training & development
Verification and Validation in Scientific Computing

Verification and Validation in Scientific Computing

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To download the course brochure, please click HERE.

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 seminar 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 are assumed to be 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 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.

Each attendee will receive a copy of the book, Verification and Validation in Scientific Computing, Cambridge University Press, 2010, written by Dr. William Oberkampf and Dr. Christopher Roy, which this course closely follows.

You Will Learn 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
 - 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

Click HERE to review the course outline.

Who Should Attend
This course benefits model developers, computational analysts, code developers, experimentalists, and software engineers. Managers directing this work and project engineers relying on computational simulations for decision-making will also find this course to be 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 recommended. Training and experience in computational simulation or experimental testing is also helpful.

  • Course Type: Masterclass
  • Order Number: MC133
  • Language: English
Final invoices will include applicable sales and use tax.


William Oberkampf, Ph.D., is an engineering consultant with 43 years of experience in research and development in fluid dynamics, heat transfer, flight dynamics, and solid mechanics. He spent his entire career in both computational and experimental areas. During the last 20 years, Dr. Oberkampf emphasized research and development in methodologies and procedures for verification, validation, and uncertainty quantification in computational simulations. He has written over 177 journal articles, book chapters, conference papers, and technical reports. He has taught 44 short courses in the field of verification, validation, and uncertainty quantification.

Dr. Oberkampf received his B.S. in Aerospace Engineering in 1966 from the University of Notre Dame, his M.S. in Mechanical Engineering from the University of Texas at Austin in 1968, and his Ph.D. in 1970 in Aerospace Engineering from the University of Notre Dame. Dr. Oberkampf served on the faculty of the Mechanical Engineering Department at the University of Texas at Austin for nine years. After 29 years of service in both staff member and management positions at Sandia National Laboratories, he retired as a Distinguished Member of the Technical Staff. Since this time, he has been a consultant to the National Aeronautics and Space Administration, the U.S. Air Force, various Department of Energy laboratories, and corporations in the U.S. and Europe. He is a fellow of the American Institute of Aeronautics and Astronautics

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. From 1998 to 2003, he worked as a senior member of the technical staff in the Engineering Sciences Center at Sandia National Laboratories in Albuquerque, New Mexico. From 2003 to 2007, he was an Assistant Professor in the Aerospace Engineering Department at Auburn University.

In 2007, Dr. Roy joined the Aerospace and Ocean Engineering Department at Virginia Tech and currently holds the rank of full professor. He has written over 120 journal articles, books, book chapters, conference papers, and technical reports in the areas of verification, validation, and uncertainty quantification. He has taught 30 short courses in the field of verification, validation, and uncertainty quantification.
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