9 Verification, Validation, and Error
9.1 Do not confuse the solver with the model
A PDE discretization can be implemented correctly yet describe the wrong physical phenomenon. Verification asks whether the equations are being solved correctly. Validation asks whether the equations and parameters adequately represent the intended real-world system.
9.2 Three practical verification tools
- Manufactured solutions: Prescribe an exact smooth field, derive the required forcing terms, then test convergence.
- Grid and time-step refinement: Observe whether quantities of interest approach a consistent limit.
- Conservation checks: Evaluate mass fluxes, momentum balances, and boundary-condition residuals.
9.3 Error sources
Model-form, discretization, iteration, roundoff, geometric representation, and measurement errors should be distinguished whenever possible. A plot that looks physically plausible is not sufficient evidence.
9.4 A developing case-study sequence
Future editions can add Poiseuille flow, the lid-driven cavity, and channel-flow configurations, each with documented parameters and carefully chosen comparisons. These are planned examples, not completed benchmarks in the current draft.
Living chapter. This is an initial working treatment. Derivations, examples, and references will be expanded in future editions.