Verification and Validation (V&V) is a branch of Engineering that aims at quantifying numerical and modeling errors in Computational Field Simulations, i.e. numerical solutions of mathematical models that describe physical processes involved in Engineering applications. Although there are several definitions available in the open literature, the main definitions of V&V are described below.


Verification can be summarized as “Check if we are solving the equations right”, i.e. a mathematical problem that aims at quantifying numerical errors. However, it actually contains two different types of activities:

  1. Code Verification that aims at checking if there are no coding mistakes, i.e. there are no “bugs”.
  2. Solution Verification that intends to determine the numerical uncertainty of numerical solutions for which the exact solution is unknown.


The simplest way to describe Validation is to say that it corresponds to “Check if we are solving the right equations”. Therefore, it is related to the quantification of modeling errors, i.e. the difference between a mathematical model and the physical reality. Therefore, it requires a numerical solution of a mathematical model and experimental measurements.

Numerical and Modeling Errors

V&V handles numerical and modeling errors, which are often confused. Therefore, it is important to distinguish the different errors involved in V&V.

  • Numerical Errors
    • Round-off error
    • Iterative error
    • Discretization error (time and space)
    • Statistical error (only for unsteady problems with inexact initial conditions)
  • Modeling errors