Course Materials (included in purchase of course)
Verification and Validation in Scientific Computing, Cambridge University Press, 2010, written by Dr. William Oberkampf and Dr. Christopher Roy and a downloadable version of the course presentation.

Topics covered in this course include:

  • Terminology and Fundamental Concepts
  • Code Verification
  • Solution Verification
  • Validation Experiments
  • Model Accuracy Assessment
  • Predictive Capability of Modeling and Simulation

This ASME Virtual Classroom course is held live with an instructor on our online learning platform. Certificate of completion will be issued to registrants who successfully attend and complete the course.


Topics covered in this course include:

Introduction, Background, and Motivation

  • Terminology and Fundamental Concepts
  • Brief history of terminology
  • Present definitions and interpretations
  • Alternate definitions used by related communities
  • Additional important terms
  • Who should conduct verification, validation, and uncertainty quantification?

Code Verification

  • Software engineering
  • Criteria and definitions
  • Order of accuracy
  • Order of verification procedures
  • Traditional exact solutions
  • Method of manufactured solutions
  • Approximate solution methods

Solution Verification

  • Round-off error
  • Iterative convergence
  • Iterative error estimation
  • Classification of discretization error estimators
  • Reliability of discretization error estimators
  • Discretization error and uncertainty estimation
  • Solution adaption procedures

Validation Experiments

  • Validation fundamentals
  • Validation experiment hierarchy
  • Validation experiments vs. traditional experiments
  • Six characteristics of validation experiments
  • Detailed example of a wind tunnel validation experiment

Model Accuracy Assessment

  • What are validation metrics?
  • Various approaches to validation metrics
  • Recommended characteristics for validation metrics
  • Confidence interval approach
  • Cumulative distribution functions approach

Predictive Capability of Modeling and Simulation

  • Identify all sources of uncertainty
  • Characterize each source of uncertainty
  • Estimate solution error in system responses of interest
  • Estimate uncertainty in system responses of interest
  • Procedures for updating model parameters
  • Types of sensitivity analyses

Final Topics

  • Planning and prioritization in modeling and simulation
  • Maturity assessment of modeling and simulation
  • Difficulties in implementing verification, validation, and uncertainty quantification (VVUQ)

Christopher Roy, Ph.D.

Professor, Virginia Tech

Christopher Roy, Ph.D., Virginia Tech, holds a B.S. in Mechanical Engineering from Duke University, an M.S. in Aerospace Engineering from Texas A&M University, and a Ph.D. in Aerospace Engineering from North Carolina State University.

William Oberkampf, Ph.D.

W. L. Oberkampf Consulting

William Oberkampf, Ph.D. is an engineering consultant with 50 years of experience in research and development in fluid dynamics, heat transfer, flight dynamics, and solid mechanics.

More Information


Virtual Classroom

Live course with an instructor and peers held in an online learning environment with digital enhancements and online materials.
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