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Verification & Validation in Scientific Computing 

2-Day On-Site Training Course


About the Course:

Engineering systems must increasingly rely on computational simulation for predicted performance, reliability, and safety. Computational analysts, designers, decision makers, and project managers who rely on simulation must have practical techniques and methods for assessing simulation credibility. This short course presents modern terminology and effective procedures for verification of numerical simulations, validation of mathematical models, and uncertainty quantification of nondeterministic simulations. 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. A framework is provided for incorporating a wide range error and uncertainty sources identified during the modeling, verification, and validation processes with the goal of estimating the total prediction uncertainty of the simulation. 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. Application examples are primarily taken from the fields of fluid dynamics and heat transfer, but the techniques and procedures apply to all application areas in engineering and science. The course closely follows the course instructors’ book, Verification and Validation in Scientific Computing, Cambridge University Press (2010).


Upon completion of this course, attendees will be able to:
  • Define the objectives of verification, validation, and uncertainty quantification
  • Implement procedures for code verification and software quality assurance  
  • Implement procedures for solution verification, i.e., numerical error estimation
  • Plan and design validation experiments
  • Understand procedures for model accuracy assessment
  • Comprehend 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, software engineers, and experimentalists working with computational analysts. Managers directing simulation work and project engineers relying on computational simulations for decision-making will also find this course beneficial. The course will discuss the responsibilities of organizations and individuals serving in various positions where computational simulation software, mathematical models, and simulation results are produced. 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.

The course is open to both members and non-members of NAFEMS.


Course Materials Provided

Verification & Validation in Scientific Computing

Course attendees will be provided with a copy of the book Verification and Validation in Scientific Computing, Cambridge University Press (2010). The 780-page book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification, validation, and uncertainty quantification for models and simulations. The book contains several examples of the most common procedures in VVUQ, including an example of the design and execution of a high quality validation experiment. Attendees will also be provided with an electronic (PDF) file and color print copies of over 270 short course slides presented during the course.

The course is completely code independent, attendees are welcome to bring laptops to take notes, but they are not required.


Course Program

The contents are presented in eight lectures, tentatively organized as shown. The two-day schedule allows for ample discussion and interaction with the instructors and other attendees. The instructors reserve the right to modify the contents to address the audience’s needs and preferences.

Day 1

Lecture 1. Introduction, Background, and Motivation

Lecture 2. 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?

Lecture 3: Code Verification

  • Software engineering
  • Criteria and definitions–Order of accuracy
  • Traditional exact solutions
  • Method of manufactured solutions

Lecture 4: Solution Verification

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

Day 2

Lecture 5: 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 

Lecture 6: Model Accuracy Assessment

  • What are validation metrics?
  • Various approaches to validation metrics
  • Recommended characteristics for validation metrics
  • Identification of model discrepancy
  • Cumulative distribution function approach

Lecture 7: 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 total uncertainty in system responses of interest
  • Procedures for updating model parameters
  • Types of sensitivity analysis

Lecture 8: Final Topics

  • Planning and prioritization in modeling and simulation
  • Maturity assessment of modeling and simulation
  • Practical difficulties in implementing VVUQ technologies


Interested in this Course? 

Please contact Matthew Ladzinski (Americas) or Rosie Cranston (Europe) if you are interested in scheduling an on-site training session, or if you would like to be notified of the next public course session.


Member Discounts

NAFEMS members can attend this course at a significantly discounted rate. 

Members can also attend a number of seminars and workshops each year as part of their membership, as well as a library of free publications when they join.

If you are a member, please login above to take advantage of this exclusive discount. If you are not a member, find out more about the benefits of membership here.




Course Tutors

Dr William Oberkampf

Dr William Oberkampf, NAFEMS instructor








Read Dr William Oberkampf's bio on the NAFEMS tutors page



Professor Christopher Roy

Professor Christopher Roy, NAFEMS Tutors







Read Pr Christopher Roy's bio on the NAFEMS tutors page 





Events - Cancellation Policy

Please note NAFEMS cancellation policy for all training courses is as follows:-

  • Suitably qualified delegates may be substituted at any time prior to the start of the course

  • Bookings are accepted upon condition that either full payment is received before the course commences, or that a valid purchase order is received from a company that has a credit agreement with us

  • In the event of a delegate being unable to attend a course that they have booked upon then, NAFEMS will discuss the possibility of transferring to an alternative course. However, a suitable administration charge will be levied.

  • A refund of 50% of the course fees will be paid to delegates who cancel their booking and do not re-schedule to an alternative course, provided that the cancellation is received by NAFEMS at least four weeks in advance of the course. No refunds can be given for cancellations made after this time.

  • NAFEMS reserves the right to cancel the course, without liability, in which case all training fees will be refunded in full. However, NAFEMS cannot be held liable for any other expenses incurred by participants or their companies due to the cancellation.

NAFEMS will discuss the possibility of transferring to an alternative event/course, however an administration charge will be applicable.

For full terms and conditions, click here. This policy is subject to change.

*Special discounts are being made available to members for this course. For more information on joining NAFEMS, please visit ourmembership section