The Foundations of Verification in Modeling and Simulation

Abstract

The practice of verification is grounded in mathematics highlighting the fundamental nature of its practice. Models of reality are fundamentally mathematical and verification assures the connection between the modeling intended and achieved in code. Code verification is a process where the correctness of a computer code for simulation and modeling is proven. This “proof” is defined by the collection of evidence that the numerical approximations are congruent with the model for the physical phenomena. The key metric in code verification is the order of accuracy of the approximation that should match theoretical expectations. In contrast, solution verification is an aspect of uncertainty estimation associated with numerical error in simulations. Solution verification uses many of the same approaches as code verification, but its principal outcome is an estimate of the numerical error. The order of convergence is a secondary outcome. Together these two practices form an important part of the foundation of quality and credibility in modeling and simulation.